Higher dimensional automata (HDA) are a model of concurrency [5, 8] that can express most of the traditional partial order models like Mazurkiewicz traces, pomsets, event structures, or Petri nets. Modal logics, interpreted over Kripke structures, are the logics for reasoning about sequential behavior and interleaved concurrency. Modal logic is a well behaved subset of first-order logic; many v...

We investigate a modal logic of probability with a unary modal operator expressing that a proposition is more probable than its negation. Such an operator is not closed under conjunction, and its modal logic is therefore non-normal. Within this framework we study the relation of probability with other modal concepts: belief and action. We focus on the evolution of belief, and propose an integra...

We generalise the result of Ganzinger, Meyer and Veanes [14] on decidability of the two variable monadic guarded fragment of first order logic with constraints on the guard relations expressible in monadic second order logic. In [14], such constraints apply to one relation at a time. We modify their proof to obtain decidability for constraints involving several relations. Now we can use this re...

The aim of this paper is to introduce a new formalism for multi-agent systems that captures (true) concurrency and independence. We begin describing a complete and decidable propositional multi-modal logic. The language, similar to Propositional Dynamic Logic in many aspects, di ers from usual modal logic: modal operators are non-atomic (they are built out of basic actions) and capture concurre...

Modal logic is sometimes characterized as the logic of necessity and possibility, of “must be” and “may be”. The aim of this book is to present both semantical and syntactical features of the subject and to illustrate gy detailed analysis of the three most popular modal systems S5,S4 and K. The text presupposes some knowledge of classical logic, although the necessary information is briefly rec...

Coalgebras provide a unifying semantic framework for a wide variety of modal logics. It has previously been shown that the class of coalgebras for an endofunctor can always be axiomatised in rank 1. Here we establish the converse, i.e. every rank 1 modal logic has a sound and strongly complete coalgebraic semantics. As a consequence, recent results on coalgebraic modal logic, in particular gene...