Logics for Contravariant Simulations

Fábregas, Ignacio; Frutos-Escrig, David de; Palomino, Miguel

doi:10.1007/978-3-642-13464-7_18

Cited by 12 publications

(20 citation statements)

References 13 publications

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“…We have continued with the study of covariant-contravariant simulation and conformance simulation semantics started in [12,11] by considering the axiomatization of the preorders and equivalences that they define.…”

Section: Discussionmentioning

confidence: 99%

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Aceto¹,

Sobociński²

2010

Electron. Proc. Theor. Comput. Sci.

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Covariant-contravariant simulation and conformance simulation generalize plain simulation and try to capture the fact that it is not always the case that "the larger the number of behaviors, the better". We have previously studied their logical characterizations and in this paper we present the axiomatizations of the preorders defined by the new simulation relations and their induced equivalences. The interest of our results lies in the fact that the axiomatizations help us to know the new simulations better, understanding in particular the role of the contravariant characteristics and their interplay with the covariant ones; moreover, the axiomatizations provide us with a powerful tool to (algebraically) prove results of the corresponding semantics. But we also consider our results interesting from a metatheoretical point of view: the fact that the covariant-contravariant simulation equivalence is indeed ground axiomatizable when there is no action that exhibits both a covariant and a contravariant behaviour, but becomes non-axiomatizable whenever we have together actions of that kind and either covariant or contravariant actions, offers us a new subtle example of the narrow border separating axiomatizable and non-axiomatizable semantics. We expect that by studying these examples we will be able to develop a general theory separating axiomatizable and non-axiomatizable semantics.

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Section: Discussionmentioning

confidence: 99%

“…In [11] we have also briefly presented the logical characterizations of the two semantics. Now that we already know quite well the behaviour of the two new notions of simulation we can give their algebraic presentation.…”

Section: Introduction and Some Related Workmentioning

confidence: 99%

Untitled

Aceto¹,

Sobociński²

2010

Electron. Proc. Theor. Comput. Sci.

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“…A variant of the covariantcontravariant simulation, as described in Fábregas et al (2010), is given in Definition 11, and a helpful notation for conjunctive formulas in Definition 12. Definition 11.…”

Section: Validitymentioning

confidence: 99%

“…The first two results can be straightforwardly obtained using structural induction on f . The proof for (C) can be derived via results in Fábregas et al (2010).…”

Section: Validitymentioning

confidence: 99%

Maximal Synthesis for Hennessy-Milner Logic with the Box Modality

Hulst

Reniers

Fokkink

2014

IFAC Proceedings Volumes

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This paper presents a novel approach to adapt a behavioral model in order to satisfy a requirement in Hennessy-Milner Logic, including an additional box modality operator, expressing an invariant formula. Control system synthesis, as defined in this way, retains all noninvalidating behavior, and thereby guarantees maximal permissiveness for supervisory control. This research extends earlier work by embracing a broader synthesized logic, enabling synthesis with respect to invariant formulas for non-deterministic behavioral models. All definitions and proofs in this paper have been computer verified using the Coq proof assistant.

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“…Among them, the notion of simulation is often used to describe the refinement between reactive systems. However, for the systems having generative (active) actions (e.g., input/output (I/O) automata), such notion is inappropriate to describe the refinement relations between these systems [2], [3]. To remedy it, the notion of covariant-contravariant refinement (CC-refinement, for short) is presented in [2], which is a behavioral preorder over LTSs and in which all actions are partitioned into three sorts: covariant, contravariant, and bivariant actions.…”

Section: Introductionmentioning

confidence: 99%

Refinement Modal Logic Based on Finite Approximation of Covariant-Contravariant Refinement

Huang¹

2019

IEEE Access

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The notion of covariant-contravariant refinement (CC-refinement) is a generalization of the notions of bisimulation and refinement, which is coinductively defined to describe behavior relation, i.e., two related processes are required to be always able to provide matched transitions each other. The notion of CC-n-refinement, where n is a natural number, presented in this paper, finitely approximates the notion of CC-refinement through weakening the above-mentioned requirement. A process is said to CC-n-refine another process whenever they can, within n-steps, match the transitions each other, and a CC-n-refinement relation may be considered to be a CC-refinement relation if n is big enough. Based on this kind of finite approximation, this paper presents CC-n-refinement modal logic (nCCRML) obtained from the modal system K by adding CC-n-refinement quantifiers, establishes an axiom system for nCCRML, and explores some important properties of this axiom system: soundness, completeness, and decidability. CC-n-refinement quantifiers can be used to formalize some interesting problems in the field of formal method. INDEX TERMS Approximation, axiom system, covariant-contravariant n-refinement, modal logic.

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Logics for Contravariant Simulations

Cited by 12 publications

References 13 publications

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Maximal Synthesis for Hennessy-Milner Logic with the Box Modality

Refinement Modal Logic Based on Finite Approximation of Covariant-Contravariant Refinement

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