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Sigma knowledge engineering system is an system for developing, viewing and debugging theories in first
order logic. It works with Knowledge Interchange Format (KIF) and is optimized for the Suggested Upper Merged
Ontology (SUMO) www.ontologyportal.org.
/* This code is copyright Articulate Software (c) 2003.
This software is released under the GNU Public License .
Users of this code are also requested, to credit Articulate Software in any
writings, briefings, publications, presentations, or
other representations of any software which incorporates,
builds on, or uses this code. Please cite the following
article in any publication with references:
Pease, A., (2003). The Sigma Ontology Development Environment,
in Working Notes of the IJCAI-2003 Workshop on Ontology and Distributed Systems,
August 9, Acapulco, Mexico. See also http://sigmakee.sourceforge.net
*/
package com.articulate.sigma;
import java.io.BufferedWriter;
import java.io.File;
import java.io.FileWriter;
import java.util.*;
import com.articulate.sigma.KB;
/** **************************************************************
* The code in the section below implements an algorithm for
* translating SUO-KIF expressions to clausal form. The
* public methods are:
*
* public Formula clausify()
* public ArrayList clausifyWithRenameInfo()
* public ArrayList toNegAndPosLitsWithRenameInfo()
*
* The result is a single formula in conjunctive normal form
* (CNF), which is actually a set of (possibly negated) clauses
* surrounded by an "or".
*/
public class Clausifier {
private Formula thisFormula = null;
// This static variable holds the int value that is used to
// generate unique variable names.
private static int VAR_INDEX = 0;
// This static variable holds the int value that is used to
// generate unique Skolem terms.
private static int SKOLEM_INDEX = 0;
/** ***************************************************************
*/
public Clausifier(String s) {
thisFormula = new Formula();
thisFormula.read(s);
}
/** ***************************************************************
*/
public String toString() {
return thisFormula.theFormula;
}
/** ***************************************************************
* Turn a conjunction into an ArrayList of separate statements
*/
public ArrayList separateConjunctions() {
if (!thisFormula.car().equals("and")) {
System.out.println("Error Formula.separateConjunctions(): not a conjunction " + thisFormula);
return null;
}
ArrayList result = new ArrayList();
Formula temp = new Formula();
temp.read(thisFormula.cdr());
while (!temp.empty()) {
Formula clause = new Formula();
clause.read(temp.car());
result.add(clause);
temp.read(temp.cdr());
}
return result;
}
/** ***************************************************************
* convenience method
*/
public static ArrayList separateConjunctions(Formula f) {
Clausifier temp = new Clausifier(f.theFormula);
return temp.separateConjunctions();
}
/** ***************************************************************
* convenience method
*/
public static Formula clausify(Formula f) {
Clausifier temp = new Clausifier(f.theFormula);
return temp.clausify();
}
/** ***************************************************************
* Note this returns a List of mixed types! Fixme!
*
* @return an ArrayList that contains three items: The new
* clausal-form Formula, the original (input) SUO-KIF Formula, and
* a Map containing a graph of all the variable substitions done
* during the conversion to clausal form. This Map makes it
* possible to retrieve the correspondence between the variables
* in the clausal form and the variables in the original
* Formula. Some elements might be null if a clausal form
* cannot be generated.
*
* @see clausify()
* @see toNegAndPosLitsWithRenameInfo()
* @see toCanonicalClausalForm();
*/
public ArrayList clausifyWithRenameInfo() {
Formula old = new Formula();
old.theFormula = thisFormula.theFormula;
ArrayList result = new ArrayList();
Formula ans = null;
HashMap topLevelVars = new HashMap();
HashMap scopedRenames = new HashMap();
HashMap allRenames = new HashMap();
HashMap standardizedRenames = new HashMap();
thisFormula = equivalencesOut();
thisFormula = implicationsOut();
thisFormula = negationsIn();
thisFormula = renameVariables(topLevelVars, scopedRenames, allRenames);
thisFormula = existentialsOut();
thisFormula = universalsOut();
thisFormula = disjunctionsIn();
thisFormula = standardizeApart(standardizedRenames);
allRenames.putAll(standardizedRenames);
result.add(thisFormula);
result.add(old);
result.add(allRenames);
// resetClausifyIndices();
return result;
}
/** ***************************************************************
* TODO: Note mixed types in return List! Fixme!
*
* This method converts the SUO-KIF Formula to an ArrayList of
* clauses. Each clause is an ArrayList containing an ArrayList
* of negative literals, and an ArrayList of positive literals.
* Either the neg lits list or the pos lits list could be empty.
* Each literal is a Formula object.
*
* The first object in the returned ArrayList is an ArrayList of
* clauses.
*
* The second object in the returned ArrayList is the original
* (input) Formula object (this).
*
* The third object in the returned ArrayList is a Map that
* contains a graph of all the variable substitions done during
* the conversion of this Formula to clausal form. This Map makes
* it possible to retrieve the correspondences between the
* variables in the clausal form and the variables in the original
* Formula.
*
* @see clausify()
* @see clausifyWithRenameInfo()
* @see toCanonicalClausalForm();
*
* @return A three-element ArrayList,
*
* [
* // 1. clauses
* [
* // a clause
* [
* // negative literals
* [ Formula1, Formula2, ..., FormulaN ],
* // positive literals
* [ Formula1, Formula2, ..., FormulaN ]
* ],
*
* // another clause
* [
* // negative literals
* [ Formula1, Formula2, ..., FormulaN ],
* // positive literals
* [ Formula1, Formula2, ..., FormulaN ]
* ],
*
* ...,
* ],
*
* // 2.
* ,
*
* // 3.
* {a-Map-of-variable-renamings},
*
* ]
*/
public ArrayList toNegAndPosLitsWithRenameInfo() {
ArrayList ans = new ArrayList();
List clausesWithRenameInfo = this.clausifyWithRenameInfo();
if (clausesWithRenameInfo.size() == 3) {
Formula clausalForm = (Formula) clausesWithRenameInfo.get(0);
Clausifier cForm = new Clausifier(clausalForm.theFormula);
ArrayList clauses = cForm.operatorsOut();
if ((clauses != null) && !clauses.isEmpty()) {
// System.out.println("\nclauses == " + clauses);
ArrayList newClauses = new ArrayList();
Formula clause = null;
for (Iterator it = clauses.iterator(); it.hasNext();) {
ArrayList negLits = new ArrayList();
ArrayList posLits = new ArrayList();
ArrayList literals = new ArrayList();
literals.add(negLits);
literals.add(posLits);
clause = (Formula) it.next();
if (clause.listP()) {
while (!clause.empty()) {
boolean isNegLit = false;
String lit = clause.car();
Formula litF = new Formula();
litF.read(lit);
if (litF.listP() && litF.car().equals(Formula.NOT)) {
litF.read(litF.cadr());
isNegLit = true;
}
if (litF.theFormula.equals(Formula.LOG_FALSE))
isNegLit = true;
if (isNegLit)
negLits.add(litF);
else
posLits.add(litF);
clause = clause.cdrAsFormula();
}
}
else if (clause.theFormula.equals(Formula.LOG_FALSE))
negLits.add(clause);
else
posLits.add(clause);
newClauses.add(literals);
}
// Collections.sort(negLits);
// Collections.sort(posLits);
ans.add(newClauses);
}
if (ans.size() == 1) {
int cwriLen = clausesWithRenameInfo.size();
for (int j = 1; j < cwriLen; j++)
ans.add(clausesWithRenameInfo.get(j));
}
}
return ans;
}
/** ***************************************************************
* convenience method
*/
public static ArrayList toNegAndPosLitsWithRenameInfo(Formula f) {
Clausifier temp = new Clausifier(f.theFormula);
return temp.toNegAndPosLitsWithRenameInfo();
}
/** ***************************************************************
* This method converts the SUO-KIF Formula to a canonical version
* of clausal (resolution, conjunctive normal) form with Skolem
* functions, following the procedure described in Logical
* Foundations of Artificial Intelligence, by Michael Genesereth
* and Nils Nilsson, 1987, pp. 63-66. In canonical form, all
* variables are renamed from index 0 and all literals are
* alphabetically sorted.
