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Completeness and Logical Full Abstraction in Modal Logics for Typed Mobile Processes
"... Abstract. We study an extension of HennessyMilner logic for the πcalculus which gives a sound and complete characterisation of representative behavioural preorders and equivalences over typed processes. New connectives are introduced representing actual and hypothetical typed parallel composition ..."
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Abstract. We study an extension of HennessyMilner logic for the πcalculus which gives a sound and complete characterisation of representative behavioural preorders and equivalences over typed processes. New connectives are introduced representing actual and hypothetical typed parallel composition and hiding. We study three compositional proof systems, characterising the May/Must testing preorders and bisimilarity. The proof systems are uniformly applicable to different type disciplines. Logical axioms distill proof rules for parallel composition studied by Amadio and Dam. We demonstrate the expressiveness of our logic embeddings of program logics for higherorder functions. 1
SOS formats and metatheory: 20 years after
, 2007
"... In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [G.D. Plotkin, A structural approach to operational semantics, Technical ..."
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Cited by 14 (5 self)
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In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [G.D. Plotkin, A structural approach to operational semantics, Technical
Bialgebraic Methods and Modal Logic in Structural Operational Semantics
 Electronic Notes in Theoretical Computer Science
, 2007
"... Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about wellbehaved structural operational semantics (SOS). An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various ..."
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Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about wellbehaved structural operational semantics (SOS). An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various kinds of operational descriptions in a uniform fashion. In this paper, bialgebraic semantics is combined with a coalgebraic approach to modal logic in a novel, general approach to proving the compositionality of process equivalences for languages defined by structural operational semantics. To prove compositionality, one provides a notion of behaviour for logical formulas, and defines an SOSlike specification of modal operators which reflects the original SOS specification of the language. This approach can be used to define SOS congruence formats as well as to prove compositionality for specific languages and equivalences. Key words: structural operational semantics, coalgebra, bialgebra, modal logic, congruence format 1
Operational and Epistemic Approaches to Protocol Analysis: Bridging the Gap
"... Abstract. Operational models of (security) protocols, on one hand, are readable and conveniently match their implementation (at a certain abstraction level). Epistemic models, on the other hand, are appropriate for specifying knowledgerelated properties such as anonymity or secrecy. These two appro ..."
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Abstract. Operational models of (security) protocols, on one hand, are readable and conveniently match their implementation (at a certain abstraction level). Epistemic models, on the other hand, are appropriate for specifying knowledgerelated properties such as anonymity or secrecy. These two approaches to specification and verification have so far developed in parallel and one has either to define ad hoc correctness criteria for the operational model or use complicated epistemic models to specify the operational behavior. We work towards bridging this gap by proposing a combined framework which allows for modeling the behavior of a protocol in a process language with an operational semantics and supports reasoning about properties expressed in a rich logic which combines temporal and epistemic operators. 1
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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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
Decompositional reasoning about the history of parallel processes
, 2010
"... Abstract. This paper presents a decomposition technique for HennessyMilner logic with past and its extension with recursively defined formulae. In order to highlight the main ideas and technical tools, processes are described using a subset of CCS with parallel composition, nondeterministic choice, ..."
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Abstract. This paper presents a decomposition technique for HennessyMilner logic with past and its extension with recursively defined formulae. In order to highlight the main ideas and technical tools, processes are described using a subset of CCS with parallel composition, nondeterministic choice, action prefixing and the inaction constant. The study focuses on developing decompositional reasoning techniques for parallel contexts in that language. 1
A Proof System for Compositional Verification of Probabilistic Concurrent Processes
"... Abstract. We present a formal proof system for compositional verification of probabilistic concurrent processes. Processes are specified using an SOSstyle process algebra with probabilistic operators. Properties are expressed using a probabilistic modal µcalculus. And the proof system is formulate ..."
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Abstract. We present a formal proof system for compositional verification of probabilistic concurrent processes. Processes are specified using an SOSstyle process algebra with probabilistic operators. Properties are expressed using a probabilistic modal µcalculus. And the proof system is formulated as a sequent calculus in which sequents are given a quantitative interpretation. A key feature is that the probabilistic scenario is handled by introducing the notion of Markov proof, according to which proof trees contain probabilistic branches and are required to satisfy a condition formulated byinterpretingthemas Markov Decision Processes. We present simple but illustrative examples demonstrating the applicability of the approach to the compositional verification of infinite state processes. Our main result is the soundness of the proof system, which is proved by applying the coupling method from probability theory to the game semantics of the probabilistic modal µcalculus. 1
Modal Logics for Typed Mobile Processes
"... Abstract. We propose an extension of HennessyMilner logic for the πcalculus which gives sound and complete characterisation of representative behavioural preorder and equivalence over typed processes. New connectives are introduced representing actual and hypothetical typed parallel composition an ..."
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Abstract. We propose an extension of HennessyMilner logic for the πcalculus which gives sound and complete characterisation of representative behavioural preorder and equivalence over typed processes. New connectives are introduced representing actual and hypothetical typed parallel composition and hiding. We study two compositional proof systems, characterising the May/Must testing preorders for infinite processes. The mixture of the two proof systems corresponds to bisimilarity. These proof systems are uniformly usable for different type disciplines. Logical axioms for composition originate from the corresponding proof rules studied by the preceding researchers including Amadio and Dam, allowing elimination of new connectives depending on types. We demonstrate how the use of types facilitates highlevel logical reasoning through examples, including
Bialgebraic Operational Semantics and Modal Logic (extended abstract)
"... A novel, general approach is proposed to proving the compositionality of process equivalences on languages defined by Structural Operational Semantics (SOS). The approach, based on modal logic, is inspired by the simple observation that if the set of formulas satisfied by a process can be derived fr ..."
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A novel, general approach is proposed to proving the compositionality of process equivalences on languages defined by Structural Operational Semantics (SOS). The approach, based on modal logic, is inspired by the simple observation that if the set of formulas satisfied by a process can be derived from the corresponding sets for its subprocesses, then the logical equivalence is a congruence. Striving for generality, SOS rules are modeled categorically as bialgebraic distributive laws for some notions of process syntax and behaviour, and modal logics are modeled via coalgebraic polyadic modal logic. Compositionality is proved by providing a suitable notion of behaviour for the logic together with a dual distributive law, reflecting the one modeling the SOS specification. Concretely, the dual laws may appear as SOSlike rules where logical formulas play the role of processes, and their behaviour models logical decomposition over process syntax. The approach can be used either to proving compositionality for specific languages or for defining SOS congruence formats.