Algebraization of hybrid logic with binders

Authors:
Tadeusz Litak
Affiliations:
School of Information Science, JAIST, Ishikawa-ken, Japan
Venue:
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
Year:
2006

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Abstract

This paper introduces an algebraic semantics for hybrid logic with binders ${\mathcal{H}(\downarrow,@)}$. It is known that this formalism is a modal counterpart of the bounded fragment of the first-order logic, studied by Feferman in the 1960's. The algebraization process leads to an interesting class of boolean algebras with operators, called substitution-satisfaction algebras. We provide a representation theorem for these algebras and thus provide an algebraic proof of completeness of hybrid logic.