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Second-Order Quantifier Elimination in Higher-Order Contexts with Applications to the Semantical Analysis of Conditionals

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Abstract

Second-order quantifier elimination in the context of classical logic emerged as a powerful technique in many applications, including the correspondence theory, relational databases, deductive and knowledge databases, knowledge representation, commonsense reasoning and approximate reasoning. In the current paper we first generalize the result of Nonnengart and Szałas [17] by allowing second-order variables to appear within higher-order contexts. Then we focus on a semantical analysis of conditionals, using the introduced technique and Gabbay’s semantics provided in [10] and substantially using a third-order accessibility relation. The analysis is done via finding correspondences between axioms involving conditionals and properties of the underlying third-order relation.

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Authors and Affiliations

  1. Department of Computer Science, King’s College, London, UK

    Dov M. Gabbay

  2. Institute of Informatics, University of Warsaw, ul. Banacha 2, 02-097, Warsaw, Poland

    Andrzej Szałas

  3. Dept. of Comp. and Information Sci, University of Linköping, Linköping, Sweden

    Andrzej Szałas

Authors
  1. Dov M. Gabbay
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  2. Andrzej Szałas
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Correspondence to Dov M. Gabbay.

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Gabbay, D.M., Szałas, A. Second-Order Quantifier Elimination in Higher-Order Contexts with Applications to the Semantical Analysis of Conditionals. Stud Logica 87, 37–50 (2007). https://doi.org/10.1007/s11225-007-9075-4

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