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The ProofTheory and Semantics of Intuitionistic Modal Logic
, 1994
"... Possible world semantics underlies many of the applications of modal logic in computer science and philosophy. The standard theory arises from interpreting the semantic definitions in the ordinary metatheory of informal classical mathematics. If, however, the same semantic definitions are interpret ..."
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Possible world semantics underlies many of the applications of modal logic in computer science and philosophy. The standard theory arises from interpreting the semantic definitions in the ordinary metatheory of informal classical mathematics. If, however, the same semantic definitions are interpreted in an intuitionistic metatheory then the induced modal logics no longer satisfy certain intuitionistically invalid principles. This thesis investigates the intuitionistic modal logics that arise in this way. Natural deduction systems for various intuitionistic modal logics are presented. From one point of view, these systems are selfjustifying in that a possible world interpretation of the modalities can be read off directly from the inference rules. A technical justification is given by the faithfulness of translations into intuitionistic firstorder logic. It is also established that, in many cases, the natural deduction systems induce wellknown intuitionistic modal logics, previously given by Hilbertstyle axiomatizations. The main benefit of the natural deduction systems over axiomatizations is their
Model Checking Partial State Spaces with 3Valued Temporal Logics (Extended Abstract)
 In Proceedings of the 11th Conference on Computer Aided Verification
, 1999
"... ) Glenn Bruns and Patrice Godefroid Bell Laboratories, Lucent Technologies fgrb,godg@belllabs.com Abstract. We address the problem of relating the result of model checking a partial state space of a system to the properties actually possessed by the system. We represent incomplete state space ..."
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Cited by 95 (7 self)
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) Glenn Bruns and Patrice Godefroid Bell Laboratories, Lucent Technologies fgrb,godg@belllabs.com Abstract. We address the problem of relating the result of model checking a partial state space of a system to the properties actually possessed by the system. We represent incomplete state spaces as partial Kripke structures, and give a 3valued interpretation to modal logic formulas on these structures. The third truth value ? means "unknown whether true or false". We define a preorder on partial Kripke structures that reflects their degree of completeness. We then provide a logical characterization of this preorder. This characterization thus relates properties of less complete structures to properties of more complete structures. We present similar results for labeled transition systems and show a connection to intuitionistic modal logic. We also present a 3valued CTL model checking algorithm, which returns ? only when the partial state space lacks information needed ...
Presheaf Models for Concurrency
, 1999
"... In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their wo ..."
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Cited by 45 (19 self)
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In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their work inspired this thesis by suggesting that presheaf categories could provide abstract models for concurrency with a builtin notion of bisimulation. We show how
History Dependent Automata
, 2001
"... In this paper we present historydependent automata (HDautomata in brief). They are an extension of ordinary automata that overcomes their limitations in dealing with historydependent formalisms. In a historydependent formalism the actions that a system can perform carry information generated i ..."
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Cited by 28 (8 self)
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In this paper we present historydependent automata (HDautomata in brief). They are an extension of ordinary automata that overcomes their limitations in dealing with historydependent formalisms. In a historydependent formalism the actions that a system can perform carry information generated in the past history of the system. The most interesting example is calculus: channel names can be created by some actions and they can then be referenced by successive actions. Other examples are CCS with localities and the historypreserving semantics of Petri nets. Ordinary
Petri Nets and Bisimulations
 THEORETICAL COMPUTER SCIENCE
, 1995
"... Several categorical relationships (adjunctions) between models for concurrency have been established, allowing the translation of concepts and properties from one model to another. A central example is a coreflection between Petri nets and asynchronous transition systems. The purpose of the pres ..."
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Cited by 16 (7 self)
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Several categorical relationships (adjunctions) between models for concurrency have been established, allowing the translation of concepts and properties from one model to another. A central example is a coreflection between Petri nets and asynchronous transition systems. The purpose of the present paper is to illustrate the use of such relationships by transferring to Petri nets a general concept of bisimulation.
HistoryDependent Automata
 ELECTR. NOTES IN TH. COMP. SCI
, 1998
"... In this paper we present historydependent automata (HDautomata in brief). They are an extension of ordinary automata that overcomes their limitations in dealing with historydependent formalisms. In a historydependent formalism the actions that a system can perform carry information generated in ..."
