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Lower Bound Founded Logic of Here-and-There

Calabar, Pedro and Fandinno, Jorge and Schaub, Torsten and Schellhorn, Sebastian Lower Bound Founded Logic of Here-and-There. (2019) In: 16th European Conference on Logics in Artificial Intelligence (JELIA 2019), 7 May 2019 - 11 May 2019 (Rende, Italy).

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Official URL: https://doi.org/10.1007/978-3-030-19570-0_34

Abstract

A distinguishing feature of Answer Set Programming is that all atoms belonging to a stable model must be founded. That is, an atom must not only be true but provably true. This can be made precise by means of the constructive logic of Here-and-There, whose equilibrium models correspond to stable models. One way of looking at foundedness is to regard Boolean truth values as ordered by letting true be greater than false. Then, each Boolean variable takes the smallest truth value that can be proven for it. This idea was generalized by Aziz to ordered domains and applied to constraint satisfaction problems. As before, the idea is that a, say integer, variable gets only assigned to the smallest integer that can be justified. In this paper, we present a logical reconstruction of Aziz’ idea in the setting of the logic of Here-and-There. More precisely, we start by defining the logic of Here-and-There with lower bound founded variables along with its equilibrium models and elaborate upon its formal properties. Finally, we compare our approach with related ones and sketch future work.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to Springer editor. This papers appears in volume 11468 of Lecture Notes in Computer Science ISSN : 0302-9743 ISBN 978-3-030-19570-0 The original PDF is available at: https://link.springer.com/chapter/10.1007/978-3-030-19570-0_34
HAL Id:hal-02486108
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 > Universität Potsdam (GERMANY)
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Deposited On:06 Feb 2020 13:41

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