Combining logics has become a rapidly expanding enterprise that is inspired mainly by concerns about modularity and the wish to join together tailored made logical tools into more powerful but still manageable ones. A natural

. In this paper, we present two logics that allow for specifying distributed information systems, emphasizing communication among sites. The low-level logic D 0 offers features that are easy to implement but awkward to use for specification, while the high-level logic D 1 offers convenient specification features that are not easy to implement. We show that D 1 specifications may be automatically translated to D 0 in a sound and complete way. In order to prove soundness and completeness, we define our translation as a simple map of institutions. Our result may be useful for making implementation platforms like Corba easier accessible by providing high-level planning and specification methods for communication. 1 Introduction Two logics are presented that allow for specifying distributed information systems, emphasizing communication among sites. The low-level logic D 0 offers features that are easy to implement but awkward to use for specification, while the high-level logic D 1 offers...

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. Several mechanisms for combining logics have appeared in the literature. Synchronization is one of the simplest: the language of the combined logic is the disjoint union of the given languages, but the class of models of the resulting logic is a subset of the cartesian product of the given classes of models (the interaction between the two logics is imposed by constraining the class of pairs of models). Herein, we give both a model-theoretic and a proof-theoretic account of synchronization as a categorial construction (using coproducts and cocartesian liftings) . We also prove that soundness is preserved by possibly constrained synchronization and state sufficient conditions for preservation of model existence and strong completeness. We provide an application to the combination of dynamic logic and linear temporal logic. Keywords: combination of logics, synchronization of logics, model existence, completeness, dynamic logic, temporal logic. 1 Introduction There has been a recent g...

. Combined logics have recently deserved much attention. In this paper we develop a detailed study of a form of combination that generalises the temporalisation construction proposed in [9]. It consists of replacing an atomic part (formal parameter) of one (parameterised) logic by another (actual parameter) logic. We provide a categorial characterisation of parameterisation and illustrate it with an example. Under reasonable assumptions, we show that the result logic is a conservative extension of both the parameterised and parameter logics and also that soundness, completeness and decidability are transferred. 1 Introduction We need to work with evermore complex systems. The challenge is to identify abstractions that may lead to a modular and integrated management of this complexity. One such approach is the combination of logics. In practice, it is geared by the need for integrating heterogeneous platforms and tools. Theoretically, the study of logics for combined structures has bee...

Motivated by applications in software engineering, we propose two forms of combination of logics: synchronization on formulae and synchronization on models. We start by reviewing satisfaction systems, consequence systems, one-step derivation systems and theory spaces, as well as their functorial relationships. We define the synchronization on formulae of two consequence systems and provide a categorial characterization of the construction. For illustration we consider the synchronization of linear temporal logic and equational logic. We define the synchronization on models of two satisfaction systems and provide a categorial characterization of the construction. We illustrate the technique in two cases: linear temporal logic versus equational logic; and linear temporal logic versus branching temporal logic. Finally, we lift the synchronization on formulae to the category of logics over consequence systems. Key words: combination of logics, synchronization on formulae, sync...

. We investigate the notion of bred tableaux which naturally arises from the idea of bred semantics. Dierent implication operators peacefully cohabit and co-operate within the same labelled tableau method. 1 Introduction The last decade has seen a proliferation of dierent logical systems proposed for a variety of dierent purposes, both theoretical and practical. These logics appear to satisfy the needs of dierent application areas or to capture dierent interpretations of the logical operators. This is particularly apparent in the case of the conditional operator. All the dierent implication logics which have been proposed in the literature seem to succeed in modelling some aspect of the ordinary use of this operator, or in suggesting useful non-standard interpretations. What emerges from these developments is a class of operators bearing a family resemblance to each other, each of which may t a dierent application. So, a crucial problem, both in pure and applied logic, is th...

Suitable extensions of monadic second-order theories of k successors have been proposed in the literature to specify in a concise way reactive systems whose behaviour can be naturally modeled with respect to a (possibly infinite) set of differently-grained temporal domains. This is the case, for instance, of the wide-ranging class of real-time reactive systems whose components have dynamic behaviours regulated by very different time constants, e.g., days, hours, and seconds. In this paper, we focus on the theory of k-refinable downward unbounded layered structures i=0 ], that is, the theory of infinitely refinable structures consisting of a coarsest domain and an infinite number of finer and finer domains, whose satisfiability problem is nonelementarily decidable. We define a propositional temporal logic counterpart of MSO[< tot , (# i ) i=0 ] with set quantification restricted to infinite paths, called CTSL # k , which features an original mix of linear and branching temporal operators. We prove the expressive completeness of CTSL # k with respect to such a path fragment of MSO[< tot , (# i ) i=0 ] and show that its satisfiability problem is 2EXPTIME-complete.

In this paper, we develop model checking procedures for three ways of combining (temporal) logics: temporalization, independent combination, and join. We prove that they are terminating, sound, and complete, we analyze their computational complexity, and we report on experiments with implementations. We take a close look at mobile systems and show how the proposed combined model checking framework can be successfully applied to the specification and verification of their properties.

. In this paper we briefly survey the main contributions of our research on time granularity and outline some directions for current and future researches. The original motivation of our research was the design of a temporal logic embedding the notion of time granularity, suitable for the specification of complex real-time systems, whose components evolve according to different time units. However, there are significant similarities between the problems we encountered in pursuing our goal, and those addressed by current research on combining logics, theories, and structures. Furthermore, exploiting interesting connections between multi-level temporal logics and automata theory that we recently established, a complementary point of view on time granularity arises: time granularity can be viewed not only as an important feature of a representation language, but as well as a formal tool to investigate expressiveness and decidability properties of temporal theories. Finally, a...