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Hennessy-Milner Logic with Greatest Fixed Points as a Complete Behavioural Specification Theory
[article]
2013
arXiv
pre-print
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In this paper we provide translations between the logical formalism of Hennessy-Milner logic with greatest fixed points and the behavioural formalism of disjunctive modal transition systems. ...
The logical approach makes use of specifications given as formulae of temporal or modal logics and relies on efficient model checking algorithms; the behavioural approach exploits various equivalence or ...
Hennessy-Milner logic with greatest fixed points (νHML) is equivalent to ν-calculus, i.e. µ-calculus with greatest fixed points only. ...
arXiv:1306.0741v1
fatcat:kqqtq22zj5gz7b6c5frbop57l4
Hennessy-Milner Logic with Greatest Fixed Points as a Complete Behavioural Specification Theory
[chapter]
2013
Lecture Notes in Computer Science
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In this paper we provide translations between the logical formalism of Hennessy-Milner logic with greatest fixed points and the behavioural formalism of disjunctive modal transition systems. ...
The logical approach makes use of specifications given as formulae of temporal or modal logics and relies on efficient model checking algorithms; the behavioural approach exploits various equivalence or ...
Hennessy-Milner logic with greatest fixed points (νHML) is equivalent to ν-calculus, i.e. µ-calculus with greatest fixed points only. ...
doi:10.1007/978-3-642-40184-8_7
fatcat:vfmzytwymjdp3kzwwce37ttune
Characteristic Formulae: From Automata to Logic
2007
BRICS Report Series
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This paper discusses the classic notion of characteristic formulae for processes using variations on Hennessy-Milner logic as the underlying logical specification language. ...
It is shown how to characterize logically (states of) finite labelled transition systems modulo bisimilarity using a single formula in Hennessy-Milner logic with recursion. ...
The Logic L ν The logic L ν is a real-time version of Hennessy-Milner Logic with greatest fixed points that stems from [29] . ...
doi:10.7146/brics.v14i2.21925
fatcat:vqjt3zcvqrf6noxi4s7axtfbqa
Characteristic formulae for fixed-point semantics: a general framework
2012
Mathematical Structures in Computer Science
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that are defined in terms of fixed points of suitable functions. ...
This study provides a general view of characteristic formulae that are expressed in terms of logics with a facility for the recursive definition of formulae. ...
Joshua Sack has been further supported by a grant from Reykjavik University's Development Fund. Paul Blain Levy has been supported by the ESPRC Advanced Research Fellowship EP/E056091/1. ...
doi:10.1017/s0960129511000375
fatcat:sby6aet74bfzjaaysby66pkcke
Characteristic Formulae for Fixed-Point Semantics: A General Framework
2009
Electronic Proceedings in Theoretical Computer Science
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that are defined in terms of fixed points of suitable functions. ...
This study provides a general view of characteristic formulae that are expressed in terms of logics with a facility for the recursive definition of formulae. ...
Joshua Sack has been further supported by a grant from Reykjavik University's Development Fund. Paul Blain Levy has been supported by the ESPRC Advanced Research Fellowship EP/E056091/1. ...
doi:10.4204/eptcs.8.1
fatcat:voq3znlxlndkvhhp4ajqvww2fm
On the origins of bisimulation and coinduction
2009
ACM Transactions on Programming Languages and Systems
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As all finitely branching models are saturated, van Benthem's construction also yields the familiar Hennessy-Milner Theorem for modal logics [Hennessy and Milner 1985] (an earlier version is [Hennessy ...
He then defines bisimilarity as the greatest fixed point of the functional, and derives the bisimulation proof method from the theory of greatest fixed points. ...
doi:10.1145/1516507.1516510
fatcat:m5uvypq4xnbqxclecr3eadpwsu
Concurrency Theory: A Historical Perspective on Coinduction and Process Calculi
[chapter]
2014
Handbook of the History of Logic
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He then defines bisimilarity as the greatest fixed point of the functional, and derives the bisimulation proof method from the theory of greatest fixed points. ...
The authors note that F is monotone over a complete lattice, hence it has a greatest fixed point (the largest f -admissible relation). ...
doi:10.1016/b978-0-444-51624-4.50009-5
fatcat:o4fvjxxppvf2pkpjkcpj3erfym
A Quantified Coalgebraic van Benthem Theorem
[chapter]
2021
Lecture Notes in Computer Science
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AbstractThe classical van Benthem theorem characterizes modal logic as the bisimulation-invariant fragment of first-order logic; put differently, modal logic is as expressive as full first-order logic ...
transition systems as in the existing examples, e.g. also metric transition systems; and we generalize from real-valued to quantale-valued behavioural distances, e.g. nondeterministic behavioural distances ...
