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On an Intuitionistic Modal Logic
 Studia Logica
, 2001
"... . In this paper we consider an intuitionistic variant of the modal logic S4 (which we call IS4). The novelty of this paper is that we place particular importance on the natural deduction formulation of IS4our formulation has several important metatheoretic properties. In addition, we study models ..."
Abstract

Cited by 19 (4 self)
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. In this paper we consider an intuitionistic variant of the modal logic S4 (which we call IS4). The novelty of this paper is that we place particular importance on the natural deduction formulation of IS4our formulation has several important metatheoretic properties. In addition, we study models of IS4, not in the framework of Kripke semantics, but in the more general framework of category theory. This allows not only a more abstract definition of a whole class of models but also a means of modelling proofs as well as provability. 1. Introduction Modal logics are traditionally extensions of classical logic with new operators, or modalities, whose operation is intensional. Modal logics are most commonly justified by the provision of an intuitive semantics based upon `possible worlds', an idea originally due to Kripke. Kripke also provided a possible worlds semantics for intuitionistic logic, and so it is natural to consider intuitionistic logic extended with intensional modalities...
Denotational Semantics for ProcessBased Simulation Languages. Part I: piDemos
, 1997
"... In this paper we present a method for translating the synchronisation behaviour of a process oriented discrete event simulation language into a process algebra. Such translations serve two purposes. The first exploits the formal structure of the target process algebraic representations to provide pr ..."
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Cited by 15 (10 self)
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In this paper we present a method for translating the synchronisation behaviour of a process oriented discrete event simulation language into a process algebra. Such translations serve two purposes. The first exploits the formal structure of the target process algebraic representations to provide proofs of properties of the source system (such as deadlock freedom, fairness, liveness, ...) which can be very difficult to establish by simulation experiment. The second exploits the denotational semantics to better understand the language constructs as abstract entities and to reason about simulation models. Here we give the intuition and present the basic mechanisms using the ßDemos simulation language and the CCS and SCCS process algebras. The analysis of the synchronisations of full Demos is treated in a companion paper.
A Compositional Proof System for the Modal µCalculus
, 1994
"... We present a proof system for determining satisfaction between processes in a fairly general process algebra and assertions of the modal µcalculus. The proof system is compositional in the structure of processes. It extends earlier work on compositional reasoning within the modal µcalculus and com ..."
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Cited by 15 (0 self)
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We present a proof system for determining satisfaction between processes in a fairly general process algebra and assertions of the modal µcalculus. The proof system is compositional in the structure of processes. It extends earlier work on compositional reasoning within the modal µcalculus and combines it with techniques from work on local model checking. The proof system is sound for all processes and complete for a class of finitestate processes.
Describing the Approaches
, 1994
"... ing from the nature of the states involved, we can specify the change that an atomic program a effects by means of a two place transition relation R a on a set of states. This perspective gives rise to the study of socalled transition systems. The most general style of reasoning about programs and ..."
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ing from the nature of the states involved, we can specify the change that an atomic program a effects by means of a two place transition relation R a on a set of states. This perspective gives rise to the study of socalled transition systems. The most general style of reasoning about programs and transition system is found in propositional dynamic logics (Pratt [ Pratt, 1976 ] [ Pratt, 1980 ] , Harel [ Harel, 1984 ] ) and in algebras of processes (Hennessy [ Hennessy, 1988 ] ). Processes and transition systems are studied from the perspective of modal logic in Stirling [ Stirling, 1987 ] and Van Benthem and Bergstra [ Benthem and Bergstra, 1993 ] . Dynamic semantics can be put to use to stipulate relational denotations for propositions. In this perspective, a state of information is a set of possible worlds, and a program updates a state of information by removing the worlds incompatible with the new information. Thus, the semantics of language is defined in terms of its potential to...