Ultraproducts and possible worlds semantics in institutions
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 Informatiae55 (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. (c) 2007 Elsevier B.V. All rights reserved.
ultraproducts possible worlds institutions modal logic kripke models