*
* @see clausify()
* @see clausifyWithRenameInfo()
* @see toNegAndPosLitsWithRenameInfo()
*
* @return The Formula in a canonicalized version of clausal form
*/
public Formula toCanonicalClausalForm() {
Formula ans = new Formula();
List clauseData = this.toNegAndPosLitsWithRenameInfo();
if (clauseData.isEmpty())
ans = thisFormula;
else {
List clauses = (List) clauseData.get(0);
if (!clauses.isEmpty()) {
List sortedClauses = new ArrayList();
StringBuilder sb = null;
Iterator itc = null;
for (itc = clauses.iterator(); itc.hasNext();) {
List clause = (List) itc.next();
if (!clause.isEmpty() && (clause.size() == 2)) {
sb = new StringBuilder();
Iterator itl = null;
List neglits = (List) clause.get(0);
if (neglits.size() > 1) Collections.sort(neglits);
int i = 0;
for (itl = neglits.iterator(); itl.hasNext(); i++) {
if (i > 0) sb.append(Formula.SPACE);
sb.append(Formula.LP);
sb.append(Formula.NOT);
sb.append(Formula.SPACE);
sb.append(itl.next().toString());
sb.append(Formula.RP);
}
List poslits = (List) clause.get(1);
if (!poslits.isEmpty()) {
Collections.sort(poslits);
for (itl = poslits.iterator(); itl.hasNext(); i++) {
if (i > 0) sb.append(Formula.SPACE);
sb.append(itl.next().toString());
}
}
if (i > 1) {
sb.insert(0, Formula.SPACE);
sb.insert(0, Formula.OR);
sb.insert(0, Formula.LP);
sb.append(Formula.RP);
}
sortedClauses.add(sb.toString());
}
}
Collections.sort(sortedClauses);
sb = new StringBuilder();
int j = 0;
for (itc = sortedClauses.iterator(); itc.hasNext(); j++) {
if (j > 0) sb.append(Formula.SPACE);
sb.append(itc.next().toString());
}
if (j > 1) {
sb.insert(0, Formula.SPACE);
sb.insert(0, Formula.AND);
sb.insert(0, Formula.LP);
sb.append(Formula.RP);
}
ans.read(normalizeVariables(sb.toString()));
}
}
return ans;
}
/** ***************************************************************
* convenience method
*/
public static Formula toCanonicalClausalForm(Formula f) {
Clausifier temp = new Clausifier(f.theFormula);
return temp.toCanonicalClausalForm();
}
/** ***************************************************************
* This method returns an open Formula that constitutes a KIF
* query expression, which is generated from the canonicalized
* negation of the original Formula. The original Formula is
* assumed to be a "rule", having both positive and negative
* literals when converted to canonical clausal form. This method
* returns a query expression that can be used to test the
* validity of the original Formula. If the query succeeds
* (evaluates to true, or retrieves variable bindings), then the
* negation of the original Formula is valid, and the original
* Formula must be invalid.
*
* Note that this method will work reliably only for standard
* first order KIF expressions, and probably will not produce
* expected (or sane) results if used with non-standard KIF.
*
* @see Formula.toCanonicalClausalForm()
*
* @return A String representing an open KIF query expression.
*/
protected Formula toOpenQueryForNegatedDualForm() {
Formula result = thisFormula;
// 1. Make quantifiers explicit.
Formula qF = new Formula();
Formula temp = new Formula();
temp.theFormula = thisFormula.theFormula;
qF.read(temp.makeQuantifiersExplicit(false));
// 2. Negate the formula.
Formula negQF = new Formula();
negQF.read("(not " + qF.theFormula + ")");
// 3. Generate the canonical clausal form of the negation
// of the formula we want to check.
Formula canonNegF = new Formula();
canonNegF.read(Clausifier.toCanonicalClausalForm(negQF).theFormula);
// 4. Finally, normalize variables, treat Skolem terms as
// variables.
Formula queryF = new Formula();
queryF.read(normalizeVariables(canonNegF.theFormula,
true));
result = queryF;
return result;
}
/** ***************************************************************
* This method returns a canonical version of this Formula,
* assumed to be a KIF "special" form, in which all internal
* first-order KIF formulae are replaced by their canonical
* versions, and all variables are renamed, in left to right
* depth-first order of occurrence, starting from index 1. This
* method is intended to be applied to higher-order constructs
* that expand the syntax of KIF. To canonicalize ordinary
* first-order KIF formulae, just use
* Formula.toCanonicalClausalForm().
*
* @see Formula.toCanonicalClausalForm()
*
* @param preserveSharedVariables If true, all variable sharing
* between embedded expressions will be preserved, even though all
* variables will still be renamed as part of the canonicalization
* process
*
* @return A String representing the canonicalized version of this
* special, non-standard KIF expression.
*/
protected Formula toCanonicalKifSpecialForm(boolean preserveSharedVariables) {
Formula result = thisFormula;
// First, obfuscate all variables to prevent them from
// being renamed during conversion to clausal form.
String flist = thisFormula.theFormula;
String vpref = Formula.V_PREF;
String rpref = Formula.R_PREF;
String vrepl = "vvvv";
String rrepl = "rrrr";
if (preserveSharedVariables) {
if (flist.contains(vpref)) flist = flist.replace(vpref, vrepl);
if (flist.contains(rpref)) flist = flist.replace(rpref, rrepl);
}
StringBuilder sb = new StringBuilder();
if (Formula.listP(flist)) {
if (Formula.empty(flist))
sb.append(flist);
else {
Formula f = new Formula();
f.read(flist);
String arg0 = f.car();
if (Formula.isLogicalOperator(arg0))
sb.append(Clausifier.toCanonicalClausalForm(f).theFormula);
else {
List tuple = f.literalToArrayList();
sb.append(Formula.LP);
int i = 0;
for (Iterator it = tuple.iterator(); it.hasNext(); i++) {
Formula nextF = new Formula();
nextF.read((String) it.next());
if (i > 0) sb.append(Formula.SPACE);
sb.append(Clausifier.toCanonicalKifSpecialForm(nextF,false).theFormula);
}
sb.append(Formula.RP);
}
}
}
else
sb.append(flist);
flist = sb.toString();
if (preserveSharedVariables) {
flist = flist.replace(vrepl, vpref);
flist = flist.replace(rrepl, rpref);
}
flist = normalizeVariables(flist);
Formula canonSF = new Formula();
canonSF.read(flist);
result = canonSF;
return result;
}
/** ***************************************************************
* convenience method
*/
private static Formula toCanonicalKifSpecialForm(Formula f, boolean preserveSharedVariables) {
Clausifier temp = new Clausifier(f.theFormula);
return temp.toCanonicalKifSpecialForm(preserveSharedVariables);
}
/** ***************************************************************
* Returns a String in which all variables and row variables have
* been normalized -- renamed, in depth-first order of occurrence,
* starting from index 1 -- to support comparison of Formulae for
* equality.
*
* @see normalizeVariables_1();
*
* @param input A String representing a SUO-KIF Formula, possibly
* containing variables to be normalized
*
* @return A String, typically representing a SUO-KIF Formula or
* part of a Formula, in which the original variables have been
* replaced by normalized forms
*/
public static String normalizeVariables(String input) {
return normalizeVariables(input, false);
}
/** ***************************************************************
* Returns a String in which all variables and row variables have
* been normalized -- renamed, in depth-first order of occurrence,
* starting from index 1 -- to support comparison of Formulae for
* equality.
*
* @see normalizeVariables_1();
*
* @param input A String representing a SUO-KIF Formula, possibly
* containing variables to be normalized
*
* @param replaceSkolemTerms If true, all Skolem terms in input
* are treated as variables and are replaced with normalized
* variable terms
*
* @return A String, typically representing a SUO-KIF Formula or
* part of a Formula, in which the original variables have been
* replaced by normalized forms
*/
protected static String normalizeVariables(String input, boolean replaceSkolemTerms) {
String result = input;
int[] idxs = {1, 1};
Map vmap = new HashMap();
result = normalizeVariables_1(input, idxs, vmap, replaceSkolemTerms);
return result;
}
/** ***************************************************************
* An internal helper method for normalizeVariables(String input).
*
* @see normalizeVariables();
*
* @param input A String possibly containing variables to be
* normalized
*
* @param idxs A two-place int[] in which int[0] is the current
* variable index, and int[1] is the current row variable index
*
* @param vmap A Map in which the keys are old variables and the
* values are new variables
*
* @return A String, typically a representing a SUO-KIF Formula or
* part of a Formula.
*/
protected static String normalizeVariables_1(String input,int[] idxs,
Map vmap, boolean replaceSkolemTerms) {
String result = "";
String vbase = Formula.VVAR;
String rvbase = (Formula.RVAR + "VAR");
StringBuilder sb = new StringBuilder();
String flist = input.trim();
boolean isSkolem = Formula.isSkolemTerm(flist);
if ((replaceSkolemTerms && isSkolem) || Formula.isVariable(flist)) {
String newvar = (String) vmap.get(flist);
if (newvar == null) {
newvar = ((flist.startsWith(Formula.V_PREF) || isSkolem)
? (vbase + idxs[0]++)
: (rvbase + idxs[1]++));
vmap.put(flist, newvar);
}
sb.append(newvar);
}
else if (Formula.listP(flist)) {
if (Formula.empty(flist))
sb.append(flist);
else {
Formula f = new Formula();
f.read(flist);
List tuple = f.literalToArrayList();
sb.append(Formula.LP);
int i = 0;
for (Iterator it = tuple.iterator(); it.hasNext(); i++) {
if (i > 0) sb.append(Formula.SPACE);
sb.append(normalizeVariables_1((String) it.next(),idxs,
vmap,replaceSkolemTerms));
}
sb.append(Formula.RP);
}
}
else
sb.append(flist);
result = sb.toString();
return result;
}
/** ***************************************************************
* This method converts every occurrence of '<=>' in the Formula
* to a conjunct with two occurrences of '=>'.
