Ultraproducts and possible worlds semantics in institutions

Authors:
Rzvan Diaconescu;Petros Stefaneas
Affiliations:
Institute of Mathematics of the Romanian Academy, Bucharest, Romania;National Technical University, Athens, Greece
Venue:
Theoretical Computer Science
Year:
2007

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Abstract

We develop possible worlds (Kripke) semantics at the categorical abstract model theoretic level provided by the so-called 'institutions'. Our general abstract modal logic framework provides a method for systematic Kripke semantics extensions of logical systems from computing science and logic. We also extend the institution-independent method of ultraproducts of [R. Diaconescu, Institution-independent ultraproducts, Fundamenta Informaticae 55 (3-4) (2003) 321-348] to possible worlds semantics and prove a fundamental preservation result for abstract modal satisfaction. As a consequence we develop a generic compactness result for possible worlds semantics.