AGM-Style Belief Revision of Logic Programs under Answer Set Semantics

Delgrande, James P.; Peppas, Pavlos; Woltran, Stefan

doi:10.1007/978-3-642-40564-8_27

Cited by 32 publications

(67 citation statements)

References 24 publications

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“…A continuation of our method was recently taken up by Slota and Leite [2010], who, inspired by our preliminary work [Delgrande et al 2008;2009], discussed answer set program update based on SE models using modified adaptions of the update postulates by Katsuno and Mendelzon [1992]. They define a set-based update operator and show that it satisfies their modified update postulates.…”

Section: Discussionmentioning

confidence: 99%

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A Model-Theoretic Approach to Belief Change in Answer Set Programming

Delgrande

Schaub

Tompits

et al. 2013

ACM Trans. Comput. Logic

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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 relatively uninteresting. Expansion and revision are shown to satisfy a suite of interesting properties; in particular, our revision operators satisfy all or nearly all of the AGM postulates for revision.We next consider approaches for merging a set of logic programs, P 1 , . . . , Pn. Again, our formal techniques are based on notions of relative distance between the SE models of the logic programs. Two approaches are examined. The first informally selects for each program P i those models of P i that vary the least from models of the other programs. The second approach informally selects those models of a program P 0 that are closest to the models of programs P 1 , . . . , Pn. In this case, P 0 can be thought of as a set of database integrity constraints. We examine these operators with regards to how they satisfy relevant postulate sets.Last, we present encodings for computing the revision as well as the merging of logic programs within the same logic programming framework. This gives rise to a direct implementation of our approach in terms of off-the-shelf answer set solvers. These encodings also reflect the fact that our change operators do not increase the complexity of the base formalism.

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Section: Discussionmentioning

confidence: 99%

“…Proofs of results are contained in an appendix. Preliminary versions of the material in Sections 3 and 4 appeared in previous work [Delgrande et al 2008;2009].…”

Section: Introductionmentioning

confidence: 99%

A Model-Theoretic Approach to Belief Change in Answer Set Programming

Delgrande

Schaub

Tompits

et al. 2013

ACM Trans. Comput. Logic

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“…In Delgrande et al 2008;Delgrande 2010 belief revision has been reformulated to capture the change of (non monotonic) logic programs under answer set semantics. A logic program P (i.e.…”

Section: Related Workmentioning

confidence: 99%

AGM Contraction and Revision of Rules

Boella

Pigozzi

Torre

2016

J of Log Lang and Inf

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In this paper we study AGM contraction and revision of rules using input/output logical theories. We replace propositional formulas in the AGM framework of theory change by pairs of propositional formulas, representing the rule based character of theories, and we replace the classical consequence operator Cn by an input/output logic. The results in this paper suggest that, in general, results from belief base dynamics can be transferred to rule base dynamics, but that a similar transfer of AGM theory change to rule change is much more problematic. First, we generalise belief base contraction to rule base contraction, and show that two representation results of Hansson still hold for rule base contraction. Second, we show that the six socalled basic postulates of AGM contraction are consistent only for some input/output logics, but not for others. In particular, we show that the notorious recovery postulate can be satisfied only by basic output, but not by simple-minded output. Third, we show how AGM rule revision can be defined in terms of AGM rule contraction using the Levi identity. We highlight various topics for further research. B Gabriella Pigozzi

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“…We define the syntax and semantics of logic programs, borrowing some of the notation used in (Delgrande et al 2008). …”

Section: Logic Programmingmentioning

confidence: 99%

“…In this paper, we follow a similar path, but to tackle the problem of answer-set program updates, instead of revision as in (Delgrande et al 2008).…”

Section: Introductionmentioning

confidence: 99%

The rise and fall of semantic rule updates based on`SE`-models

Slota¹,

Leite

2013

Theory and Practice of Logic Programming

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Logic programs under the stable model semantics, or answer-set programs, provide an expressive rule-based knowledge representation framework, featuring a formal, declarative and well-understood semantics. However, handling the evolution of rule bases is still a largely open problem. The AGM framework for belief change was shown to give inappropriate results when directly applied to logic programs under a non-monotonic semantics such as the stable models. The approaches to address this issue, developed so far, proposed update semantics based on manipulating the syntactic structure of programs and rules.More recently, AGM revision has been successfully applied to a significantly more expressive semantic characterisation of logic programs based on SE-models. This is an important step, as it changes the focus from the evolution of a syntactic representation of a rule base to the evolution of its semantic content.In this paper, we borrow results from the area of belief update to tackle the problem of updating (instead of revising) answer-set programs. We prove a representation theorem which makes it possible to constructively define any operator satisfying a set of postulates derived from Katsuno and Mendelzon's postulates for belief update. We define a specific operator based on this theorem, examine its computational complexity and compare the behaviour of this operator with syntactic rule update semantics from the literature. Perhaps surprisingly, we uncover a serious drawback of all rule update operators based on Katsuno and Mendelzon's approach to update and on SE-models.

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AGM-Style Belief Revision of Logic Programs under Answer Set Semantics

Cited by 32 publications

References 24 publications

A Model-Theoretic Approach to Belief Change in Answer Set Programming

A Model-Theoretic Approach to Belief Change in Answer Set Programming

AGM Contraction and Revision of Rules

The rise and fall of semantic rule updates based on`SE`-models

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AGM-Style Belief Revision of Logic Programs under Answer Set Semantics

Cited by 32 publications

References 24 publications

A Model-Theoretic Approach to Belief Change in Answer Set Programming

A Model-Theoretic Approach to Belief Change in Answer Set Programming

AGM Contraction and Revision of Rules

The rise and fall of semantic rule updates based onSE-models

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The rise and fall of semantic rule updates based on`SE`-models