*
* @return A Formula with no occurrences of '<=>'.
*
*/
private Formula equivalencesOut() {
Formula ans = thisFormula;
String theNewFormula = null;
if (thisFormula.listP() && !(thisFormula.empty())) {
String head = thisFormula.car();
if (!StringUtil.emptyString(head) && Formula.listP(head)) {
Clausifier headF = new Clausifier(head);
String newHead = headF.equivalencesOut().theFormula;
Clausifier theNewClausifier = new Clausifier(thisFormula.cdr());
theNewFormula = theNewClausifier.equivalencesOut().cons(newHead).theFormula;
}
else if (head.equals(Formula.IFF)) {
String second = thisFormula.cadr();
Clausifier secondF = new Clausifier(second);
String newSecond = secondF.equivalencesOut().theFormula;
String third = thisFormula.caddr();
Clausifier thirdF = new Clausifier(third);
String newThird = thirdF.equivalencesOut().theFormula;
theNewFormula = ("(and (=> " + newSecond + " " + newThird
+ ") (=> " + newThird + " " + newSecond + "))");
}
else {
Clausifier fourth = new Clausifier(thisFormula.cdrAsFormula().theFormula);
theNewFormula = fourth.equivalencesOut().cons(head).theFormula;
}
if (theNewFormula != null) {
ans = new Formula();
ans.read(theNewFormula);
}
}
return ans;
}
/** ***************************************************************
* This method converts every occurrence of '(=> LHS RHS' in the
* Formula to a disjunct of the form '(or (not LHS) RHS)'.
*
* @return A Formula with no occurrences of '=>'.
*
*/
private Formula implicationsOut() {
Formula ans = thisFormula;
String theNewFormula = null;
if (thisFormula.listP() && !thisFormula.empty()) {
String head = thisFormula.car();
if (!StringUtil.emptyString(head) && Formula.listP(head)) {
Clausifier headF = new Clausifier(head);
String newHead = headF.implicationsOut().theFormula;
Clausifier theNewClausifier = new Clausifier(thisFormula.cdr());
theNewFormula = theNewClausifier.implicationsOut().cons(newHead).theFormula;
}
else if (head.equals(Formula.IF)) {
String second = thisFormula.cadr();
Clausifier secondF = new Clausifier(second);
String newSecond = secondF.implicationsOut().theFormula;
String third = thisFormula.caddr();
Clausifier thirdF = new Clausifier(third);
String newThird = thirdF.implicationsOut().theFormula;
theNewFormula = ("(or (not " + newSecond + ") " + newThird + ")");
}
else {
Clausifier fourth = new Clausifier(thisFormula.cdrAsFormula().theFormula);
theNewFormula = fourth.implicationsOut().cons(head).theFormula;
}
if (theNewFormula != null) {
ans = new Formula();
ans.read(theNewFormula);
}
}
return ans;
}
/** ***************************************************************
* This method 'pushes in' all occurrences of 'not', so that each
* occurrence has the narrowest possible scope, and also removes
* from the Formula all occurrences of '(not (not ...))'.
*
* @see negationsIn_1().
*
* @return A Formula with all occurrences of 'not' accorded
* narrowest scope, and no occurrences of '(not (not ...))'.
*/
private Formula negationsIn() {
Formula f = thisFormula;
Formula ans = negationsIn_1();
// Repeatedly apply negationsIn_1() until there are no more changes
while (!f.theFormula.equals(ans.theFormula)) {
f = ans;
ans = negationsIn_1(f);
}
return ans;
}
/** ***************************************************************
* This method is used in negationsIn(). It recursively 'pushes
* in' all occurrences of 'not', so that each occurrence has the
* narrowest possible scope, and also removes from the Formula all
* occurrences of '(not (not ...))'.
*
* @see negationsIn().
*
* @return A Formula with all occurrences of 'not' accorded
* narrowest scope, and no occurrences of '(not (not ...))'.
*/
private Formula negationsIn_1() {
if (thisFormula.listP()) {
if (thisFormula.empty()) { return thisFormula; }
String arg0 = thisFormula.car();
String arg1 = thisFormula.cadr();
if (arg0.equals(Formula.NOT) && Formula.listP(arg1)) {
Formula arg1F = new Formula();
arg1F.read(arg1);
String arg0_of_arg1 = arg1F.car();
if (arg0_of_arg1.equals(Formula.NOT)) {
String arg1_of_arg1 = arg1F.cadr();
Formula arg1_of_arg1F = new Formula();
arg1_of_arg1F.read(arg1_of_arg1);
return arg1_of_arg1F;
}
if (Formula.isCommutative(arg0_of_arg1)) {
String newOp = null;
if (arg0_of_arg1.equals(Formula.AND))
newOp = Formula.OR;
else
newOp = Formula.AND;
return listAll(arg1F.cdrAsFormula(),"(not ", ")").cons(newOp);
}
if (Formula.isQuantifier(arg0_of_arg1)) {
String vars = arg1F.cadr();
String arg2_of_arg1 = arg1F.caddr();
String quant = null;
if (arg0_of_arg1.equals(Formula.UQUANT))
quant = Formula.EQUANT;
else
quant = Formula.UQUANT;
arg2_of_arg1 = ("(not " + arg2_of_arg1 + ")");
Formula arg2_of_arg1F = new Formula();
arg2_of_arg1F.read(arg2_of_arg1);
String theNewFormula = ("(" + quant + " " + vars + " "
+ negationsIn_1(arg2_of_arg1F).theFormula + ")");
Formula newF = new Formula();
newF.read(theNewFormula);
return newF;
}
String theNewFormula = ("(not " + negationsIn_1(arg1F).theFormula + ")");
Formula newF = new Formula();
newF.read(theNewFormula);
return newF;
}
if (Formula.isQuantifier(arg0)) {
String arg2 = thisFormula.caddr();
Formula arg2F = new Formula();
arg2F.read(arg2);
String newArg2 = negationsIn_1(arg2F).theFormula;
String theNewFormula = ("(" + arg0 + " " + arg1 + " " + newArg2 + ")");
Formula newF = new Formula();
newF.read(theNewFormula);
return newF;
}
if (Formula.listP(arg0)) {
Formula arg0F = new Formula();
arg0F.read(arg0);
return negationsIn_1(thisFormula.cdrAsFormula()).cons(negationsIn_1(arg0F).theFormula);
}
return negationsIn_1(thisFormula.cdrAsFormula()).cons(arg0);
}
return thisFormula;
}
/** ***************************************************************
* convenience method
*/
private static Formula negationsIn_1(Formula f) {
Clausifier temp = new Clausifier(f.theFormula);
return temp.negationsIn_1();
}
/** ***************************************************************
* This method augments each element of the Formula by
* concatenating optional Strings before and after the element.
*
* Note that in most cases the input Formula will be simply a
* list, not a well-formed SUO-KIF Formula, and that the output
* will therefore not necessarily be a well-formed Formula.
*
* @param before A String that, if present, is prepended to every
* element of the Formula.
*
* @param after A String that, if present, is postpended to every
* element of the Formula.
*
* @return A Formula, or, more likely, simply a list, with the
* String values corresponding to before and after added to each
* element.
*/
private Formula listAll(String before, String after) {
Formula ans = thisFormula;
String theNewFormula = null;
if (thisFormula.listP()) {
theNewFormula = "";
Formula f = thisFormula;
while (!(f.empty())) {
String element = f.car();
if (!StringUtil.emptyString(before))
element = (before + element);
if (!StringUtil.emptyString(after))
element += after;
theNewFormula += (Formula.SPACE + element);
f = f.cdrAsFormula();
}
theNewFormula = (Formula.LP + theNewFormula.trim() + Formula.RP);
if (!StringUtil.emptyString(theNewFormula)) {
ans = new Formula();
ans.read(theNewFormula);
}
}
return ans;
}
/** ***************************************************************
* convenience method
*/
private static Formula listAll(Formula f, String before, String after) {
Clausifier temp = new Clausifier(f.theFormula);
return temp.listAll(before,after);
}
/** ***************************************************************
* This method increments VAR_INDEX and then returns the new int
* value. If VAR_INDEX is already at Integer.MAX_VALUE, then
* VAR_INDEX is reset to 0.
*
* @return An int value between 0 and Integer.MAX_VALUE inclusive.
*/
private static int incVarIndex() {
int oldVal = VAR_INDEX;
if (oldVal == Integer.MAX_VALUE)
VAR_INDEX = 0;
else
++VAR_INDEX;
return VAR_INDEX;
}
/** ***************************************************************
* This method increments SKOLEM_INDEX and then returns the new int
* value. If SKOLEM_INDEX is already at Integer.MAX_VALUE, then
* SKOLEM_INDEX is reset to 0.
*
* @return An int value between 0 and Integer.MAX_VALUE inclusive.
*/
private static int incSkolemIndex() {
int oldVal = SKOLEM_INDEX;
if (oldVal == Integer.MAX_VALUE)
SKOLEM_INDEX = 0;
else
++SKOLEM_INDEX;
return SKOLEM_INDEX;
}
/** ***************************************************************
* This method returns a new SUO-KIF variable String, modifying
* any digit suffix to ensure that the variable will be unique.
