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On the Properties of Atom Definability and Well-Supportedness in Logic Programming

Cabalar, Pedro and Fandinno, Jorge and Fariñas del Cerro, Luis and Pearce, David and Valverde, Agustin On the Properties of Atom Definability and Well-Supportedness in Logic Programming. (2017) In: 18th Portuguese Conference on Artificial Intelligence (EPIA 2017), 5 September 2017 - 8 September 2017 (Porto, Portugal).

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Official URL: https://doi.org/10.1007/978-3-319-65340-2_51

Abstract

We analyse alternative extensions of stable models for non-disjunctive logic programs with arbitrary Boolean formulas in the body, and examine two semantic properties. The first property, we call atom definability, allows one to replace any expression in rule bodies by an auxiliary atom defined by a single rule. The second property, well-supportedness, was introduced by Fages and dictates that it must be possible to establish a derivation ordering for all true atoms in a stable model so that self-supportedness is not allowed. We start from a generic fixpoint definition for well-supportedness that deals with: (1) a monotonic basis, for which we consider the whole range of intermediate logics; and (2), an assumption function, that determines which type of negated formulas can be added as defaults. Assuming that we take the strongest underlying logic in such a case, we show that only Equilibrium Logic satisfies both atom definability and strict well-suportedness.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to Springer editor. This papers appears in volume 10423 of Lecture Notes in Computer Science ISSN : 0302-9743 ISBN: 978-3-319-65339-6 The original PDF is available at: https://link.springer.com/chapter/10.1007/978-3-319-65340-2_51
HAL Id:hal-02604102
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Universidad Politécnica de Madrid (SPAIN)
Other partners > Universidade da Coruña - UDC (SPAIN)
Laboratory name:
Funders:
Xunta de Galicia : Comunidade Autónoma de Galicia (Espagne) - ERDF : Electricité Réseau Distribution France (France) - CIMI : Centre International de Mathématiques et d’Informatique de Toulouse (France) - ANR : Agence Nationale de la Recherche (France) - UPM : Universidad Politécnica de Madrid (Espagne) - MINECO : Ministerio de Economía y Competitividad (Espagne)
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Deposited On:28 Apr 2020 13:11

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