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

Dov M. Gabbay and Andrzej Szałas
Studia Logica: An International Journal for Symbolic Logic
Vol. 87, No. 1 (Oct., 2007), pp. 37-50
Published by: Springer
Stable URL: http://www.jstor.org/stable/40210797
Page Count: 14
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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 powerfui 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 Szalas [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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