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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.
package com.articulate.sigma.semRewrite;
/*
Copyright 2014-2015 IPsoft
Author: Adam Pease [email protected]
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program ; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston,
MA 02111-1307 USA
*/
import java.lang.reflect.Method;
import com.articulate.sigma.semRewrite.*;
// Note that because the language is so simple we only have to
// handle moving negations and disjunctions. The clausifier
// creates an expression in Conjunctive Normal Form (CNF).
// This is a special case of a general clausification algorithm,
// such as described in (Sutcliffe&Melville, 1996)
// http://www.cs.miami.edu/~geoff/Papers/Journal/1996_SM96_SACJ.pdf
// CNF has only three operators - negation, conjunction and disjunction
public class Clausifier {
public static boolean changed = false;
/** ***************************************************************
* -(p | q) becomes -p , -q
* -(p , q) becomes -p | -q
*/
private static LHS moveNegationsInRecurse(LHS lhs, boolean flip) {
//System.out.println("Info in Clausifier.moveNegationsInRecurse(): flip: " + flip + "\n" + lhs);
LHS newlhs = new LHS();
newlhs.clause = lhs.clause;
newlhs.lhs1 = lhs.lhs1;
newlhs.lhs2 = lhs.lhs2;
newlhs.operator = lhs.operator;
newlhs.method = lhs.method;
if (flip) {
switch (lhs.operator) {
case AND : newlhs.lhs1 = moveNegationsInRecurse(lhs.lhs1,true);
newlhs.lhs2 = moveNegationsInRecurse(lhs.lhs2,true);
newlhs.operator = LHS.LHSop.OR;
break;
case OR : newlhs.lhs1 = moveNegationsInRecurse(lhs.lhs1,true);
newlhs.lhs2 = moveNegationsInRecurse(lhs.lhs2,true);
newlhs.operator = LHS.LHSop.AND;
break;
case DELETE : newlhs.clause.negated = !newlhs.clause.negated;
break;
case PRESERVE : newlhs.clause.negated = !newlhs.clause.negated;
break;
case NOT : newlhs = moveNegationsInRecurse(lhs.lhs1,false);
break;
case PROC : break;
}
}
else {
switch(lhs.operator) {
case AND : newlhs.lhs1 = moveNegationsInRecurse(lhs.lhs1,false);
newlhs.lhs2 = moveNegationsInRecurse(lhs.lhs2,false);
break;
case OR : newlhs.lhs1 = moveNegationsInRecurse(lhs.lhs1,false);
newlhs.lhs2 = moveNegationsInRecurse(lhs.lhs2,false);
break;
case DELETE : break;
case PRESERVE : break;
case NOT : newlhs = moveNegationsInRecurse(lhs.lhs1,true);
break;
case PROC : break;
}
}
//System.out.println("Info in Clausifier.moveNegationsInRecurse(): returning: " + newlhs);
return newlhs;
}
/** ***************************************************************
* -(p | q) becomes -p , -q
* -(p , q) becomes -p | -q
*/
private static LHS moveNegationsIn(LHS lhs) {
return moveNegationsInRecurse(lhs,false);
}
/** ***************************************************************
* (a & b) | c becomes (a | c) & (b | c)
*/
private static LHS distributeAndOverOrRecurse(LHS form) {
//System.out.println("INFO in Clausifier.distributeAndOverOrRecurse(): " + form);
LHS result = form.deepCopy();
if (form.lhs1 != null)
result.lhs1 = distributeAndOverOr(form.lhs1);
if (form.lhs2 != null)
result.lhs2 = distributeAndOverOr(form.lhs2);
//System.out.println("INFO in Clausifier.distributeAndOverOrRecurse(): (2): " + KIF.format(form.toKIFString()));
if (form.operator.equals(LHS.LHSop.OR)) {
//System.out.println("INFO in Clausifier.distributeAndOverOrRecurse(): top level or: " + form);
if (result.lhs1 != null && result.lhs1.operator.equals(LHS.LHSop.AND)) {
//System.out.println("INFO in Clausifier.distributeAndOverOrRecurse(): lhs1 and: " + form);
LHS newParent = new LHS();
newParent.operator = LHS.LHSop.AND;
LHS newChild1 = new LHS();
newChild1.operator = LHS.LHSop.OR;
if (result.lhs1.lhs1 != null)
newChild1.lhs1 = result.lhs1.lhs1;
if (result.lhs1.clause != null)
newChild1.clause = result.lhs1.clause;
if (result.lhs2 != null)
newChild1.lhs2 = result.lhs2;
LHS newChild2 = new LHS();
newChild2.operator = LHS.LHSop.OR;
if (result.lhs1.lhs2 != null)
newChild2.lhs1 = result.lhs1.lhs2;
if (result.lhs1.clause != null)
newChild2.clause = result.lhs1.clause;
if (result.lhs2 != null)
newChild2.lhs2 = result.lhs2;
if (result.clause != null)
newChild2.clause = result.clause;
newParent.lhs1 = newChild1;
newParent.lhs2 = newChild2;
changed = true;
