Zero-one laws with respect to models of provability logic and two Grzegorczyk logics

It has been shown in the late 1960s that each formula of first-order logic without constants and function symbols obeys a zero-one law: As the number of elements of finite models increases, every formula holds either in almost all or in almost no models of that size. Therefore, many properties of models, such as having an even number of elements, cannot be expressed in the language of first-order logic. Halpern and Kapron proved zero-one laws for classes of models corresponding to the modal logics K, T, S4, and S5 and for frames corresponding to S4 and S5. In this paper, we prove zero-one laws for provability logic and its two siblings Grzegorczyk logic and weak Grzegorczyk logic, with respect to model validity. Moreover, we axiomatize validity in almost all relevant finite models, leading to three different axiom systems

Exploring the power of converse events

Dynamic epistemic logic as viewed by Baltag, Moss and Solecki (DEL) and propositional dynamic logic (PDL) offer different semantics of events. On the one hand, DEL adds dynamics to epistemic logic by introducing so-called event models as syntactic objects into the language. On the other hand, PDL has instead transition relations between possible worlds. This last approach allows to easily introduce converse events. In this paper we add epistemics to this, and call the resulting logic epistemic dynamic logic (EDL). We show that DEL can be translated into EDL thanks to this use of the converse operator: it enables us to translate the structure of the event model directly within a particular axiomatization of EDL, without having to refer to a particular epistemic event model in the language (as done in DEL). It follows that EDL is more expressive and general than DEL and we characterize semantically and syntactically in EDL this embedding of DEL

A process algebra based framework for promise theory

We present a process algebra based approach to formalize the interactions of computing devices such as the representation of policies and the resolution of conflicts. As an example we specify how promises may be used in coming to an agreement regarding a simple though practical transportation problem.Comment: 9 pages, 4 figure