*
* @param prefix An optional variable prefix string.
*
* @return A new SUO-KIF variable.
*/
private static String newVar(String prefix) {
String base = Formula.VX;
String varIdx = Integer.toString(incVarIndex());
if (!StringUtil.emptyString(prefix)) {
List woDigitSuffix = KB.getMatches(prefix, "var_with_digit_suffix");
if (woDigitSuffix != null)
base = (String) woDigitSuffix.get(0);
else if (prefix.startsWith(Formula.RVAR))
base = Formula.RVAR;
else if (prefix.startsWith(Formula.VX))
base = Formula.VX;
else
base = prefix;
if (!(base.startsWith(Formula.V_PREF) || base.startsWith(Formula.R_PREF)))
base = (Formula.V_PREF + base);
}
return (base + varIdx);
}
/** ***************************************************************
* This method returns a new SUO-KIF variable String, adding a
* digit suffix to ensure that the variable will be unique.
*
* @return A new SUO-KIF variable
*/
private static String newVar() {
return newVar(null);
}
/** ***************************************************************
* This method returns a new SUO-KIF row variable String,
* modifying any digit suffix to ensure that the variable will be
* unique.
*
* @return A new SUO-KIF row variable.
*/
private static String newRowVar() {
return newVar(Formula.RVAR);
}
/** ***************************************************************
* Replace term2 with term1
*/
public Formula rename(String term2, String term1) {
Formula newFormula = new Formula();
newFormula.read("()");
if (thisFormula.atom()) {
if (thisFormula.theFormula.equals(term2))
thisFormula.theFormula = term1;
return thisFormula;
}
if (!thisFormula.empty()) {
Formula f1 = new Formula();
f1.read(thisFormula.car());
if (f1.listP())
newFormula = newFormula.cons(f1.rename(term2,term1));
else
newFormula = newFormula.append(f1.rename(term2,term1));
Formula f2 = new Formula();
f2.read(thisFormula.cdr());
newFormula = newFormula.append(f2.rename(term2,term1));
}
return newFormula;
}
/** ***************************************************************
* Replace variables with a value as given by the map argument
*/
public Formula substituteVariables(Map m) {
Formula newFormula = new Formula();
newFormula.read("()");
if (thisFormula.atom()) {
if (m.keySet().contains(thisFormula.theFormula)) {
thisFormula.theFormula = (String) m.get(thisFormula.theFormula);
if (thisFormula.listP())
thisFormula.theFormula = "(" + thisFormula.theFormula + ")";
}
return thisFormula;
}
if (!thisFormula.empty()) {
Formula f1 = new Formula();
f1.read(thisFormula.car());
if (f1.listP())
newFormula = newFormula.cons(f1.substituteVariables(m));
else
newFormula = newFormula.append(f1.substituteVariables(m));
Formula f2 = new Formula();
f2.read(thisFormula.cdr());
newFormula = newFormula.append(f2.substituteVariables(m));
}
return newFormula;
}
/** ***************************************************************
* Extract all variables in a list
*/
public static Set extractVariables(Formula f) {
Set result = new TreeSet();
extractVariablesRecursively(f, result);
return result;
}
private static void extractVariablesRecursively(Formula f, Set vars) {
if (f.atom()) {
if (f.isVariable() || Formula.isSkolemTerm(f.theFormula)) {
vars.add(f.theFormula);
}
} else if (!f.empty()) {
Formula f1 = new Formula();
f1.read(f.car());
extractVariablesRecursively(f1, vars);
Formula f2 = new Formula();
f2.read(f.cdr());
extractVariablesRecursively(f2, vars);
}
}
/** **************************************************************
* Counter for instantiateVariables() to make sure generated
* symbols are unique.
*/
private static int _GENSYM_COUNTER = 0;
/** **************************************************************
* Create constants to fill variables.
*/
public Formula instantiateVariables() {
Formula f = renameVariables();
ArrayList> varList = f.collectVariables();
TreeMap vars = new TreeMap();
ArrayList al = (ArrayList) varList.get(0);
al.addAll((ArrayList) varList.get(1));
for (int i = 0; i < al.size(); i++) {
String s = (String) al.get(i);
_GENSYM_COUNTER++;
String value = "GenSym" + String.valueOf(_GENSYM_COUNTER);
vars.put(s,value);
}
return f.substituteVariables(vars);
}
/** ***************************************************************
* This method returns a new Formula in which all variables have
* been renamed to ensure uniqueness.
*
* @see clausify()
* @see renameVariables(Map topLevelVars, Map scopedRenames)
*
* @return A new SUO-KIF Formula with all variables renamed.
*/
private Formula renameVariables() {
HashMap topLevelVars = new HashMap();
HashMap scopedRenames = new HashMap();
HashMap allRenames = new HashMap();
return renameVariables(topLevelVars, scopedRenames, allRenames);
}
/** ***************************************************************
* convenience method
*/
public static Formula renameVariables(Formula f) {
Clausifier temp = new Clausifier(f.theFormula);
return temp.renameVariables();
}
/** ***************************************************************
* convenience method
*/
public static Formula renameVariables(Formula f, Map topLevelVars, Map scopedRenames, Map allRenames) {
Clausifier temp = new Clausifier(f.theFormula);
return temp.renameVariables(topLevelVars,scopedRenames,allRenames);
}
/** ***************************************************************
* This method returns a new Formula in which all variables have
* been renamed to ensure uniqueness.
*
* @see renameVariables().
*
* @param topLevelVars A Map that is used to track renames of
* implicitly universally quantified variables.
*
* @param scopedRenames A Map that is used to track renames of
* explicitly quantified variables.
*
* @param allRenames A Map from all new vars in the Formula to
* their old counterparts.
*
* @return A new SUO-KIF Formula with all variables renamed.
*/
private Formula renameVariables(Map topLevelVars, Map scopedRenames, Map allRenames) {
if (thisFormula.listP()) {
if (thisFormula.empty()) { return thisFormula; }
String arg0 = thisFormula.car();
if (Formula.isQuantifier(arg0)) {
// Copy the scopedRenames map to protect variable scope as we descend below this quantifier.
Map newScopedRenames = new HashMap(scopedRenames);
String oldVars = thisFormula.cadr();
Formula oldVarsF = new Formula();
oldVarsF.read(oldVars);
String newVars = "";
while (!oldVarsF.empty()) {
String oldVar = oldVarsF.car();
String newVar = newVar();
newScopedRenames.put(oldVar, newVar);
allRenames.put(newVar, oldVar);
newVars += (Formula.SPACE + newVar);
oldVarsF = oldVarsF.cdrAsFormula();
}
newVars = (Formula.LP + newVars.trim() + Formula.RP);
String arg2 = thisFormula.caddr();
Formula arg2F = new Formula();
arg2F.read(arg2);
String newArg2 = Clausifier.renameVariables(arg2F,topLevelVars,newScopedRenames,
allRenames).theFormula;
String theNewFormula = (Formula.LP + arg0 + Formula.SPACE + newVars + Formula.SPACE + newArg2 + Formula.RP);
Formula newF = new Formula();
newF.read(theNewFormula);
return newF;
}
Formula arg0F = new Formula();
arg0F.read(arg0);
String newArg0 = Clausifier.renameVariables(arg0F,topLevelVars,scopedRenames,
allRenames).theFormula;
String newRest = Clausifier.renameVariables(thisFormula.cdrAsFormula(),topLevelVars,scopedRenames,
allRenames).theFormula;
Formula newRestF = new Formula();
newRestF.read(newRest);
String theNewFormula = newRestF.cons(newArg0).theFormula;
Formula newF = new Formula();
newF.read(theNewFormula);
return newF;
}
if (Formula.isVariable(thisFormula.theFormula)) {
String rnv = (String) scopedRenames.get(thisFormula.theFormula);
if (StringUtil.emptyString(rnv)) {
rnv = (String) topLevelVars.get(thisFormula.theFormula);
if (StringUtil.emptyString(rnv)) {
rnv = newVar();
topLevelVars.put(thisFormula.theFormula, rnv);
allRenames.put(rnv, thisFormula.theFormula);
}
}
Formula newF = new Formula();
newF.read(rnv);
return newF;
}
return thisFormula;
}
/** ***************************************************************
* This method returns a new, unique skolem term with each
* invocation.
*
* @param vars A sorted TreeSet of the universally quantified
* variables that potentially define the skolem term. The set may
* be empty.
*
* @return A String. The string will be a skolem functional term
* (a list) if vars contains variables. Otherwise, it will be an
* atomic constant.
*/
private static String newSkolemTerm(TreeSet vars) {
String ans = Formula.SK_PREF;
int idx = incSkolemIndex();
if ((vars != null) && !vars.isEmpty()) {
// ans += (Formula.FN_SUFF + Formula.SPACE + idx);
ans += (Formula.FN_SUFF + idx);
Iterator it = vars.iterator();
while (it.hasNext()) {
String var = (String) it.next();
ans += (Formula.SPACE + var);
}
ans = (Formula.LP + ans + Formula.RP);
}
else
ans += idx;
return ans;
}
/** ***************************************************************
* This method returns a new Formula in which all existentially
* quantified variables have been replaced by Skolem terms.