//System.out.println("INFO in Clausifier.distributeAndOverOrRecurse(): result: " + form);
return newParent;
}
else if (result.lhs2 != null && result.lhs2.operator.equals(LHS.LHSop.AND)) {
//System.out.println("INFO in Clausifier.distributeAndOverOrRecurse(): lhs2 and: " + form);
LHS newParent = new LHS();
newParent.operator = LHS.LHSop.AND;
LHS newChild1 = new LHS();
newChild1.operator = LHS.LHSop.OR;
if (result.lhs2.lhs1 != null)
newChild1.lhs1 = result.lhs2.lhs1;
if (result.lhs2.clause != null)
newChild1.clause = result.lhs2.clause;
if (result.lhs1 != null)
newChild1.lhs2 = result.lhs1;
if (result.clause != null)
newChild1.clause = result.clause;
LHS newChild2 = new LHS();
newChild2.operator = LHS.LHSop.OR;
if (result.lhs2.lhs2 != null)
newChild2.lhs1 = result.lhs2.lhs2;
if (result.lhs2.clause != null)
newChild2.clause = result.lhs2.clause;
if (result.lhs1 != null)
newChild2.lhs2 = result.lhs1;
if (result.clause != null)
newChild2.clause = result.clause;
newParent.lhs1 = newChild1;
newParent.lhs2 = newChild2;
changed = true;
//System.out.println("INFO in Clausifier.distributeAndOverOrRecurse(): result: " + form);
return newParent;
}
}
return result;
}
/** ***************************************************************
* (a , b) | c becomes (a | c) , (b | c)
*/
private static LHS distributeAndOverOr(LHS form) {
LHS result = form.deepCopy();
changed = true;
while (changed) {
changed = false;
result = distributeAndOverOrRecurse(result);
}
return result;
}
/** ***************************************************************
* @return the CNF of a an LHS. This turns a nested set of
* conjunctions into a flat list of conjunctions.
*/
private static CNF separateConjunctions(LHS lhs) {
CNF cnf = new CNF();
if (lhs.operator.equals(LHS.LHSop.AND)) {
if (lhs.lhs1.clause != null) {
Clause d = new Clause();
d.disjuncts.add(lhs.lhs1.clause);
cnf.clauses.add(d);
}
else
cnf.clauses.addAll(separateConjunctions(lhs.lhs1).clauses);
if (lhs.lhs2.clause != null){
Clause d = new Clause();
d.disjuncts.add(lhs.lhs2.clause);
cnf.clauses.add(d);
}
else
cnf.clauses.addAll(separateConjunctions(lhs.lhs2).clauses);
}
else if (lhs.operator.equals(LHS.LHSop.OR)) {
Clause d = new Clause();
d.disjuncts.add(lhs.lhs1.clause);
d.disjuncts.add(lhs.lhs2.clause);
cnf.clauses.add(d);
}
else if (lhs.clause != null) {
Clause d = new Clause();
d.disjuncts.add(lhs.clause);
cnf.clauses.add(d);
}
else {
System.out.println("Error in Clausifier.separateConjunctions(): bad operator: " + lhs.operator);
}
return cnf;
}
/** ***************************************************************
* @return the CNF equivalent for the given LHS of a rule. This is
* a very limited case of clausification since we have no quantification.
* and no implication or equivalence to worry about.
*/
public static CNF clausify(LHS lhs) {
//System.out.println("INFO in Clausifier.clausify(): (lhs) " + lhs);
LHS result = moveNegationsIn(lhs);
result = distributeAndOverOr(result);
return separateConjunctions(result);
}
/** ***************************************************************
* @return a RuleSet that is the result of clausifying the LHS of
* each rule in the input RuleSet
*/
public static RuleSet clausify(RuleSet rs) {
RuleSet newrs = new RuleSet();
for (int i = 0; i < rs.rules.size(); i++) {
Rule r = rs.rules.get(i);
//System.out.println("INFO in Clausifier.clausify(): " + r.lhs);
LHS result = moveNegationsIn(r.lhs);
result = distributeAndOverOr(result);
r.cnf = separateConjunctions(result);
newrs.rules.add(r);
}
return newrs;
}
/** ***************************************************************
*/
public static void main(String[] args) {
String rule = "(sense(212345678,?E) , nsubj(?E,?X) | dobj(?E,?Y) , a(?E,?Y)) ==> " +
"{(exists (?X ?E ?Y) " +
"(and " +
"(instance ?X Organization) " +
"(instance ?Y Human)" +
"(instance ?E Hiring)" +
"(agent ?E ?X) " +
"(patient ?E ?Y)))}.";
Rule r = new Rule();
r = Rule.parseString(rule);
System.out.println(r.toString());
r.lhs = Clausifier.moveNegationsIn(r.lhs);
System.out.println("moved negations in: \n" + r.lhs);
LHS lhs = Clausifier.distributeAndOverOr(r.lhs);
System.out.println("Distributed OR: \n" + lhs);
CNF cnf = separateConjunctions(lhs);
System.out.println("Flattened: \n" + cnf);
}
}