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Representing Paraconsistent Reasoning via Quantified Propositional Logic

  • Chapter
Inconsistency Tolerance

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3300))

Abstract

Quantified propositional logic is an extension of classical propositional logic where quantifications over atomic formulas are permitted. As such, quantified propositional logic is a fragment of second-order logic, and its sentences are usually referred to as quantified Boolean formulas (QBFs). The motivation to study quantified propositional logic for paraconsistent reasoning is based on two fundamental observations. Firstly, in recent years, practicably efficient solvers for quantified propositional logic have been presented. Secondly, complexity results imply that there is a wide range of paraconsistent reasoning problems which can be efficiently represented in terms of QBFs. Hence, solvers for QBFs can be used as a core engine in systems prototypically implementing several of such reasoning tasks, most of them lacking concrete realisations. To this end, we show how certain paraconsistent reasoning principles can be naturally formulated or reformulated by means of quantified Boolean formulas. More precisely, we describe polynomial-time constructible encodings providing axiomatisations of the given reasoning tasks. In this way, a whole variety of a priori distinct approaches to paraconsistent reasoning become comparable in a uniform setting.

The third and fourth author were partially supported by the Austrian Science Foundation (FWF) under grant P15068, as well as by the European Commission under project IST-2001-33570 INFOMIX and the IST-2001-33123 CologNeT Network of Excellence.

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Authors and Affiliations

  1. IRIT-CNRS, 118, route de Narbonne, F–31062 Cedex, Toulouse, France

    Philippe Besnard

  2. Institut für Informatik, Universität Potsdam, Postfach 90 03 27, D–14439, Potsdam, Germany

    Torsten Schaub

  3. Institut für Informationssysteme 184/3, Technische Universität Wien, Favoritenstraße 9–11, A–1040, Vienna, Austria

    Hans Tompits & Stefan Woltran

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  1. Philippe Besnard
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  2. Torsten Schaub
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  3. Hans Tompits
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  4. Stefan Woltran
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Editors and Affiliations

  1. School of Computer Science, Carleton University, Ottawa, Canada

    Leopoldo Bertossi

  2. Department of Computer Science, University College London, Gower Street, WC1E 6BT, London, UK

    Anthony Hunter

  3. Institut für Informatik, Universität Potsdam, August-Bebel-Str. 89, D-14482, Potsdam, Germany

    Torsten Schaub

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Besnard, P., Schaub, T., Tompits, H., Woltran, S. (2005). Representing Paraconsistent Reasoning via Quantified Propositional Logic. In: Bertossi, L., Hunter, A., Schaub, T. (eds) Inconsistency Tolerance. Lecture Notes in Computer Science, vol 3300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30597-2_4

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