*
* @see existentialsOut(Map evSubs, TreeSet iUQVs, TreeSet scopedUQVs)
* @see collectIUQVars(TreeSet iuqvs, TreeSet scopedVars)
*
* @return A new SUO-KIF Formula without existentially quantified
* variables.
*/
private Formula existentialsOut() {
// Existentially quantified variable substitution pairs:
// var -> skolem term.
Map evSubs = new HashMap();
// Implicitly universally quantified variables.
TreeSet iUQVs = new TreeSet();
// Explicitly quantified variables.
TreeSet scopedVars = new TreeSet();
// Explicitly universally quantified variables.
TreeSet scopedUQVs = new TreeSet();
// Collect the implicitly universally qualified variables from
// the Formula.
collectIUQVars(iUQVs, scopedVars);
// Do the recursive term replacement, and return the results.
return existentialsOut(evSubs, iUQVs, scopedUQVs);
}
/** ***************************************************************
* This method returns a new Formula in which all existentially
* quantified variables have been replaced by Skolem terms.
*
* @see existentialsOut()
*
* @param evSubs A Map of variable - skolem term substitution
* pairs.
*
* @param iUQVs A TreeSet of implicitly universally quantified
* variables.
*
* @param scopedUQVs A TreeSet of explicitly universally
* quantified variables.
*
* @return A new SUO-KIF Formula without existentially quantified
* variables.
*/
private Formula existentialsOut(Map evSubs, TreeSet iUQVs, TreeSet scopedUQVs) {
if (thisFormula.listP()) {
if (thisFormula.empty()) { return thisFormula; }
String arg0 = thisFormula.car();
if (arg0.equals(Formula.UQUANT)) {
// Copy the scoped variables set to protect variable scope as we descend below this
// quantifier.
TreeSet newScopedUQVs = new TreeSet(scopedUQVs);
String varList = thisFormula.cadr();
Formula varListF = new Formula();
varListF.read(varList);
while (!(varListF.empty())) {
String var = varListF.car();
newScopedUQVs.add(var);
varListF.read(varListF.cdr());
}
String arg2 = thisFormula.caddr();
Formula arg2F = new Formula();
arg2F.read(arg2);
String theNewFormula = ("(forall " + varList + " "
+ existentialsOut(arg2F, evSubs, iUQVs,
newScopedUQVs).theFormula + ")");
thisFormula.read(theNewFormula);
return thisFormula;
}
if (arg0.equals(Formula.EQUANT)) {
// Collect the relevant universally quantified variables.
TreeSet uQVs = new TreeSet(iUQVs);
uQVs.addAll(scopedUQVs);
// Collect the existentially quantified variables.
ArrayList eQVs = new ArrayList();
String varList = thisFormula.cadr();
Formula varListF = new Formula();
varListF.read(varList);
while (!(varListF.empty())) {
String var = varListF.car();
eQVs.add(var);
varListF.read(varListF.cdr());
}
// For each existentially quantified variable, create a corresponding skolem term, and
// store the pair in the evSubs map.
for (int i = 0; i < eQVs.size() ; i++) {
String var = (String) eQVs.get(i);
String skTerm = newSkolemTerm(uQVs);
evSubs.put(var, skTerm);
}
String arg2 = thisFormula.caddr();
Formula arg2F = new Formula();
arg2F.read(arg2);
return existentialsOut(arg2F,evSubs, iUQVs, scopedUQVs);
}
Formula arg0F = new Formula();
arg0F.read(arg0);
String newArg0 = existentialsOut(arg0F,evSubs,iUQVs,scopedUQVs).theFormula;
return existentialsOut(thisFormula.cdrAsFormula(),evSubs, iUQVs, scopedUQVs).cons(newArg0);
}
if (Formula.isVariable(thisFormula.theFormula)) {
String newTerm = (String) evSubs.get(thisFormula.theFormula);
if (!StringUtil.emptyString(newTerm))
thisFormula.read(newTerm);
return thisFormula;
}
return thisFormula;
}
/** ***************************************************************
* convenience method
*/
private static Formula existentialsOut(Formula f, Map evSubs, TreeSet iUQVs, TreeSet scopedUQVs) {
Clausifier temp = new Clausifier(f.theFormula);
return temp.existentialsOut(evSubs, iUQVs, scopedUQVs);
}
/** ***************************************************************
* This method collects all variables in Formula that appear to be
* only implicitly universally quantified and adds them to the
* TreeSet iuqvs. Note the iuqvs must be passed in.
*
* @param iuqvs A TreeSet for accumulating variables that appear
* to be implicitly universally quantified.
*
* @param scopedVars A TreeSet containing explicitly quantified
* variables.
*
* @return void
*/
private void collectIUQVars(TreeSet iuqvs, TreeSet scopedVars) {
if (thisFormula.listP() && !thisFormula.empty()) {
String arg0 = thisFormula.car();
if (Formula.isQuantifier(arg0)) {
// Copy the scopedVars set to protect variable scope as we descend below this quantifier.
TreeSet newScopedVars = new TreeSet(scopedVars);
String varList = thisFormula.cadr();
Formula varListF = new Formula();
varListF.read(varList);
while (!(varListF.empty())) {
String var = varListF.car();
newScopedVars.add(var);
varListF = varListF.cdrAsFormula();
}
String arg2 = thisFormula.caddr();
Formula arg2F = new Formula();
arg2F.read(arg2);
collectIUQVars(arg2F,iuqvs,newScopedVars);
}
else {
Formula arg0F = new Formula();
arg0F.read(arg0);
collectIUQVars(arg0F,iuqvs,scopedVars);
collectIUQVars(thisFormula.cdrAsFormula(),iuqvs,scopedVars);
}
}
else if (Formula.isVariable(thisFormula.theFormula)
&& !(scopedVars.contains(thisFormula.theFormula))) {
iuqvs.add(thisFormula.theFormula);
}
}
/** ***************************************************************
* convenience method
*/
private static void collectIUQVars(Formula f, TreeSet iuqvs, TreeSet scopedVars) {
Clausifier temp = new Clausifier(f.theFormula);
temp.collectIUQVars(iuqvs,scopedVars);
}
/** ***************************************************************
* This method returns a new Formula in which explicit univeral
* quantifiers have been removed.
*
* @see clausify()
*
* @return A new SUO-KIF Formula without explicit universal
* quantifiers.
*/
private Formula universalsOut() {
if (thisFormula.listP()) {
if (thisFormula.empty()) { return thisFormula; }
String arg0 = thisFormula.car();
if (arg0.equals(Formula.UQUANT)) {
String arg2 = thisFormula.caddr();
thisFormula.read(arg2);
return universalsOut(thisFormula);
}
Formula arg0F = new Formula();
arg0F.read(arg0);
String newArg0 = universalsOut(arg0F).theFormula;
return universalsOut(thisFormula.cdrAsFormula()).cons(newArg0);
}
return thisFormula;
}
/** ***************************************************************
* convenience method
*/
public static Formula universalsOut(Formula f) {
Clausifier temp = new Clausifier(f.theFormula);
return temp.universalsOut();
}
/** ***************************************************************
* This method returns a new Formula in which nested 'and', 'or',
* and 'not' operators have been unnested:
*
* (not (not ...)) ->
*
* (and (and ...)) -> (and ...)
*
* (or (or ...)) -> (or ...)
*
* @see clausify()
* @see nestedOperatorsOut_1()
*
* @return A new SUO-KIF Formula in which nested commutative
* operators and 'not' have been unnested.
*/
private Formula nestedOperatorsOut() {
Formula f = thisFormula;
Formula ans = nestedOperatorsOut_1();
// Here we repeatedly apply nestedOperatorsOut_1() until there are no
// more changes.
while (!f.theFormula.equals(ans.theFormula)) {
//System.out.println();
//System.out.println("f.theFormula == " + f.theFormula);
//System.out.println("ans.theFormula == " + ans.theFormula + "\n");
f = ans;
ans = nestedOperatorsOut_1(f);
}
return ans;
}
/** ***************************************************************
* convenience method
*/
private static Formula nestedOperatorsOut(Formula f) {
Clausifier temp = new Clausifier(f.theFormula);
return temp.nestedOperatorsOut();
}
/** ***************************************************************
* @see clausify()
* @see nestedOperatorsOut_1()
*
* @return A new SUO-KIF Formula in which nested commutative
* operators and 'not' have been unnested.
