Studia Logica

, Volume 87, Issue 1, pp 37–50 | Cite as

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

  • Dov M. GabbayEmail author
  • Andrzej Szałas


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.


conditionals second-order quantifier elimination higher-order relations 


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© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Computer ScienceKing’s CollegeLondonUK
  2. 2.Institute of InformaticsUniversity of WarsawWarsawPoland
  3. 3.Dept. of Comp. and Information SciUniversity of LinköpingLinköpingSweden

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