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16
Domain Theory in Logical Form
 Annals of Pure and Applied Logic
, 1991
"... The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: • Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for denotational semantics. • The theory of concurrency and system ..."
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Cited by 231 (10 self)
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The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: • Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for denotational semantics. • The theory of concurrency and systems behaviour developed by Milner, Hennessy et al. based on operational semantics. • Logics of programs. Stone duality provides a junction between semantics (spaces of points = denotations of computational processes) and logics (lattices of properties of processes). Moreover, the underlying logic is geometric, which can be computationally interpreted as the logic of observable properties—i.e. properties which can be determined to hold of a process on the basis of a finite amount of information about its execution. These ideas lead to the following programme:
Semantic Domains for Combining Probability and NonDeterminism
 ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE
, 2005
"... ..."
Compositionality via cutelimination: HennessyMilner logic for an arbitrary GSOS
 In Logic in Computer Science
, 1995
"... We present a sequent calculus for proving that processes in a process algebra satisfy assertions in HennessyMilner logic. The main novelty lies in the use of the operational semantics to derive introduction rules (on the left and right of sequents) for the different operators of the process calculu ..."
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Cited by 16 (3 self)
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We present a sequent calculus for proving that processes in a process algebra satisfy assertions in HennessyMilner logic. The main novelty lies in the use of the operational semantics to derive introduction rules (on the left and right of sequents) for the different operators of the process calculus. This gives a generic proof system applicable to any process algebra with an operational semantics specified in the GSOS format. We identify the desirable property of compositionality with cutelimination, and we prove that this holds for a class of sequents. Further, we show that the proof system enjoys good completeness and !completeness properties relative to its intended model. 1 Introduction The provision of proof systems for program logics is an important research goal, as such systems enable one to give formal proofs guaranteeing that programs satisfy required properties. A desirable feature of such proof systems is that they should allow a compositional style of proof developme...
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.
Sequent Calculi for Process Verification: HennessyMilner Logic for an Arbitrary GSOS
, 2003
"... We argue that, by supporting a mixture of “compositional” and “structural” styles of proof, sequentbased proof systems provide a useful framework for the formal verification of processes. As a worked example, we present a sequent calculus for establishing that processes from a process algebra satis ..."
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Cited by 11 (1 self)
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We argue that, by supporting a mixture of “compositional” and “structural” styles of proof, sequentbased proof systems provide a useful framework for the formal verification of processes. As a worked example, we present a sequent calculus for establishing that processes from a process algebra satisfy assertions in HennessyMilner logic. The main novelty lies in the use of the operational semantics to derive introduction rules, on the left and right of sequents, for the operators of the process calculus. This gives a generic proof system applicable to any process algebra with an operational semantics specified in the GSOS format. Using a general algebraic notion of GSOS model, we prove a completeness theorem for the cutfree fragment of the proof system, thereby establishing the admissibility of the cut rule. Under mild (and necessary) conditions on the process algebra, an ωcompleteness result, relative to the “intended” model of closed process terms, follows.
Compositionality of HennessyMilner logic through structural operational semantics
 Huang and M. E. Glicksman, Acta Met
, 2003
"... Abstract. This paper presents a method for the decomposition of HML formulae. It can be used to decide whether a process algebra term satisfies a HML formula, by checking whether subterms satisfy certain formulae, obtained by decomposing the original formula. The method uses the structural operation ..."
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Cited by 8 (1 self)
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Abstract. This paper presents a method for the decomposition of HML formulae. It can be used to decide whether a process algebra term satisfies a HML formula, by checking whether subterms satisfy certain formulae, obtained by decomposing the original formula. The method uses the structural operational semantics of the process algebra. The main contribution of this paper is that an earlier decomposition method from Larsen [14] for the De Simone format is extended to the more general ntyft/ntyxt format without lookahead. 1
Full Abstractness for a Functional/Concurrent Language With HigherOrder ValuePassing
, 1998
"... We study an applied typed callbyvalue calculus which in addition to the usual types for higherorder functions contains an extra type called proc, for processes. The constructors for terms of this type are similar to those found in standard process calculi such as CCS. We first give an operationa ..."
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Cited by 6 (2 self)
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We study an applied typed callbyvalue calculus which in addition to the usual types for higherorder functions contains an extra type called proc, for processes. The constructors for terms of this type are similar to those found in standard process calculi such as CCS. We first give an operational semantics for this language in terms of a labelled transition system which is then used to give a behavioural preorder based on contexts: the expression N dominates M if in every appropriate context if M can produce a boolean value then so can N. Based on standard domain constructors we define a model, a prime algebraic lattice, which is fully abstract with respect to this behaviour preorder.
A Refinement Logic for the Fork Calculus
 Protocol Specification, Testing and Verification XIV
, 1995
"... The Fork Calculus FC presents a theory of communicating systems in family with CCS, but it differs in the way that processes are put in parallel. In CCS there is a binary parallel operator j, whereas FC contains a unary fork operator. We provide FC with an operational semantics, together with a co ..."
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Cited by 3 (0 self)
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The Fork Calculus FC presents a theory of communicating systems in family with CCS, but it differs in the way that processes are put in parallel. In CCS there is a binary parallel operator j, whereas FC contains a unary fork operator. We provide FC with an operational semantics, together with a congruence relation between processes. Further, a refinement logic for program specification and design is presented. In this logic it is possible to freely mix programming constructs with specification constructs, thereby allowing us to define a compositional proof system. The proof rules of this system are applied to a nontrivial example. 1 Introduction One goal for work within program specification is to provide a theory for the formal refinement of specifications into programs via sequences of verifiedcorrect development steps. In this paper we shall pursue this goal by focusing on specification and stepwise refinement into programs in the Fork Calculus. The Fork Calculus, FC, first pre...