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Cited by 14 (1 self)
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In this paper we present historydependent automata (HDautomata in brief). They are an extension of ordinary automata that overcomes their limitations in dealing with historydependent formalisms. In a historydependent formalism the actions that a system can perform carry information generated in the past history of the system. The most interesting example is calculus: channel names can be created by some actions and they can then be referenced by successive actions. Other examples are CCS with localities and the historypreserving semantics of Petri nets. Ordinary automata are an unsatisfactory operational model for these formalisms: infinite automata are obtained for all the systems with in nite computations, even for very simple ones; moreover, the ordinary definition of bisimulation does not apply in these cases, thus preventing the reusage of standard theories and algorithms. In this paper we show that HDautomata are an adequate model for the historydependent formalisms. We pr...
On the Expressive Power of CTL*
 IN PROC. 14TH IEEE SYMP. LOGIC IN COMPUTER SCIENCE (LICS'99
, 1999
"... We show that the expressive power of the branching time logic CTL coincides with that of the class of bisimulation invariant properties expressible in socalled monadic path logic: monadic second order logic in which set quantification is restricted to paths. In order to prove this result, we first ..."
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Cited by 13 (4 self)
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We show that the expressive power of the branching time logic CTL coincides with that of the class of bisimulation invariant properties expressible in socalled monadic path logic: monadic second order logic in which set quantification is restricted to paths. In order to prove this result, we first prove a new Composition Theorem for trees. This approach is adapted from the approach of Hafer and Thomas in their proof that CTL coincides with the whole of monadic path logic over the class of full binary trees.
History Preserving Bisimulation for Contextual Nets ⋆
"... Abstract. We investigate the notion of history preserving bisimulation [15,18,3] for contextual P/T nets, a generalization of ordinary P/T Petrinetswhereatransitionmaycheckforthepresenceoftokenswithout consuming them (nondestructive read operations). A first equivalence, simply called HPbisimulati ..."
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Abstract. We investigate the notion of history preserving bisimulation [15,18,3] for contextual P/T nets, a generalization of ordinary P/T Petrinetswhereatransitionmaycheckforthepresenceoftokenswithout consuming them (nondestructive read operations). A first equivalence, simply called HPbisimulation, is based on Winskel’s prime event structures. A finer equivalence, called RHPbisimulation (where “R ” stands for “read”), relies on asymmetric event structures [1], a generalization of prime event structures which gives a more faithful account of the dependencies among transition occurrences arising in contextual net computations. Extending the work in [11,19], we show that HPbisimulation is decidable for finite nsafe contextual nets. Moreover by resorting to causal automata [12] — a variation of ordinary automata introduced to deal with history dependent formalisms — we can obtain an algorithm for deciding HPbisimulation and for getting a minimal realization. Decidability of RHPbisimulation, instead, remains an open question. 1
Proceedings Of The 1992 Workshop On Types For Proofs And Programs
, 1992
"... The aim of this note is first to set up some general theory for discussing different aspects of the notion of a logic and then to draw attention to the schematic aspects of logic and suggest a way of capturing this aspect without making any commitment to the kind of syntax a logic should have. Intro ..."
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The aim of this note is first to set up some general theory for discussing different aspects of the notion of a logic and then to draw attention to the schematic aspects of logic and suggest a way of capturing this aspect without making any commitment to the kind of syntax a logic should have. Introduction Nowadays we are well aware that there are many different logics. There are computer systems which are meant to be used to implement many logics. But there is no generally accepted account of what a logic is. Perhaps this is as it should be. We need imprecision in our vocabulary to mirror the flexible imprecision of our thinking. There are a number of related phrases that seem to have a similar imprecision; e.g. formal system, language, axiom system, theory, deductive system, logical system, etc... These are sometimes given technical meanings, often without adequate consideration of the informal notions. When a logic has been implemented in a computer system the logic has been repres...
Towards a Categorical Axiomatics of Bisimulation
, 1999
"... We give an axiomatic category theoretic account of bisimulation in process algebras based on the idea of functional bisimulations as open maps. The axiomatisation centres on 2monads, T , on Cat. Operations on processes, such as nondeterministic sum, prefixing and parallel composition are modelled u ..."
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We give an axiomatic category theoretic account of bisimulation in process algebras based on the idea of functional bisimulations as open maps. The axiomatisation centres on 2monads, T , on Cat. Operations on processes, such as nondeterministic sum, prefixing and parallel composition are modelled using functors in the Kleisli category for the 2monad T . We may define the notion of open map for any such 2monad; in examples of interest, the definition agrees exactly with the usual notion of functional bisimulation. Under a condition on T , namely that it be a dense KZmonad, which we define, it follows that functors in Kl(T ) preserve open maps, i.e., they respect functional bisimulation. We further investigate structures on Kl(T ) that exist for axiomatic reasons, primarily because T is a dense KZmonad, and we study how those structures help to model operations on processes. We outline how this analysis gives ideas for modelling higher order processes. We conclude by making compariso...