We present Kripke modal transition systems (Kripke MTSs), a generalization of modal transition systems [27,26], as a foundation for three-valued program analysis. The semantics of Kripke MTSs are presented by means of a mixed power domain of states; soundness and consistency are proved. Two major applications, model checking partial state spaces and three-valued program shape analysis, are pres...

Model Repair George Chatzieleftheriou, Borzoo Bonakdarpour, Scott A. Smolka, and Panagiotis Katsaros 1 Department of Informatics, Aristotle University of Thessaloniki 54124 Thessaloniki, Greece 2 School of Computer Science, University of Waterloo 200 University Avenue West Waterloo N2L3G1, Canada 3 Department of Computer Science, Stony Brook University Stony Brook, NY 11794-4400, USA Abstract. ...

The main goal of model checking is to verify whether a model of a given program satisfies some given specification. In this paper models are regarded as fair or ordinary Kripke structures whereas specifications are represented by formulae branching-time temporal logics (CTL∗X or ACTL ∗ X ). Model checking can be substantially enhanced by reducing the size of models under consideration. Usually ...

This paper continues the investigations of Kripke [63]. Not only is Kripke [63] presupposed; the reader is advised to have it on hand for ready reference. The notations and terminology of that paper are used freely; in particular, P, Q, R, ... are atomic formulae, and A, B, 0, ... are arbitrary formulae built from them using the connectives A, ~, O. All propositional calculi in this paper have ...

This paper proves some independence results for weak fragments of Heyting arithmetic by using Kripke models. We present a necessary condition for linear Kripke models of arithmetical theories which are closed under the negative translation and use it to show that the union of the worlds in any linear Kripke model of HA satisfies PA. We construct a two-node PA-normal Kripke structure which does ...

Let T be a first-order theory. A T -normal Kripke structure is one in which every world is a classical model of T . This paper gives a characterization of the intuitionistic theory HT of sentences intuitionistically valid (forced) in all T -normal Kripke structures and proves the corresponding soundness and completeness theorems. For Peano arithmetic (PA), the theory HPA is a proper subtheory o...

In this paper we investigate Kripke models, used to model knowledge or belief in a static situation, and action models, used to model communicative actions that change this knowledge or belief. The appropriate notion for structural equivalence between modal structures such as Kripke models is bisimulation: Kripke models that are bisimilar are modally equivalent. We would like to find a structur...

This is a sequel to two previous papers, where it was shown that, for the Heyting propositional calculus H, we can give Kripke-style models whose accessibility relation R need not be a quasi-ordering relation, provided we have: x\=A &Vy(xRy=* y VA). From left to right, this is the heredity condition of standard Kripke models for H, but, since R need not be reflexive, the converse is not automat...

The well-known Dyckoff’s 1992 calculus/procedure for intuitionistic propositional logic is considered and analyzed. It is shown that the calculus is Kripke complete and the procedure in fact works in polynomial space. Then a multi-conclusion intuitionistic calculus is introduced, obtained by adding one new rule to known calculi. A simple proof of Kripke completeness and polynomial-space decidab...

Partial Kripke structures model incomplete state spaces with unknown parts. The evaluation of temporal logic formulae on partial Kripke structures is thus based on three-valued interpretations; the additional truth value ⊥ stands for “unknown whether property true or false”. There are existing model checking algorithms as well as tools employing this three-valued interpretation. In this paper w...