*/
private Formula nestedOperatorsOut_1() {
if (thisFormula.listP()) {
if (thisFormula.empty()) { return thisFormula; }
String arg0 = thisFormula.car();
if (Formula.isCommutative(arg0) || arg0.equals(Formula.NOT)) {
ArrayList literals = new ArrayList();
Formula restF = thisFormula.cdrAsFormula();
while (!(restF.empty())) {
String lit = restF.car();
Formula litF = new Formula();
litF.read (lit);
if (litF.listP()) {
String litFarg0 = litF.car();
if (litFarg0.equals(arg0)) {
if (arg0.equals(Formula.NOT)) {
String theNewFormula = litF.cadr();
Formula newF = new Formula();
newF.read(theNewFormula);
return nestedOperatorsOut_1(newF);
}
Formula rest2F = litF.cdrAsFormula();
while (!(rest2F.empty())) {
String rest2arg0 = rest2F.car();
Formula rest2arg0F = new Formula();
rest2arg0F.read(rest2arg0);
literals.add(nestedOperatorsOut_1(rest2arg0F).theFormula);
rest2F = rest2F.cdrAsFormula();
}
}
else
literals.add(nestedOperatorsOut_1(litF).theFormula);
}
else
literals.add(lit);
restF = restF.cdrAsFormula();
}
String theNewFormula = (Formula.LP + arg0);
for (int i = 0 ; i < literals.size() ; i++)
theNewFormula += (Formula.SPACE + (String)literals.get(i));
theNewFormula += Formula.RP;
Formula newF = new Formula();
newF.read(theNewFormula);
return newF;
}
Formula arg0F = new Formula();
arg0F.read(arg0);
String newArg0 = nestedOperatorsOut_1(arg0F).theFormula;
return nestedOperatorsOut_1(thisFormula.cdrAsFormula()).cons(newArg0);
}
return thisFormula;
}
/** ***************************************************************
* convenience method
*/
private static Formula nestedOperatorsOut_1(Formula f) {
Clausifier temp = new Clausifier(f.theFormula);
return temp.nestedOperatorsOut_1();
}
/** ***************************************************************
* This method returns a new Formula in which all occurrences of
* 'or' have been accorded the least possible scope.
*
* (or P (and Q R)) -> (and (or P Q) (or P R))
*
* @see clausify()
* @see disjunctionsIn_1()
*
* @return A new SUO-KIF Formula in which occurrences of 'or' have
* been 'moved in' as far as possible.
*/
private Formula disjunctionsIn() {
Formula f = thisFormula;
Formula ans = disjunctionsIn_1(nestedOperatorsOut());
// Here we repeatedly apply disjunctionIn_1() until there are no more changes
while (! f.theFormula.equals(ans.theFormula)) {
f = ans;
ans = disjunctionsIn_1(nestedOperatorsOut(f));
}
return ans;
}
/** ***************************************************************
* @see clausify()
* @see disjunctionsIn()
*
* @return A new SUO-KIF Formula in which occurrences of 'or' have
* been 'moved in' as far as possible.
*/
private Formula disjunctionsIn_1() {
if (thisFormula.listP()) {
if (thisFormula.empty()) { return thisFormula; }
String arg0 = thisFormula.car();
if (arg0.equals(Formula.OR)) {
List disjuncts = new ArrayList();
List conjuncts = new ArrayList();
Formula restF = thisFormula.cdrAsFormula();
while (!(restF.empty())) {
String disjunct = restF.car();
Formula disjunctF = new Formula();
disjunctF.read(disjunct);
if (disjunctF.listP()
&& disjunctF.car().equals(Formula.AND)
&& conjuncts.isEmpty()) {
Formula rest2F = disjunctionsIn_1(disjunctF.cdrAsFormula());
while (!(rest2F.empty())) {
conjuncts.add(rest2F.car());
rest2F = rest2F.cdrAsFormula();
}
}
else
disjuncts.add(disjunct);
restF = restF.cdrAsFormula();
}
if (conjuncts.isEmpty()) { return thisFormula; }
Formula resultF = new Formula();
resultF.read("()");
String disjunctsString = "";
for (int i = 0; i < disjuncts.size() ; i++)
disjunctsString += (Formula.SPACE + (String)disjuncts.get(i));
disjunctsString = (Formula.LP + disjunctsString.trim() + Formula.RP);
Formula disjunctsF = new Formula();
disjunctsF.read(disjunctsString);
for (int ci = 0 ; ci < conjuncts.size() ; ci++) {
String newDisjuncts =
disjunctionsIn_1(disjunctsF.cons((String)conjuncts.get(ci)).cons(Formula.OR)).theFormula;
resultF = resultF.cons(newDisjuncts);
}
resultF = resultF.cons(Formula.AND);
return resultF;
}
Formula arg0F = new Formula();
arg0F.read(arg0);
String newArg0 = disjunctionsIn_1(arg0F).theFormula;
return disjunctionsIn_1(thisFormula.cdrAsFormula()).cons(newArg0);
}
return thisFormula;
}
/** ***************************************************************
* convenience method
*/
private static Formula disjunctionsIn_1(Formula f) {
Clausifier temp = new Clausifier(f.theFormula);
return temp.disjunctionsIn_1();
}
/** ***************************************************************
* This method returns an ArrayList of clauses. Each clause is a
* LISP list (really, a Formula) containing one or more Formulas.
* The LISP list is assumed to be a disjunction, but there is no
* 'or' at the head.
*
* @see clausify()
*
* @return An ArrayList of LISP lists, each of which contains one
* or more Formulas.
*/
private ArrayList operatorsOut() {
ArrayList result = new ArrayList();
ArrayList clauses = new ArrayList();
if (!StringUtil.emptyString(thisFormula.theFormula)) {
if (thisFormula.listP()) {
String arg0 = thisFormula.car();
if (arg0.equals(Formula.AND)) {
Formula restF = thisFormula.cdrAsFormula();
while (!(restF.empty())) {
String fStr = restF.car();
Formula newF = new Formula();
newF.read(fStr);
clauses.add(newF);
restF = restF.cdrAsFormula();
}
}
}
if (clauses.isEmpty())
clauses.add(thisFormula);
for (int i = 0 ; i < clauses.size() ; i++) {
Formula clauseF = new Formula();
clauseF.read("()");
Formula f = (Formula) clauses.get(i);
if (f.listP()) {
if (f.car().equals(Formula.OR)) {
f = f.cdrAsFormula();
while (!(f.empty())) {
String lit = f.car();
clauseF = clauseF.cons(lit);
f = f.cdrAsFormula();
}
}
}
if (clauseF.empty())
clauseF = clauseF.cons(f.theFormula);
result.add(clauseF);
}
}
return result;
}
/** ***************************************************************
* This method returns a Formula in which variables for separate
* clauses have been 'standardized apart'.
*
* @see clausify()
* @see standardizeApart(Map renameMap)
* @see standardizeApart_1(Map renames, Map reverseRenames)
*
* @return A Formula.
*/
private Formula standardizeApart() {
HashMap reverseRenames = new HashMap();
return standardizeApart(thisFormula,reverseRenames);
}
/** ***************************************************************
* convenience method
*/
private static Formula standardizeApart(Formula f, Map renameMap) {
Clausifier temp = new Clausifier(f.theFormula);
return temp.standardizeApart(renameMap);
}
/** ***************************************************************
* This method returns a Formula in which variables for separate
* clauses have been 'standardized apart'.
*
* @see clausify()
* @see standardizeApart()
* @see standardizeApart_1(Map renames, Map reverseRenames)
*
* @param renameMap A Map for capturing one-to-one variable rename
* correspondences. Keys are new variables. Values are old
* variables.
*
* @return A Formula.
*/
private Formula standardizeApart(Map renameMap) {
Formula result = thisFormula;
Map reverseRenames = null;
if (renameMap instanceof Map)
reverseRenames = renameMap;
else
reverseRenames = new HashMap();
// First, break the Formula into separate clauses, if necessary.
ArrayList clauses = new ArrayList();
if (!StringUtil.emptyString(thisFormula.theFormula)) {
if (thisFormula.listP()) {
String arg0 = thisFormula.car();
if (arg0.equals(Formula.AND)) {
Formula restF = thisFormula.cdrAsFormula();
while (!(restF.empty())) {
String fStr = restF.car();
Formula newF = new Formula();
newF.read(fStr);
clauses.add(newF);
restF = restF.cdrAsFormula();
}
}
}
if (clauses.isEmpty())
clauses.add(thisFormula);
// 'Standardize apart' by renaming the variables in each clause.
int n = clauses.size();
for (int i = 0 ; i < n ; i++) {
HashMap renames = new HashMap();
Formula oldClause = (Formula) clauses.remove(0);
clauses.add(standardizeApart_1(oldClause,renames,reverseRenames));
}
// Construct the new Formula to return.
if (n > 1) {
String theNewFormula = "(and";
for (int i = 0 ; i < n ; i++) {
Formula f = (Formula) clauses.get(i);
theNewFormula += (Formula.SPACE + f.theFormula);
}
theNewFormula += Formula.RP;
Formula newF = new Formula();
newF.read(theNewFormula);
result = newF;
}
else
result = clauses.get(0);
}
return result;
}
/** ***************************************************************
* This is a helper method for standardizeApart(renameMap). It
* assumes that the Formula will be a single clause.
