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Towards a First Order Equilibrium Logic for Nonmonotonic Reasoning

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Logics in Artificial Intelligence (JELIA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3229))

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Abstract

Equilibrium logic, introduced in [20], is a conservative extension of answer set semantics for logic programs to the full language of propositional logic. In this paper we initiate the study of first-order variants of equilibrium logic. In particular, we focus on a quantified version QN 5 of the propositional many-valued logic N 5 of here-and-there with strong negation, and define the condition of equilibrium via a minimal model construction. We verify Skolem forms and Herbrand theorems for QN 5 and show that, like its propositional counterpart, the quantified version of equilibrium logic also conservatively extends answer set semantics.

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Author information

Authors and Affiliations

  1. Universidad Rey Juan Carlos, Madrid, Spain

    David Pearce

  2. Universidad de Málaga, Málaga, Spain

    Agustín Valverde

Authors
  1. David Pearce
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  2. Agustín Valverde
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Editors and Affiliations

  1. CENTRIA, Universidade Nova de Lisboa, Portugal

    Jóse Júlio Alferes

  2. Departamento de Informática, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal

    João Leite

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Pearce, D., Valverde, A. (2004). Towards a First Order Equilibrium Logic for Nonmonotonic Reasoning. In: Alferes, J.J., Leite, J. (eds) Logics in Artificial Intelligence. JELIA 2004. Lecture Notes in Computer Science(), vol 3229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30227-8_15

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  • DOI: https://doi.org/10.1007/978-3-540-30227-8_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23242-1

  • Online ISBN: 978-3-540-30227-8

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