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International Conference on Logic for Programming Artificial Intelligence and Reasoning

LPAR 2010: Logic for Programming, Artificial Intelligence, and Reasoning pp 30–51Cite as

Gödel Logics – A Survey

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6397))

Abstract

The logics we present in this tutorial, Gödel logics, can be characterized in a rough-and-ready way as follows: The language is standard, defined at different levels: propositional, quantified-propositional, first-order. The logics are many-valued, and the sets of truth values considered are (closed) subsets of [0, 1] which contain both 0 and 1. 1 is the ‘designated value,’ i.e., a formula is valid if it receives the value 1 in every interpretation. The truth functions of conjunction and disjunction are minimum and maximum, respectively, and in the first-order case quantifiers are defined by infimum and supremum over subsets of the set of truth values.

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Author information

Authors and Affiliations

  1. Research Center of Integrated Science, Japan Advanced Institute of Science and Technology, Nomi-shi, Japan

    Norbert Preining

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  1. Norbert Preining
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Editors and Affiliations

  1. Institut für Computersprachen 185.2, Theory and Logic Group, TU Wien, Favoritenstraße 9-11, A-1040, Vienna, Austria

    Christian G. Fermüller

  2. School of Computer Science, University of Manchester, Oxford Road, Kilburn Building, M13 9PL, Manchester, United Kingdom

    Andrei Voronkov

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Preining, N. (2010). Gödel Logics – A Survey. In: Fermüller, C.G., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2010. Lecture Notes in Computer Science, vol 6397. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16242-8_4

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  • DOI: https://doi.org/10.1007/978-3-642-16242-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16241-1

  • Online ISBN: 978-3-642-16242-8

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