*
* @see clausify()
* @see standardizeApart()
* @see standardizeApart(Map renameMap)
*
* @param renames A Map of correspondences between old variables
* and new variables.
*
* @param reverseRenames A Map of correspondences between new
* variables and old variables.
*
* @return A Formula
*/
private Formula standardizeApart_1(Map renames, Map reverseRenames) {
Formula ans = thisFormula;
if (thisFormula.listP() && !(thisFormula.empty())) {
String arg0 = thisFormula.car();
Formula arg0F = new Formula();
arg0F.read(arg0);
arg0F = standardizeApart_1(arg0F,renames,reverseRenames);
ans = standardizeApart_1(thisFormula.cdrAsFormula(),renames,reverseRenames).cons(arg0F.theFormula);
}
else if (Formula.isVariable(thisFormula.theFormula)) {
String rnv = (String) renames.get(thisFormula.theFormula);
if (StringUtil.emptyString(rnv)) {
rnv = newVar();
renames.put(thisFormula.theFormula, rnv);
reverseRenames.put(rnv, thisFormula.theFormula);
}
Formula rnvF = new Formula();
rnvF.read(rnv);
ans = rnvF;
}
return ans;
}
/** ***************************************************************
* convenience method
*/
private static Formula standardizeApart_1(Formula f, Map renames, Map reverseRenames) {
Clausifier temp = new Clausifier(f.theFormula);
return temp.standardizeApart_1(renames, reverseRenames);
}
/** ***************************************************************
* This method finds the original variable that corresponds to a new
* variable. Note that the clausification algorithm has two variable
* renaming steps, and that after variables are standardized apart an
* original variable might correspond to multiple clause variables.
*
* @param var A SUO-KIF variable (String)
*
* @param varMap A Map (graph) of successive new to old variable
* correspondences.
*
* @return The original SUO-KIF variable corresponding to the input.
*
**/
public static String getOriginalVar(String var, Map varMap) {
String ans = null;
String next = null;
if (!StringUtil.emptyString(var) && (varMap instanceof Map)) {
ans = var;
next = varMap.get(ans);
while (! ((next == null) || next.equals(ans))) {
ans = next;
next = varMap.get(ans);
}
if (ans == null)
ans = var;
}
return ans;
}
/** ***************************************************************
* This method converts the SUO-KIF Formula to a version of
* clausal (resolution, conjunctive normal) form with Skolem
* functions, following the procedure described in Logical
* Foundations of Artificial Intelligence, by Michael Genesereth
* and Nils Nilsson, 1987, pp. 63-66.
*
* A literal is an atomic formula. (Note, however, that
* because SUO-KIF allows higher-order formulae, not all SUO-KIF
* literals are really atomic.) A clause is a disjunction of
* literals that share no variable names with literals in any
* other clause in the KB. Note that even a relatively simple
* SUO-KIF formula might generate multiple clauses. In such
* cases, the Formula returned will be a conjunction of clauses.
* (A KB is understood to be a conjunction of clauses.) In all
* cases, the Formula returned by this method should be a
* well-formed SUO-KIF Formula if the input (original formula) is
* a well-formed SUO-KIF Formula. Rendering the output in true
* (LISPy) clausal form would require an additional step, the
* removal of all commutative logical operators, and the result
* would not be well-formed SUO-KIF.
*
* @see clausifyWithRenameInfo()
* @see toNegAndPosLitsWithRenameInfo()
* @see toCanonicalClausalForm();
*
* @return A SUO-KIF Formula in clausal form, or null if a clausal
* form cannot be generated.
*/
public Formula clausify() {
Formula ans = null;
thisFormula = equivalencesOut();
thisFormula = implicationsOut();
thisFormula = negationsIn();
thisFormula = renameVariables();
thisFormula = existentialsOut();
thisFormula = universalsOut();
thisFormula = disjunctionsIn();
thisFormula = standardizeApart();
return thisFormula;
}
/** ***************************************************************
* A test method.
*/
public static void test1() {
Formula f = new Formula();
f.read("(forall (?ROW1 ?ITEM) (equal (ListOrderFn (ListFn ?ROW1 ?ITEM) (ListLengthFn (ListFn ?ROW1 ?ITEM))) ?ITEM))");
System.out.println("INFO in Clausifier.test1(): input formula: " + f);
Formula clausalForm = Clausifier.clausify(f);
System.out.println("INFO in Clausifier.test1(): output formula: " + clausalForm);
}
/** ***************************************************************
* A test method.
*/
public static void testClausifier(String[] args) {
BufferedWriter bw = null;
try {
long t1 = System.currentTimeMillis();
int count = 0;
String inpath = args[0];
String outpath = args[1];
if (!StringUtil.emptyString(inpath) && !StringUtil.emptyString(outpath)) {
File infile = new File(inpath);
if (infile.exists()) {
KIF kif = new KIF();
kif.setParseMode(KIF.RELAXED_PARSE_MODE);
kif.readFile(infile.getCanonicalPath());
if (! kif.formulas.isEmpty()) {
File outfile = new File(outpath);
if (outfile.exists()) { outfile.delete(); }
bw = new BufferedWriter(new FileWriter(outfile, true));
Iterator it = kif.formulas.values().iterator();
Iterator it2 = null;
Formula f = null;
Formula clausalForm = null;
while (it.hasNext()) {
it2 = ((List) it.next()).iterator();
while (it2.hasNext()) {
f = (Formula) it2.next();
clausalForm = Clausifier.clausify(f);
if (clausalForm != null) {
bw.write(clausalForm.theFormula);
bw.newLine();
count++;
}
}
}
try {
bw.flush();
bw.close();
bw = null;
}
catch (Exception bwe) {
bwe.printStackTrace();
}
}
}
}
long dur = (System.currentTimeMillis() - t1);
System.out.println(count + " clausal forms written in " + (dur / 1000.0) + " seconds");
}
catch (Exception ex) {
ex.printStackTrace();
}
finally {
if (bw != null) {
try {
bw.close();
}
catch (Exception e2) {
e2.printStackTrace();
}
}
}
}
/** ***************************************************************
*/
private static void testRemoveImpEq() {
System.out.println();
System.out.println("================== testRemoveImpEq ======================");
Clausifier f = new Clausifier("(=> a b)");
System.out.println("input: " + f);
Formula form = f.equivalencesOut();
System.out.println(form);
f = new Clausifier(form.theFormula);
form = f.implicationsOut();
System.out.println(form);
System.out.println();
System.out.println("--------------------------------------------------");
f = new Clausifier("(<=> a b)");
System.out.println("input: " + f);
form = f.equivalencesOut();
System.out.println(form);
f = new Clausifier(form.theFormula);
form = f.implicationsOut();
System.out.println(form);
System.out.println();
System.out.println("--------------------------------------------------");
f = new Clausifier("(<=> (or (or (forall (?X) (a ?X)) (b ?X)) (exists (?X) (exists (?Y) (p ?X (f ?Y))))) (q (g a) ?X))");
System.out.println("input: " + f);
form = f.equivalencesOut();
System.out.println(form);
f = new Clausifier(form.theFormula);
form = f.implicationsOut();
System.out.println(form);
System.out.println();
}
/** ***************************************************************
*/
private static void testMoveQuantifiersLeft() {
System.out.println();
System.out.println("================== testMoveQuantifiersLeft ======================");
Clausifier f = new Clausifier("(or p (forall (?X) (q ?X)))");
System.out.println("input: " + f);
Formula form = f.existentialsOut();
System.out.println("result: " + form);
f = new Clausifier(form.theFormula);
form = f.universalsOut();
System.out.println("result: " + form);
System.out.println();
/*
System.out.println("input: " + form);
form = moveQuantifiersLeft(form);
System.out.println("result should be ![X]:p | q(X): " + form);
System.out.println();
form = BareFormula.string2form("~((![X]:a(X)) | b(X))");
System.out.println("input: " + form);
form = moveQuantifiersLeft(form);
System.out.println("result: " + form);
System.out.println();
form = BareFormula.string2form("~(((![X]:a(X)) | b(X)) | (?[X]:(?[Y]:p(X, f(Y)))))");
System.out.println("input: " + form);
form = moveQuantifiersLeft(form);
System.out.println("result: " + form);
System.out.println();
form = BareFormula.string2form("( (~(((![X]:a(X)) | b(X)) | (?[X]:(?[Y]:p(X, f(Y)))))) | q(g(a), X))");
System.out.println("input: " + form);
form = moveQuantifiersLeft(form);
System.out.println("result: " + form);
System.out.println();
*/
/* System.out.println("--------------------------------------------------");
f = new Clausifier("( ( (~(((![X]:a(X)) | b(X)) | (?[X]:(?[Y]:p(X, f(Y)))))) | q(g(a), X)) & " +
"((~q(g(a), X)) | (((![X]:a(X)) | b(X)) | (?[X]:(?[Y]:p(X, f(Y)))))))");
System.out.println("input: " + f);
form = f.existentialsOut();
