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Second-order quantifier elimination in higher-order contexts with applications to the semantical analysis of conditionals
2007 (English)In: Studia Logica: An International Journal for Symbolic Logic, ISSN 0039-3215, E-ISSN 1572-8730, Vol. 87, no 1, 37-50Article in journal (Refereed) Published
Abstract [en]

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 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. © 2007 Springer Science+Business Media B.V.

Keyword [en]
Conditionals, Higher-order relations, Second-order quantifier elimination
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-48366 (URN)10.1007/s11225-007-9075-4 (DOI)oai:DiVA.org:liu-48366 (OAI)diva2:269262 (DiVA)
Available from2009-10-11 Created:2009-10-11 Last updated:2011-02-26

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Gabbay, D.M.Szalas, Andrzej
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The Institute of TechnologyKPLAB - Knowledge Processing Lab
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Studia Logica: An International Journal for Symbolic Logic
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