/
FOLFCAsk.java
225 lines (197 loc) · 6.6 KB
/
FOLFCAsk.java
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
package aima.core.logic.fol.inference;
import java.util.ArrayList;
import java.util.List;
import java.util.Map;
import java.util.Set;
import aima.core.logic.fol.inference.proof.Proof;
import aima.core.logic.fol.inference.proof.ProofFinal;
import aima.core.logic.fol.inference.proof.ProofStep;
import aima.core.logic.fol.inference.proof.ProofStepFoChAlreadyAFact;
import aima.core.logic.fol.inference.proof.ProofStepFoChAssertFact;
import aima.core.logic.fol.kb.FOLKnowledgeBase;
import aima.core.logic.fol.kb.data.Clause;
import aima.core.logic.fol.kb.data.Literal;
import aima.core.logic.fol.parsing.ast.AtomicSentence;
import aima.core.logic.fol.parsing.ast.NotSentence;
import aima.core.logic.fol.parsing.ast.Sentence;
import aima.core.logic.fol.parsing.ast.Term;
import aima.core.logic.fol.parsing.ast.Variable;
/**
* Artificial Intelligence A Modern Approach (3rd Edition): Figure 9.3, page
* 332.<br>
* <br>
*
* <pre>
* function FOL-FC-ASK(KB, alpha) returns a substitution or false
* inputs: KB, the knowledge base, a set of first order definite clauses
* alpha, the query, an atomic sentence
* local variables: new, the new sentences inferred on each iteration
*
* repeat until new is empty
* new <- {}
* for each rule in KB do
* (p1 ˆ ... ˆ pn => q) <- STANDARDIZE-VARAIBLES(rule)
* for each theta such that SUBST(theta, p1 ˆ ... ˆ pn) = SUBST(theta, p'1 ˆ ... ˆ p'n)
* for some p'1,...,p'n in KB
* q' <- SUBST(theta, q)
* if q' does not unify with some sentence already in KB or new then
* add q' to new
* theta <- UNIFY(q', alpha)
* if theta is not fail then return theta
* add new to KB
* return false
* </pre>
*
* Figure 9.3 A conceptually straightforward, but very inefficient
* forward-chaining algo- rithm. On each iteration, it adds to KB all the atomic
* sentences that can be inferred in one step from the implication sentences and
* the atomic sentences already in KB. The function STANDARDIZE-VARIABLES
* replaces all variables in its arguments with new ones that have not been used
* before.
*
* @author Ciaran O'Reilly
*
*/
public class FOLFCAsk implements InferenceProcedure {
public FOLFCAsk() {
}
//
// START-InferenceProcedure
/**
* FOL-FC-ASK returns a substitution or false.
*
* @param KB
* the knowledge base, a set of first order definite clauses
* @param query
* the query, an atomic sentence
*
* @return a substitution or false
*/
public InferenceResult ask(FOLKnowledgeBase KB, Sentence query) {
// Assertions on the type of queries this Inference procedure
// supports
if (!(query instanceof AtomicSentence)) {
throw new IllegalArgumentException(
"Only Atomic Queries are supported.");
}
FCAskAnswerHandler ansHandler = new FCAskAnswerHandler();
Literal alpha = new Literal((AtomicSentence) query);
// local variables: new, the new sentences inferred on each iteration
List<Literal> newSentences = new ArrayList<>();
// Ensure query is not already a know fact before
// attempting forward chaining.
Set<Map<Variable, Term>> answers = KB.fetch(alpha);
if (answers.size() > 0) {
ansHandler.addProofStep(new ProofStepFoChAlreadyAFact(alpha));
ansHandler.setAnswers(answers);
return ansHandler;
}
// repeat until new is empty
do {
// new <- {}
newSentences.clear();
// for each rule in KB do
// (p1 ^ ... ^ pn => q) <-STANDARDIZE-VARIABLES(rule)
for (Clause impl : KB.getAllDefiniteClauseImplications()) {
impl = KB.standardizeApart(impl);
// for each theta such that SUBST(theta, p1 ^ ... ^ pn) =
// SUBST(theta, p'1 ^ ... ^ p'n)
// --- for some p'1,...,p'n in KB
for (Map<Variable, Term> theta : KB.fetch(invert(impl
.getNegativeLiterals()))) {
// q' <- SUBST(theta, q)
Literal qDelta = KB.subst(theta, impl.getPositiveLiterals()
.get(0));
// if q' does not unify with some sentence already in KB or
// new then do
if (!KB.isRenaming(qDelta)
&& !KB.isRenaming(qDelta, newSentences)) {
// add q' to new
newSentences.add(qDelta);
ansHandler.addProofStep(impl, qDelta, theta);
// theta <- UNIFY(q', alpha)
theta = KB.unify(qDelta.getAtomicSentence(),
alpha.getAtomicSentence());
// if theta is not fail then return theta
if (null != theta) {
for (Literal l : newSentences) {
Sentence s = null;
if (l.isPositiveLiteral()) {
s = l.getAtomicSentence();
} else {
s = new NotSentence(l.getAtomicSentence());
}
KB.tell(s);
}
ansHandler.setAnswers(KB.fetch(alpha));
return ansHandler;
}
}
}
}
// add new to KB
for (Literal l : newSentences) {
Sentence s = null;
if (l.isPositiveLiteral()) {
s = l.getAtomicSentence();
} else {
s = new NotSentence(l.getAtomicSentence());
}
KB.tell(s);
}
} while (newSentences.size() > 0);
// return false
return ansHandler;
}
// END-InferenceProcedure
//
//
// PRIVATE METHODS
//
private List<Literal> invert(List<Literal> lits) {
List<Literal> invLits = new ArrayList<Literal>();
for (Literal l : lits) {
invLits.add(new Literal(l.getAtomicSentence(), (l
.isPositiveLiteral() ? true : false)));
}
return invLits;
}
class FCAskAnswerHandler implements InferenceResult {
private ProofStep stepFinal = null;
private List<Proof> proofs = new ArrayList<Proof>();
public FCAskAnswerHandler() {
}
//
// START-InferenceResult
public boolean isPossiblyFalse() {
return proofs.size() == 0;
}
public boolean isTrue() {
return proofs.size() > 0;
}
public boolean isUnknownDueToTimeout() {
return false;
}
public boolean isPartialResultDueToTimeout() {
return false;
}
public List<Proof> getProofs() {
return proofs;
}
// END-InferenceResult
//
public void addProofStep(Clause implication, Literal fact,
Map<Variable, Term> bindings) {
stepFinal = new ProofStepFoChAssertFact(implication, fact,
bindings, stepFinal);
}
public void addProofStep(ProofStep step) {
stepFinal = step;
}
public void setAnswers(Set<Map<Variable, Term>> answers) {
for (Map<Variable, Term> ans : answers) {
proofs.add(new ProofFinal(stepFinal, ans));
}
}
}
}