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Hennessy-Milner Logic with Greatest Fixed Points as a Complete Behavioural Specification Theory [article]

Nikola Beneš, Benoît Delahaye, Uli Fahrenberg, Jan Křetínský, Axel Legay
2013 arXiv   pre-print
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]

Nikola Beneš, Benoît Delahaye, Uli Fahrenberg, Jan Křetínský, Axel Legay
2013 Lecture Notes in Computer Science  
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

Luca Aceto, Anna Ingólfsdóttir
2007 BRICS Report Series  
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

LUCA ACETO, ANNA INGOLFSDOTTIR, PAUL BLAIN LEVY, JOSHUA SACK
2012 Mathematical Structures in Computer Science  
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

Luca Aceto, Anna Ingolfsdottir, Joshua Sack
2009 Electronic Proceedings in Theoretical Computer Science  
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

Davide Sangiorgi
2009 ACM Transactions on Programming Languages and Systems  
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]

Jos C.M. Baeten, Davide Sangiorgi
2014 Handbook of the History of Logic  
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]

Paul Wild, Lutz Schröder
2021 Lecture Notes in Computer Science  
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

Clemens Kupke, Jurriaan Rot, Michael Wagner
2020 Annual Conference for Computer Science Logic  
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

Egidio Astesiano, Alessandro Giovini, Gianna Reggio
1992 Theoretical Computer Science  
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]

Yuxin Deng, Wenjie Du
2011 arXiv   pre-print
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

Clemens Kupke, Dirk Pattinson
2011 Theoretical Computer Science  
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]

Clemens Kupke, Jurriaan Rot
2021 arXiv   pre-print
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

Barbara König, Christina Mika-Michalski, Michael Wagner
2018 International Conference on Concurrency Theory  
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]

Jim de Groot, Helle Hvid Hansen, Alexander Kurz
2020 arXiv   pre-print
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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