Dynamic Logic Programming: Various Semantics Are Equal on Acyclic Programs

Homola, Martin

doi:10.1007/11533092_5

Cited by 9 publications

(6 citation statements)

References 8 publications

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“…The sixth syntactic property stems from the fact that all rule update semantics based on causal rejection coincide on acyclic DLPs (Homola 2004;Alferes et al 2005). Thus, the behaviour of any rule update semantics on acyclic DLPs can be used as a way to compare it to all these semantics simultaneously.…”

Section: Example 44mentioning

confidence: 99%

A Brief History of Updates of Answer-Set Programs

Leite¹,

Slota²

2021

Preprint

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Over the last couple of decades there has been a considerable effort devoted to the problem of updating logic programs under the stable model semantics (a.k.a. answer-set programs) or, in other words, the problem of characterising the result of bringing up-to-date a logic program when the world it describes changes. Whereas the state-of-the-art approaches are guided by the same basic intuitions and aspirations as belief updates in the context of classical logic, they build upon fundamentally different principles and methods, which have prevented a unifying framework that could embrace both belief and rule updates. In this paper we will overview some of the main approaches and results related to answer-set programming updates, while pointing out some of the main challenges that research in this topic has faced.Under consideration in Theory and Practice of Logic Programming (TPLP)

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Section: Example 44mentioning

confidence: 99%

A Brief History of Updates of Answer-Set Programs

Leite¹,

Slota²

2021

Preprint

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“…The final syntactic property stems from the fact that all rule update semantics based on causal rejection coincide on acyclic DLPs [5,36]. Thus, the behaviour of any rule update semantics on acyclic DLPs can be used as a way to compare it to all these semantics simultaneously.…”

Section: Syntactic Property 3 (Causal Rejection)mentioning

confidence: 99%

Exception-Based Knowledge Updates

Slota,

Leite

2017

Preprint

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Existing methods for dealing with knowledge updates differ greatly depending on the underlying knowledge representation formalism. When Classical Logic is used, updates are typically performed by manipulating the knowledge base on the model-theoretic level. On the opposite side of the spectrum stand the semantics for updating Answer-Set Programs that need to rely on rule syntax. Yet, a unifying perspective that could embrace both these branches of research is of great importance as it enables a deeper understanding of all involved methods and principles and creates room for their cross-fertilisation, ripening and further development. Furthermore, from a more pragmatic viewpoint, such a unification is a necessary step in addressing updates of hybrid knowledge bases consisting of both a classical and a rule component.This paper bridges the seemingly irreconcilable approaches to updates. It introduces a novel monotonic characterisation of rules, dubbed RE-models, and shows it to be a more suitable semantic foundation for rule updates than SE-models. Then it proposes a generic scheme for specifying semantic rule update operators, based on the idea of viewing a program as the set of sets of RE-models of its rules; updates are performed by introducing additional interpretations -exceptions -to the sets of RE-models of rules in the original program. The introduced scheme is then used to define particular rule update operators that are closely related to both classical update principles and traditional approaches to rules updates, enjoying a range of plausible syntactic as well as semantic properties. In addition, these operators serve as a basis for a solution to the long-standing problem of state condensing for two of the foundational rule update semantics, showing how they can be equivalently defined as binary operators on some class of logic programs.Finally, the essence of these ideas is extracted to define an abstract framework for exception-based update operators, viewing a knowledge base as the set of sets of models of its elements. It is shown that the framework can capture a wide range of both model-and formula-based classical update operators, and thus serves as the first firm formal ground connecting classical and rule updates.

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“…The existence of such undesirable behaviors suggests the need of analyzing alternative semantics for logic program updates, considering for instance the semantics presented in (Banti et al 2005) and (Homola 2005). We consider this to be an interesting direction for future work.…”

Section: Examplementioning

confidence: 99%

Updates in answer set programming: An approach based on basic structural properties

Osorio

Cuevas

2007

Theory and Practice of Logic Programming

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We have studied the update operator ⊕1 defined for update sequences by Eiter et al. without tautologies and we have observed that it satisfies an interesting property 1 . This property, which we call Weak Independence of Syntax (WIS), is similar to one of the postulates proposed by Alchourrón, Gärdenfors, and Makinson (AGM); only that in this case it applies to nonmonotonic logic. In addition, we consider other five additional basic properties about update programs and we show that ⊕1 satisfies them. This work continues the analysis of the AGM postulates with respect to the ⊕1 operator under a refined view that considers N2 as a monotonic logic which allows us to expand our understanding of answer sets. Moreover, N2 helped us to derive an alternative definition of ⊕1 avoiding the use of unnecessary extra atoms.

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Dynamic Logic Programming: Various Semantics Are Equal on Acyclic Programs

Cited by 9 publications

References 8 publications

A Brief History of Updates of Answer-Set Programs

A Brief History of Updates of Answer-Set Programs

Exception-Based Knowledge Updates

Updates in answer set programming: An approach based on basic structural properties

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