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A Free Logic for Stable Models with Partial Intensional Functions

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Logics in Artificial Intelligence (JELIA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8761))

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Abstract

In this paper we provide a new logical characterisation of stable models with partial functions that consists in a free-logic extension of Quantified Equilibrium Logic (QEL). In so-called “free” logics, terms may denote objects that are outside the domain of quantification, something that can be immediately used to capture partial functions. We show that this feature can be naturally accommodated in the monotonic basis of QEL (the logic of Quantified Here-and-There, QHT) by allowing variable quantification domains that depend on the world where the formula is being interpreted. The paper provides two main contributions: (i) a correspondence with Cabalar’s semantics for stable models with partial functions; and (ii) a Gentzen system for free QHT, the monotonic basis of free QEL.

This research was partially supported by: European French-Spanish Lab IREP; MEC project TIN2012-39353-C04; Junta de Andalucía project TIC115; Xunta de Galicia, Spain, grant GPC2013/070; and Universidad de Málaga, Campus de Excelencia Internacional Andalucía Tech.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Corunna, Spain

    Pedro Cabalar

  2. University of Toulouse IRIT, CNRS, France

    Luis Fariñas del Cerro

  3. Universidad Politécnica de Madrid, Spain

    David Pearce

  4. Universidad de Málaga, Spain

    Agustin Valverde

Authors
  1. Pedro Cabalar
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  2. Luis Fariñas del Cerro
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  3. David Pearce
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  4. Agustin Valverde
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Editor information

Editors and Affiliations

  1. University of Madeira, Funchal, Madeira, Portugal

    Eduardo Fermé

  2. CENTRIA, Universidade Nova de Lisboa, Caparica, Portugal

    João Leite

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© 2014 Springer International Publishing Switzerland

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Cabalar, P., del Cerro, L.F., Pearce, D., Valverde, A. (2014). A Free Logic for Stable Models with Partial Intensional Functions. In: Fermé, E., Leite, J. (eds) Logics in Artificial Intelligence. JELIA 2014. Lecture Notes in Computer Science(), vol 8761. Springer, Cham. https://doi.org/10.1007/978-3-319-11558-0_24

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  • DOI: https://doi.org/10.1007/978-3-319-11558-0_24

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11557-3

  • Online ISBN: 978-3-319-11558-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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