message passing systems, completeness. We introduce and investigate quantified interpreted systems, a semantics to reason about knowledge and time in a firstorder setting. We provide an axiomatisation, which we show to be sound and complete. We utilise the formalism to study message passing systems (Lamport 1978; Fagin et al 1995) in a first-order setting, and compare the results obtained to those available for the propositional case.

It is well known that many two-dimensional products of modal logics with at least one `transitive' (but not `symmetric') component lack the product finite model property. Here we show that products of two `transitive' logics (such as, e.g., K4 K4, S4 S4, GrzGrz and GLGL) do not have the (abstract) finite model property either. These are the first known examples of 2D modal product logics without the finite model property where both components are natural unimodal logics having the finite model property.

We consider quantifier-free spatial logics, designed for qualitative spatial representation and reasoning in AI, and extend them with the means to represent topological connectedness of regions and restrict the number of their connected components. We investigate the computational complexity of these logics and show that the connectedness constraints can increase complexity from NP to PSpace, ExpTime and, if component counting is allowed, to NExpTime.

We propose a general semantic notion of modal many-valued logic. Then, we explore the difficulties to characterize this notation in a syntactic way and analyze the existing literature with respect to this framework.

It is shown that every normal intuitionistic modal logic L over MIPC has the finite model property if there exists a universal firstorder sentence 8 such that (1) L is characterized by the class of Kripke frames satisfying 8 and (2) every Kripke frame that validates L satisfies 8. Here, MIPC is a well-known intuitionistic modal logic introduced by Prior (1957).

Introduction Alethic modalities are the necessity, contingency, possibility or impossibility of something being true. Alethic means `concerned with truth'. [28, p. 132] The above dictionary characterization of alethic modalities states the central notions of alethic modal logic: necessity, and other notions that are usually thought of as being definable in terms of necessity and Boolean negation: impossibility, contingency, and possibility. The syntax of modal propositional logic is inductively defined over a denumerable set of sentence letters p 0 , p 1 , p 2 , . . . as follows: A ::= p | A | (A # B) | #A The other Boolean operations (#, #, #, # and #) are defined as usual. A formula<F10.9

This paper deals with subset spaces where points are structured as pairs of states. Our aim is to approach a formal model of uniform topological reasoning in this way. That is, in case a uniformity underlies the topological space under consideration, the re ned reasoning model is to be sensitive to that. We show completeness and decidability of the basic modal logic arising from this setting, and discuss both possible extensions of the system and limitations

We describe a coalgebraic perspective on models of rewriting logic theories. After establishing a soundness and completeness result, we show how one can use modal logics for coalgebras to reason about the rewrite process. The approach is semantics-driven in the sense that the logic we propose is tailored to the class of models we consider. 1

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We view models of rewrite theories enriched with observations coalgebraically. This allows us on the one hand to use “off the shelf ” logics for coalgebras to specify and, on the other hand, to verify properties of rewriting programs and to obtain results about the expressive power of such languages. 1