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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
You can always find the topics here!Topics: Quantifier elimination, Logic, Reasoning, Semantics, Correspondence theory, Accessibility relation, Logical theorems, Databases, Mathematical relations, Computer science
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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  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  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.
Studia Logica: An International Journal for Symbolic Logic © 2007 Springer