Second-order quantifier elimination in higher-order contexts with applications to the semantical analysis of conditionals
Gabbay, D.M. Szalas, Andrzej
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
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  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. © 2007 Springer Science+Business Media B.V.
Conditionals, Higher-order relations, Second-order quantifier elimination
National CategoryEngineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-48366DOI: 10.1007/s11225-007-9075-4OAI: oai:DiVA.org:liu-48366DiVA: diva2:269262