cse@buffalo Inconsistency Tolerance in SNePS Stuart C. Shapiro Department of Computer Science and Engineering, and Center for Cognitive Science University at Buffalo, The State University of New York 201 Bell Hall, Buffalo, NY 14260-2000 [email protected]http://www. cse .buffalo. edu /~ shapiro /
Inconsistency Tolerance in SNePS. Stuart C. Shapiro Department of Computer Science and Engineering, and Center for Cognitive Science University at Buffalo, The State University of New York 201 Bell Hall, Buffalo, NY 14260-2000 [email protected] http://www.cse.buffalo.edu/~shapiro/. - PowerPoint PPT Presentation
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
cse@buff
alo
Inconsistency Tolerance in SNePS
Stuart C. Shapiro Department of Computer Science and Engineering,
and Center for Cognitive Science
University at Buffalo, The State University of New York
• NSF, Instituto Nacional de Investigação Cientifica, Rome Air Development Center, AFOSR, U.S. Army CECOM
June, 2003 S. C. Shapiro 3
cse@buff
alo
OutlineIntroductionSome Rules of Inference~I and Belief RevisionCredibility Ordering and Automatic BRReasoning in Different ContextsDefault Reasoning by Preferential OrderingSummary
OutlineIntroductionSome Rules of Inference~I and Belief RevisionCredibility Ordering and Automatic BRReasoning in Different ContextsDefault Reasoning by Preferential OrderingSummary
June, 2003 S. C. Shapiro 8
cse@buff
alo
Rules of Inference:Hypothesis
Hyp: P {<hyp,{P}>}
: whale(Willy) and free(Willy). wff3: free(Willy) and whale(Willy) {<hyp,{wff3}>}
OutlineIntroductionSome Rules of Inference~I and Belief RevisionCredibility Ordering and Automatic BRReasoning in Different ContextsDefault Reasoning by Preferential OrderingSummary
June, 2003 S. C. Shapiro 15
cse@buff
alo
~I and Belief Revision
• ~I triggered when a contradiction is derived.
• Proposition to be negated must be one of the hypotheses underlying the contradiction.
• Origin set is the rest of the hypotheses.
• SNeBR [Martins & Shapiro ’88] involved in choosing the culprit.
Since wff21: all(x)(fish(x) <=> has(x,scales)) {<hyp,{wff21}>}and wff23: fish(Willy) {<der,{wff3,wff19}>}
I infer has(Willy,scales) {<der,{wff3,wff19,wff21}>}
Since wff20: all(x)(andor(0,1){mammal(x), fish(x)}) {<hyp,{wff20}>}and wff11: mammal(Willy) {<der,{wff3,wff10}>}
I infer it is not the case that wff23: fish(Willy)
June, 2003 S. C. Shapiro 18
cse@buff
alo
Manual Belief RevisionA contradiction was detected within context default-defaultct.
The contradiction involves the newly derived proposition: wff24: ~fish(Willy) {<der,{wff3,wff10,wff20}>} and the previously existing proposition: wff23: fish(Willy) {<der,{wff3,wff19}>}
You have the following options: 1. [c]ontinue anyway, knowing that a contradiction is derivable; 2. [r]e-start the exact same run in a different context which is not inconsistent; 3. [d]rop the run altogether.
(please type c, r or d)=><= r
June, 2003 S. C. Shapiro 19
cse@buff
alo
BR AdviceIn order to make the context consistent you must delete
at least one hypothesis from the set listed below.This set of hypotheses is known to be inconsistent: 1 : wff20: all(x)(andor(0,1){mammal(x),fish(x)}) {<hyp,{wff20}>}
• When a contradiction is explicitly found, the user is engaged in its resolution.
June, 2003 S. C. Shapiro 24
cse@buff
alo
OutlineIntroductionSome Rules of Inference~I and Belief RevisionCredibility Ordering and Automatic BRReasoning in Different ContextsDefault Reasoning by Preferential OrderingSummary
June, 2003 S. C. Shapiro 25
cse@buff
alo
Credibility Ordering and Automatic Belief Revision*
• Hypotheses may be given sources.• Sources may be given relative credibility.• Hypotheses inherit relative credibility from
sources.• Hypotheses may be given relative
credibility directly. (Not shown.)• SNeBR may use relative credibility to
choose a culprit by itself. [Shapiro & Johnson ’00]
OutlineIntroductionSome Rules of Inference~I and Belief RevisionCredibility Ordering and Automatic BRReasoning in Different ContextsDefault Reasoning by Preferential OrderingSummary
June, 2003 S. C. Shapiro 31
cse@buff
alo
Reasoning in Different Contexts
• A context is a set of hypotheses and all propositions derived from them.