A Quantified Coalgebraic van Benthem Theorem ...
doi:10.1007/978-3-030-71995-1_28
fatcat:tjktmyewcrgpdmhyd64xgbvtrq
Expressive Logics for Coinductive Predicates
2020
Annual Conference for Computer Science Logic
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The approach is illustrated with logics characterising similarity, divergence and a behavioural metric on automata. ...
The classical Hennessy-Milner theorem says that two states of an image-finite transition system are bisimilar if and only if they satisfy the same formulas in a certain modal logic. ...
If p is a CLat ∧ -fibration, then γ * • B X has a greatest fixed point ν(γ * • B X ), which is also the greatest post-fixed point. It is referred to as the coinductive predicate defined by B on γ. ...
doi:10.4230/lipics.csl.2020.26
dblp:conf/csl/KupkeR20
fatcat:fxdsbiiedrgshgqbeyasc7gina
Observational structures and their logic
1992
Theoretical Computer Science
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The main result of the paper proves that for any family of pattern sets representing the simulation law the corresponding modal observational logic is a Hennessy-Milner logic: two observable objects are ...
More importantly, we show how to associate with an observational structure various modal observational logics, related to sets of experiment schemas, that we call pattern sets. ...
In general, as it is well known, gw is not a fixed point for FOG. ...
doi:10.1016/0304-3975(92)90186-j
fatcat:lgdxisxd7jer7fvjzjsvnbtw44
Logical, Metric, and Algorithmic Characterisations of Probabilistic Bisimulation
[article]
2011
arXiv
pre-print
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Specifically, we extend the Hennessy-Milner logic and the modal mu-calculus with a new modality, resulting in an adequate and an expressive logic for probabilistic bisimilarity, respectively. ...
The correspondence of the lifting operation and the Kantorovich metric leads to a natural characterisation of bisimulations as pseudometrics which are post-fixed points of a monotone function. ...
theory that are formulated in the right way. ...
arXiv:1103.4577v1
fatcat:z626tecr4ndqdokqr3cvosn2gm
Coalgebraic semantics of modal logics: An overview
2011
Theoretical Computer Science
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Coalgebras can be seen as a natural abstraction of Kripke frames. In the same sense, coalgebraic logics are generalised modal logics. ...
We argue that coalgebras unify the semantics of a large range of different modal logics (such as probabilistic, graded, relational, conditional) and discuss unifying approaches to reasoning at this level ...
As a consequence, we cannot expect the Hennessy-Milner property to hold without a restriction on the branching degree. ...
doi:10.1016/j.tcs.2011.04.023
fatcat:ffi53okdkzeqtbyqt5phjdrfaa
Expressive Logics for Coinductive Predicates
[article]
2021
arXiv
pre-print
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The approach is illustrated with logics characterising similarity, divergence and a behavioural metric on automata. ...
The classical Hennessy-Milner theorem says that two states of an image-finite transition system are bisimilar if and only if they satisfy the same formulas in a certain modal logic. ...
Thereby, that approach relies on the Knaster-Tarski fixed point theorem, constructing the greatest fixed point as the largest post-fixed point. ...
arXiv:2006.12465v4
fatcat:idu3sha5yvbntjlc4ihq6tu5a4
(Metric) Bisimulation Games and Real-Valued Modal Logics for Coalgebras
2018
International Conference on Concurrency Theory
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For this logic we show a quantitative version of the Hennessy-Milner theorem. ...
Behavioural equivalences can be characterized via bisimulations, modal logics and spoiler-defender games. ...
Acknowledgements We thank Paul Wild, Lutz Schröder and Dirk Pattinson for inspiring discussions on fuzzy modal logic, and in particular on preservation of total boundedness. ...
doi:10.4230/lipics.concur.2018.37
dblp:conf/concur/KonigM18
fatcat:s74ixnbr6vcoxc5ptxqhbpnjgq
Logic-Induced Bisimulations
[article]
2020
arXiv
pre-print
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The main technical result is a Hennessy-Milner type theorem which states that, under certain conditions, logical equivalence implies ρ-bisimilarity. ...
We define a new logic-induced notion of bisimulation (called ρ-bisimulation) for coalgebraic modal logics given by a logical connection, and investigate its properties. ...
As a first example, we give a translation between Hennessy-Milner logic and trace logic. ...
arXiv:2008.09238v1
fatcat:yztwjqd5qzd4xobklxdg4w3esy
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