Solovay’s proof of the arithmetical completeness of the provability logic GL proceeds by simulating a finite Kripke model inside the theory of Peano Arithmetic (PA). In this article, a new perspective on the proof of GL’s arithmetical completeness will be given. Instead of simulating a Kripke structure inside the theory of PA, it will be embedded into an arithmetically defined Kripke structure....

1 We consider the semantics of predicate Kripke frames with equality (called I-frames, for short), which is equivalent to the semantics of Kripke sheaves (see [3]). Namely, a (predicate) Kripke frame is a pairM = (W,U) formed by a posetW with the least element 0W and a domain map U defined on W such that U(u)⊆U(v) for u≤v. An I-frame is a triple M = (W,U, I), in which (W,U) is a Kripke frame an...

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...

The interpretation of propositional dynamic logic (PDL) through Kripke models requires the relations constituting the interpreting Kripke model to closely observe the syntax of the modal operators. This poses a significant challenge for an interpretation of PDL through stochastic Kripke models, because the programs’ operations do not always have a natural counterpart in the set of stochastic re...

BAN logic is a propositional logic of knowledge for the verification of cryptographic protocols. While BAN logic has been successful from a practical point of view, the semantics of the epistemic (knowledge) modality is unclear. Several Kripke semantics have been proposed, but they do not attempt at anything beyond a soundness result. Completeness is prevented by the so called logical omniscien...

Kripke frame semantics is used as a concise and convenient apparatus for the study of non-classical predicate logics, but it is well-known that there exist a great many important logics which cannot be complete with respect to this semantics. Logicians have been introducing many kinds of new semantics to get rid of this difficulty. (cf. [1], [3]) Hence it is important to find a non-trivial exam...

Kripke-Armstrong argument aims to establish that the defender of existence material objects? temporal parts cannot determine whether a lonely homogeneous disc made continuous matter is rotating around its axis or not. The perdurantist distinguish between these two possibilities by appealing different instantaneous velocities disc, since doing so he would violate Humean supervenience thesis. In ...