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A Logical Characterization of the Preferred Models of Logic Programs with Ordered Disjunction

Published online by Cambridge University Press:  23 September 2021

ANGELOS CHARALAMBIDIS Open the ORCID record for ANGELOS CHARALAMBIDIS [Opens in a new window] ,
PANOS RONDOGIANNIS  and
ANTONIS TROUMPOUKIS
ANGELOS CHARALAMBIDIS
Affiliation:
Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece (e-mails: a.charalambidis@di.uoa.gr, prondo@di.uoa.gr, antru@di.uoa.gr)
PANOS RONDOGIANNIS
Affiliation:
Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece (e-mails: a.charalambidis@di.uoa.gr, prondo@di.uoa.gr, antru@di.uoa.gr)
ANTONIS TROUMPOUKIS
Affiliation:
Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece (e-mails: a.charalambidis@di.uoa.gr, prondo@di.uoa.gr, antru@di.uoa.gr)
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Abstract

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Logic programs with ordered disjunction (LPODs) extend classical logic programs with the capability of expressing alternatives with decreasing degrees of preference in the heads of program rules. Despite the fact that the operational meaning of ordered disjunction is clear, there exists an important open issue regarding its semantics. In particular, there does not exist a purely model-theoretic approach for determining the most preferred models of an LPOD. At present, the selection of the most preferred models is performed using a technique that is not based exclusively on the models of the program and in certain cases produces counterintuitive results. We provide a novel, model-theoretic semantics for LPODs, which uses an additional truth value in order to identify the most preferred models of a program. We demonstrate that the proposed approach overcomes the shortcomings of the traditional semantics of LPODs. Moreover, the new approach can be used to define the semantics of a natural class of logic programs that can have both ordered and classical disjunctions in the heads of clauses. This allows programs that can express not only strict levels of preferences but also alternatives that are equally preferred.

Keywords

ordered disjunctionanswer setslogic of here-and-therepreferences
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 21 , Issue 5: 37th International Conference on Logic Programming Special Issue I , September 2021 , pp. 629 - 645
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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