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129
Propositional Lax Logic
, 1997
"... We investigate a novel intuitionistic modal logic, called Propositional Lax Logic, with promising applications to the formal verification of computer hardware. The logic has emerged from an attempt to express correctness `up to' behavioural constraints  a central notion in hardware verificat ..."
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Cited by 66 (8 self)
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We investigate a novel intuitionistic modal logic, called Propositional Lax Logic, with promising applications to the formal verification of computer hardware. The logic has emerged from an attempt to express correctness `up to' behavioural constraints  a central notion in hardware verification  as a logical modality. The resulting logic is unorthodox in several respects. As a modal logic it is special since it features a single modal operator fl that has a flavour both of possibility and of necessity. As for hardware verification it is special since it is an intuitionistic rather than classical logic which so far has been the basis of the great majority of approaches. Finally, its models are unusual since they feature worlds with inconsistent information and furthermore the only frame condition is that the fl frame be a subrelation of the oeframe. In the paper we will provide the motivation for Propositional Lax Logic and present several technical results. We will investigate...
Hybrid Logics
"... This chapter provides a modern overview of the field of hybrid logic. Hybrid logics are extensions of standard modal logics, involving symbols that name individual states in models. The first results that are nowadays considered as part of the field date back to the early work of Arthur ..."
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Cited by 62 (18 self)
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This chapter provides a modern overview of the field of hybrid logic. Hybrid logics are extensions of standard modal logics, involving symbols that name individual states in models. The first results that are nowadays considered as part of the field date back to the early work of Arthur
A symmetric modal lambda calculus for distributed computing
 IN PROCEEDINGS OF THE 19TH IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE (LICS
, 2004
"... We present a foundational language for distributed programming, called Lambda 5, that addresses both mobilityof code and locality of resources. In order to construct our system, we appeal to the powerful propositionsastypes interpretation of logic. Specifically, we take the possible worlds of the ..."
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Cited by 57 (10 self)
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We present a foundational language for distributed programming, called Lambda 5, that addresses both mobilityof code and locality of resources. In order to construct our system, we appeal to the powerful propositionsastypes interpretation of logic. Specifically, we take the possible worlds of the intuitionistic modal logic IS5 to be nodes ona network, and the connectives 2 and 3 to reflect mobility and locality, respectively. We formulate a novel systemof natural deduction for IS5, decomposing the introduction and elimination rules for 2 and 3, thereby allowing thecorresponding programs to be more direct. We then give an operational semantics to our calculus that is typesafe, logically faithful, and computationally realistic.
A Spatial Logic for Concurrency (Part II)
 IN CONCUR2002: CONCURRENCY THEORY (13TH INTERNATIONAL CONFERENCE), LECTURE NOTES IN COMPUTER SCIENCE
, 1998
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Possible Worlds and Resources: The Semantics of BI
 THEORETICAL COMPUTER SCIENCE
, 2003
"... The logic of bunched implications, BI, is a substructural system which freely combines an additive (intuitionistic) and a multiplicative (linear) implication via bunches (contexts with two combining operations, one which admits Weakening and Contraction and one which does not). BI may be seen to a ..."
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Cited by 50 (18 self)
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The logic of bunched implications, BI, is a substructural system which freely combines an additive (intuitionistic) and a multiplicative (linear) implication via bunches (contexts with two combining operations, one which admits Weakening and Contraction and one which does not). BI may be seen to arise from two main perspectives. On the one hand, from prooftheoretic or categorical concerns and, on the other, from a possibleworlds semantics based on preordered (commutative) monoids. This semantics may be motivated from a basic model of the notion of resource. We explain BI's prooftheoretic, categorical and semantic origins. We discuss in detail the question of completeness, explaining the essential distinction between BI with and without ? (the unit of _). We give an extensive discussion of BI as a semantically based logic of resources, giving concrete models based on Petri nets, ambients, computer memory, logic programming, and money.
Labelled Propositional Modal Logics: Theory and Practice
, 1996
"... We show how labelled deductive systems can be combined with a logical framework to provide a natural deduction implementation of a large and wellknown class of propositional modal logics (including K, D, T , B, S4, S4:2, KD45, S5). Our approach is modular and based on a separation between a base lo ..."
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Cited by 41 (8 self)
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We show how labelled deductive systems can be combined with a logical framework to provide a natural deduction implementation of a large and wellknown class of propositional modal logics (including K, D, T , B, S4, S4:2, KD45, S5). Our approach is modular and based on a separation between a base logic and a labelling algebra, which interact through a fixed interface. While the base logic stays fixed, different modal logics are generated by plugging in appropriate algebras. This leads to a hierarchical structuring of modal logics with inheritance of theorems. Moreover, it allows modular correctness proofs, both with respect to soundness and completeness for semantics, and faithfulness and adequacy of the implementation. We also investigate the tradeoffs in possible labelled presentations: We show that a narrow interface between the base logic and the labelling algebra supports modularity and provides an attractive prooftheory (in comparision to, e.g., semantic embedding) but limits th...
Categorical and Kripke Semantics for Constructive S4 Modal Logic
 In International Workshop on Computer Science Logic, CSL’01, L. Fribourg, Ed. Lecture Notes in Computer Science
, 2001
"... We consider two systems of constructive modal logic which are computationally motivated. Their modalities admit several computational interpretations and are used to capture intensional features such as notions of computation, constraints, concurrency, etc. Both systems have so far been studied m ..."
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Cited by 35 (1 self)
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We consider two systems of constructive modal logic which are computationally motivated. Their modalities admit several computational interpretations and are used to capture intensional features such as notions of computation, constraints, concurrency, etc. Both systems have so far been studied mainly from typetheoretic and categorytheoretic perspectives, but Kripke models for similar systems were studied independently. Here we bring these threads together and prove duality results which show how to relate Kripke models to algebraic models and these in turn to the appropriate categorical models for these logics.
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 ..."
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Cited by 28 (6 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...
Modal proofs as distributed programs (Extended Abstract)
 EUROPEAN SYMPOSIUM ON PROGRAMMING
, 2004
"... We develop a new foundation for distributed programming languages by defining an intuitionistic, modal logic and then interpreting the modal proofs as distributed programs. More specifically, the proof terms for the various modalities have computational interpretations as remote procedure calls, c ..."
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Cited by 27 (0 self)
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We develop a new foundation for distributed programming languages by defining an intuitionistic, modal logic and then interpreting the modal proofs as distributed programs. More specifically, the proof terms for the various modalities have computational interpretations as remote procedure calls, commands to broadcast computations to all nodes in the network, commands to use portable code, and finally, commands to invoke computational agents that can find their own way to safe places in the network where they can execute. We prove some simple metatheoretic results about our logic as well as a safety theorem that demonstrates that the deductive rules act as a sound type system for a distributed programming language.