System.out.println("result: " + form);
f = new Clausifier(form.theFormula);
form = f.universalsOut();
System.out.println("result: " + form);
System.out.println();
*/
}
/** ***************************************************************
*/
private static void testMoveNegationIn() {
System.out.println();
System.out.println("================== testMoveNegationIn ======================");
Clausifier f = new Clausifier("(not (or p q))");
System.out.println("input: " + f);
Formula form = f.negationsIn();
System.out.println("result should be (and (not p) (not q)): " + form);
System.out.println();
f = new Clausifier("(not (and p q))");
System.out.println("input: " + f);
form = f.negationsIn();
System.out.println("result should be (or (not p) (not q)): " + form);
System.out.println();
f = new Clausifier("(not (forall (?X) p))");
System.out.println("input: " + f);
form = f.negationsIn();
System.out.println("result should be (exists (?X) (not p)): " + form);
System.out.println();
f = new Clausifier("(not (exists (?X) p))");
System.out.println("input: " + f);
form = f.negationsIn();
System.out.println("result should be (forall (?X) (not p)): " + form);
System.out.println();
f = new Clausifier("(not (not p))");
System.out.println("input: " + f);
form = f.negationsIn();
System.out.println("result should be (p): " + form);
System.out.println();
f = new Clausifier("(not (exists (?Y) (p ?X (f ?Y))))");
System.out.println("input: " + f);
form = f.negationsIn();
System.out.println("result: " + form);
System.out.println();
f = new Clausifier("(not (exists (?X) (exists (?Y) (p ?X (f ?Y)))))");
System.out.println("input: " + f);
form = f.negationsIn();
System.out.println("expected result: (forall (?X) (forall (?Y) (not (p ?X (f ?Y)))))");
System.out.println("result: " + form);
System.out.println();
f = new Clausifier("(not (or (or (forall (?X) (a ?X)) (b ?X)) (exists (?X) (exists (?Y) (p ?X (f ?Y))))))");
System.out.println("input: " + f);
form = f.negationsIn();
System.out.println("result should be (and (and (exists (?X) (not (a ?X))) (not (b ?X))) (forall (?X) (forall (?Y) (not (p ?X (f ?Y))))))");
System.out.println("actual: "+ form);
System.out.println();
f = new Clausifier("(and (or (not (or (or (forall (?X) (a ?X)) (b ?X)) (exists (?X) (exists (?Y) (p ?X (f ?Y)))))) (q (g a) ?X)) " +
"(or (not (q (g a) ?X)) (or (or (forall (?X) (a ?X)) (b ?X)) (exists (?X) (exists (?Y) (p ?X (f ?Y)))))) )");
System.out.println("input: " + f);
form = f.negationsIn();
System.out.println("expected: ( ( ((( (?[X]:~a(X)) & ~b(X)) & (![X]:(![Y]:~p(X, f(Y)))) )) | q(g(a), X)) & " +
"((~q(g(a), X)) | (((![X]:a(X))|b(X)) | (?[X]:(?[Y]:p(X, f(Y)))) )))");
System.out.println("result: " + form);
System.out.println();
}
/** ***************************************************************
*/
private static void testStandardizeVariables() {
System.out.println();
System.out.println("================== testStandardizeVariables ======================");
Clausifier f = new Clausifier("(not (or (forall (?X) (a ?X)) (b ?X)))");
System.out.println("input: " + f);
Formula form = f.standardizeApart();
System.out.println("result should be : (not (or (forall (?VAR2) (a ?VAR2)) (b ?VAR1)))");
System.out.println("actual: "+ form);
System.out.println();
/*
f = new Clausifier("(((~(((![X]:a(X))|b(X))|(?[X]:(?[Y]:p(X, f(Y))))))|q(g(a), X))&((~q(g(a), X))|(((![X]:a(X))|b(X))|(?[X]:(?[Y]:p(X, f(Y)))))))");
System.out.println("input: " + form);
form = f.standardizeApart();
System.out.println("actual: "+ form);
System.out.println();
*/
}
/** ***************************************************************
*/
private static void testSkolemization() {
System.out.println();
System.out.println("================== testSkolemization ======================");
Clausifier f = new Clausifier("(?[VAR0]:(![VAR3]:(![VAR2]:(?[VAR5]:(![VAR1]:(?[VAR4]:((((~a(VAR0)&~b(X))&~p(VAR2, f(VAR1)))|q(g(a), X))&(~q(g(a), X)|((a(VAR3)|b(X))|p(VAR5, f(VAR4)))))))))))");
System.out.println("input: " + f);
Formula form = f.existentialsOut();
System.out.println("actual: "+ form);
System.out.println();
}
/** ***************************************************************
*/
private static void testDistribute() {
System.out.println();
System.out.println("================== testDistribute ======================");
Clausifier f = new Clausifier("(or (and a b) c)");
System.out.println("input: " + f);
Formula form = f.disjunctionsIn();
System.out.println("actual: " + form);
/*
System.out.println("input: " + form);
form = distributeAndOverOr(form);
System.out.println("result should be : (a | c) & (b | c)");
System.out.println("actual: " + form);
System.out.println();
form = BareFormula.string2form("(a & b) | (c & d)");
System.out.println("input: " + form);
form = distributeAndOverOr(form);
System.out.println("result should be : (a | c) & (a | d) & (b | c) & (d | b)");
System.out.println("actual: " + form);
System.out.println();
*/
//KIF.init();
f = new Clausifier("(((~holdsAt(VAR2, VAR1)|releasedAt(VAR2, plus(VAR1, n1)))|(happens(skf3, VAR1)&terminates(skf3, VAR2, VAR1)))|holdsAt(VAR2, plus(VAR1, n1)))");
System.out.println("input: " + f);
form = f.disjunctionsIn();
System.out.println("actual: " + form);
//System.out.println(KIF.format(form.toKIFString()));
System.out.println();
}
/** ***************************************************************
*/
private static void testClausificationSteps(String s) {
System.out.println();
System.out.println("================== testClausification ======================");
Clausifier f = new Clausifier(s);
System.out.println("input: " + f);
System.out.println();
Formula form = f.equivalencesOut();
System.out.println("after Remove Equivalence: " + form);
System.out.println();
f = new Clausifier(form.theFormula);
form = f.implicationsOut();
System.out.println("after Implications out: " + form);
System.out.println();
f = new Clausifier(form.theFormula);
form = f.negationsIn();
System.out.println("after Move Negation In: " + form);
System.out.println();
f = new Clausifier(form.theFormula);
form = f.renameVariables();
System.out.println("after rename Variables: " + form);
System.out.println();
f = new Clausifier(form.theFormula);
form = f.existentialsOut();
System.out.println("after Move Quantifiers: " + form);
System.out.println();
f = new Clausifier(form.theFormula);
form = f.universalsOut();
System.out.println("after remove universal quantifiers: " + form);
System.out.println();
f = new Clausifier(form.theFormula);
form = f.disjunctionsIn();
System.out.println("after Distribution: " + form);
System.out.println();
f = new Clausifier(form.theFormula);
form = f.standardizeApart();
System.out.println("after Standardize apart: " + form);
System.out.println();
f = new Clausifier(form.theFormula);
ArrayList forms = f.separateConjunctions();
System.out.println("after separation: " + forms);
}
/** ***************************************************************
*/
private static void testClausification() {
//testClausificationSteps("((((![X]:a(X))|b(X))|(?[X]:(?[Y]:p(X,f(Y)))))<=>q(g(a),X))");
testClausificationSteps("(![Fluent]:(![Time]:(((holdsAt(Fluent, Time)&(~releasedAt(Fluent, plus(Time, n1))))&(~(?[Event]:(happens(Event, Time)&terminates(Event, Fluent, Time)))))=>holdsAt(Fluent, plus(Time, n1)))))).");
}
/** ***************************************************************
*/
private static void testClausificationSimple() {
System.out.println();
System.out.println("================== testClausificationSimple ======================");
Formula form = new Formula();
Clausifier c = new Clausifier("(<=> (or (or (forall (?X) (a ?X)) (b ?X)) (exists (?X) (exists (?Y) (p ?X (f ?Y))))) (q (g a) ?X))");
System.out.println("input: " + c.thisFormula);
System.out.println();
Formula result = c.clausify();
System.out.println(result);
c = new Clausifier("(<=> (and (equal (AbsoluteValueFn ?NUMBER1) ?NUMBER2) (instance ?NUMBER1 RealNumber) " +
"(instance ?NUMBER2 RealNumber)) (or (and (instance ?NUMBER1 NonnegativeRealNumber) " +
"(equal ?NUMBER1 ?NUMBER2)) (and (instance ?NUMBER1 NegativeRealNumber) (equal ?NUMBER2 " +
"(SubtractionFn 0 ?NUMBER1)))))");
System.out.println("input: " + c.thisFormula);
System.out.println();
result = c.clausify();
System.out.println(result);
}
/** ***************************************************************
*/
public static void main(String[] args) {
//testRemoveImpEq();
//testMoveNegationIn();
//testMoveQuantifiersLeft();
//testStandardizeVariables();
//testSkolemization();
//testDistribute();
//testClausification();
testClausificationSimple();
//testClausifier(args);
}
}