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Chiaki Sakama, Katsumi Inoue (2005)
Combining Answer Sets of Nonmonotonic Logic Programs
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|= s R iff there exist
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U, Z), which is a contradiction to the assumption . Hence, x ∈ Z holds. If (ii) does not hold, we get x ∈ X U. Now
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We show that the following relations hold: (i) x ∈ Z; and (ii) x ∈ U iff x ∈ X. Towards a contradiction, first suppose x / ∈ Z. Then, we have x
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Thus, an algorithm to decide P * Q |= s R is as follows We guess interpretations
Hence, according to Definition 3
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Most of the parts follow immediately from the fact that
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If the answer is yes, we already have found an SE interpretation (X, Y) such that
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The proofs of these results proceed similarly to the one for Theorem 5
Thus, from Definition 3.3, we have that there is some
Before giving the proof, we first present a lemma that is key for postulates (RA5) and (RA6)
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But then x / ∈ Y (Z ∪ {x}) which yields Y (Z ∪ {x}) ⊂ Y Z, a contradiction to our assumption. Hence, we can suppose x ∈ Z. Now, since Y ∈ Mod(Q), obviously Y \ {x} ∈ Mod(Q) as well
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the left-hand side of the given equivalence, revision corresponds with expansion via (RA2), from which the result is immediate. For absorption, we have then from Theorem 3.2, Part 3, we have that
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Article 14, Publication date
Since we deal with a globally fixed language, we first need a few lemmata. LEMMA A.3. Let P, Q be programs, Y an interpretation, and x
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Let E 1 , E 2 , and E 3 be SE interpretations
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Received December ACM Transactions on Computational Logic
Q) are well-defined by virtue of P and Q being logic programs
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Fernando Zacaŕias, Mauricio Osorio, J. Guadarrama (2005)
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F. Buccafurri, G. Gottlob (2002)
Multiagent Compromises, Joint Fixpoints, and Stable Models
A Model-Theoretic Approach to Belief Change in Answer Set Programming JAMES DELGRANDE, Simon Fraser University ¨ TORSTEN SCHAUB, Universitat Potsdam ¨ HANS TOMPITS and STEFAN WOLTRAN, Technische Universitat Wien We address the problem of belief change in (nonmonotonic) logic programming under answer set semantics. Our formal techniques are analogous to those of distance-based belief revision in propositional logic. In particular, we build upon the model theory of logic programs furnished by SE interpretations, where an SE interpretation is a model of a logic program in the same way that a classical interpretation is a model of a propositional formula. Hence we extend techniques from the area of belief revision based on distance between models to belief change in logic programs. We first consider belief revision: for logic programs P and Q, the goal is to determine a program R that corresponds to the revision of P by Q, denoted P Q. We investigate several operators, including (logic program) expansion and two revision operators based on the distance between the SE models of logic programs. It proves to be the case that expansion is an interesting operator in its own right, unlike in classical belief revision where it is
ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery
Published: Jun 1, 2013
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