Tableau Calculi for Logic Programs under Answer Set Semantics

Gebser, Martin; Schaub, Torsten

doi:10.1145/2480759.2480767

Cited by 11 publications

(3 citation statements)

References 76 publications

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“…In particular, Niemelä [35] introduces a tableau calculus for inference under circumscription. Other tableau approaches, however, do not encode inference directly, rather they characterise models (resp., extensions) associated with a particular nonmonotonic reasoning formalism [1,37,12,19].…”

Section: Discussionmentioning

confidence: 99%

Sequent-Type Proof Systems for Three-Valued Default Logic

Pkhakadze¹

2019

Preprint

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Sequent-type proof systems constitute an important and widely-used class of calculi well-suited for analysing proof search. In my master's thesis, I introduce sequent-type calculi for a variant of default logic employing Łukasiewicz's three-valued logic as the underlying base logic. This version of default logic has been introduced by Radzikowska addressing some representational shortcomings of standard default logic. More specifically, the calculi discussed in my thesis axiomatise brave and skeptical reasoning for this version of default logic, respectively following the sequent method first introduced in the context of nonmonotonic reasoning by Bonatti and Olivetti, which employ a complementary calculus for axiomatising invalid formulas, taking care of expressing the consistency condition of defaults.

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Section: Discussionmentioning

confidence: 99%

Sequent-Type Proof Systems for Three-Valued Default Logic

Pkhakadze¹

2019

Preprint

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“…Other tableau approaches, however, do not encode inference directly, rather they characterise models (resp., extensions) associated with a particular nonmonotonic reasoning formalism [63][64][65][66].…”

Section: Adequacy Of the Calculusmentioning

confidence: 99%

Sequent-Type Calculi for Three-Valued and Disjunctive Default Logic

Pkhakadze

Tompits

2020

Axioms

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Default logic is one of the basic formalisms for nonmonotonic reasoning, a well-established area from logic-based artificial intelligence dealing with the representation of rational conclusions, which are characterised by the feature that the inference process may require to retract prior conclusions given additional premisses. This nonmonotonic aspect is in contrast to valid inference relations, which are monotonic. Although nonmonotonic reasoning has been extensively studied in the literature, only few works exist dealing with a proper proof theory for specific logics. In this paper, we introduce sequent-type calculi for two variants of default logic, viz., on the one hand, for three-valued default logic due to Radzikowska, and on the other hand, for disjunctive default logic, due to Gelfond, Lifschitz, Przymusinska, and Truszczyński. The first variant of default logic employs Łukasiewicz’s three-valued logic as the underlying base logic and the second variant generalises defaults by allowing a selection of consequents in defaults. Both versions have been introduced to address certain representational shortcomings of standard default logic. The calculi we introduce axiomatise brave reasoning for these versions of default logic, which is the task of determining whether a given formula is contained in some extension of a given default theory. Our approach follows the sequent method first introduced in the context of nonmonotonic reasoning by Bonatti, which employs a rejection calculus for axiomatising invalid formulas, taking care of expressing the consistency condition of defaults.

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“…The added structure was in the form of new intermediate atoms and rules used to explicitly express rule bodies. A formal proof system was provided by Gebser and Schaub (2013) and used to prove exponentially different best-case computation lengths between different ASP algorithms. The proof system was a form of tableaux calculi.…”

Section: Related Workmentioning

confidence: 99%

Boosting Answer Set Optimization with Weighted Comparator Networks

Bomanson¹,

Janhunen²

2020

Theory and Practice of Logic Programming

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AbstractAnswer set programming (ASP) is a paradigm for modeling knowledge-intensive domains and solving challenging reasoning problems. In ASP solving, a typical strategy is to preprocess problem instances by rewriting complex rules into simpler ones. Normalization is a rewriting process that removes extended rule types altogether in favor of normal rules. Recently, such techniques led to optimization rewriting in ASP, where the goal is to boost answer set optimization by refactoring the optimization criteria of interest. In this paper, we present a novel, general, and effective technique for optimization rewriting based on comparator networks which are specific kinds of circuits for reordering the elements of vectors. The idea is to connect an ASP encoding of a comparator network to the literals being optimized and to redistribute the weights of these literals over the structure of the network. The encoding captures information about the weight of an answer set in auxiliary atoms in a structured way that is proven to yield exponential improvements during branch-and-bound optimization on an infinite family of example programs. The used comparator network can be tuned freely, for example, to find the best size for a given benchmark class. Experiments show accelerated optimization performance on several benchmark problems.

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Tableau Calculi for Logic Programs under Answer Set Semantics

Cited by 11 publications

References 76 publications

Sequent-Type Proof Systems for Three-Valued Default Logic

Sequent-Type Proof Systems for Three-Valued Default Logic

Sequent-Type Calculi for Three-Valued and Disjunctive Default Logic

Boosting Answer Set Optimization with Weighted Comparator Networks

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