• Reasoning is performed within a context.• A conclusion is available in every context that
is a superset of its origin set. [Martins & Shapiro ’83]
• Contradictory information may be isolated in different contexts.
• Reasoning is performed in a single context.
• Results are available in other contexts.
June, 2003 S. C. Shapiro 37
cse@buff
alo
OutlineIntroductionSome Rules of Inference~I and Belief RevisionCredibility Ordering and Automatic BRReasoning in Different ContextsDefault Reasoning by Preferential OrderingSummary
June, 2003 S. C. Shapiro 38
cse@buff
alo
Default Reasoning by Preferential Ordering
• No special syntax for default rules.
• If P and ~P are derived– but argument for one is undercut by an
argument for the other– don’t believe the undercut conclusion.
• Unlike BR, believe the hypotheses, but not a conclusion.
[Grosof ’97, Bhushan ’03]
June, 2003 S. C. Shapiro 39
cse@buff
alo
Preclusion Rules in SNePS*
• P undercuts ~P if– Precludes(P, ~P) or
– Every origin set of ~P has some hyp h such that there is some hyp q in an origin set of P such that Precludes(q, h).
• Precludes(P, Q) is a proposition like any other.
• DR uses preferential ordering among contradictory conclusions or among supporting hypotheses.
• Precludes forms object-language proposition that may be reasoned with or reasoned about.
June, 2003 S. C. Shapiro 52
cse@buff
alo
OutlineIntroductionSome Rules of Inference~I and Belief RevisionCredibility Ordering and Automatic BRReasoning in Different ContextsDefault Reasoning by Preferential OrderingSummary
June, 2003 S. C. Shapiro 53
cse@buff
alo
SummaryInconsistency Tolerance in SNePS
• Inconsistency across contexts is harmless.• Inconsistency about unrelated topic is harmless.• Explicit contradiction may be resolved by user.• Explicit contradiction may be resolved by
system using relative credibility of propositions or sources.
• Explicit contradiction may be resolved by system using preferential ordering of conclusions or hypotheses.
June, 2003 S. C. Shapiro 54
cse@buff
alo
For more information
http://www.cse.buffalo.edu/sneps/
June, 2003 S. C. Shapiro 55
cse@buff
alo
References IA. R. Anderson, A. R. and N. D. Belnap, Jr. (1975) Entailment Volume I
(Princeton: Princeton University Press).
B. Bhushan (2003) Preferential Ordering of Beliefs for Default Reasoning, M.S. Thesis, Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY.
J. P. Delgrande and T. Schaub (2000) The role of default logic in knowledge representation. In J. Minker, ed. Logic-Based Artificial Intelligence (Boston: Kluwer Academic Publishers) 107-126.
B. N. Grosof (1997) Courteous Logic Programs: Prioritized Conflict Handling for Rules, IBM Research Report RC 20836, revised.
June, 2003 S. C. Shapiro 56
cse@buff
alo
References IIJ. P. Martins and S. C. Shapiro (1983) Reasoning in multiple belief spaces,
Proc. Eighth IJCAI (Los Altos, CA: Morgan Kaufmann) 370-373. J. P. Martins and S. C. Shapiro (1988) A model for belief revision, Artificial
Intelligence 35, 25-79.
S. C. Shapiro (1992) Relevance logic in computer science. In A. R. Anderson, N. D. Belnap, Jr., M. Dunn, et al. Entailment Volume II (Princeton: Princeton University Press) 553-563.
S. C. Shapiro and The SNePS Implementation Group (2002)
SNePS 2.6 User's Manual, Department of Computer Science and Engineering, University at Buffalo, The State University of New York, Buffalo, NY.
S. C. Shapiro and F. L. Johnson (2000) Automatic belief revision in SNePS. In C.
Baral & M. Truszczyński, eds., Proc. 8th International Workshop on Non-Monotonic Reasoning.