Second-order quantifier elimination in higher-order contexts with applications to the semantical analysis of conditionals
Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab
Linköping University, The Institute of Technology
Article in journal (Refereed)
Studia Logica: An International Journal for Symbolic Logic(ISSN 0039-3215)(EISSN 1572-8730)
Engineering and Technology
Conditionals, Higher-order relations, Second-order quantifier elimination
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.