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

2013
*
arXiv
*
pre-print

In this paper we provide translations between the

arXiv:1306.0741v1
fatcat:kqqtq22zj5gz7b6c5frbop57l4
*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. ...##
###
Hennessy-Milner Logic with Greatest Fixed Points as a Complete Behavioural Specification Theory
[chapter]

2013
*
Lecture Notes in Computer Science
*

In this paper we provide translations between the

doi:10.1007/978-3-642-40184-8_7
fatcat:vfmzytwymjdp3kzwwce37ttune
*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. ...##
###
Characteristic Formulae: From Automata to Logic

2007
*
BRICS Report Series
*

This paper discusses the classic notion of characteristic formulae for processes using variations on

doi:10.7146/brics.v14i2.21925
fatcat:vqjt3zcvqrf6noxi4s7axtfbqa
*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] . ...##
###
Characteristic formulae for fixed-point semantics: a general framework

2012
*
Mathematical Structures in Computer Science
*

that are defined in terms of

doi:10.1017/s0960129511000375
fatcat:sby6aet74bfzjaaysby66pkcke
*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. ...##
###
Characteristic Formulae for Fixed-Point Semantics: A General Framework

2009
*
Electronic Proceedings in Theoretical Computer Science
*

that are defined in terms of

doi:10.4204/eptcs.8.1
fatcat:voq3znlxlndkvhhp4ajqvww2fm
*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. ...##
###
On the origins of bisimulation and coinduction

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*. ...

##
###
Concurrency Theory: A Historical Perspective on Coinduction and Process Calculi
[chapter]

2014
*
Handbook of the History of Logic
*

He then defines bisimilarity

doi:10.1016/b978-0-444-51624-4.50009-5
fatcat:o4fvjxxppvf2pkpjkcpj3erfym
*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). ...##
###
A Quantified Coalgebraic van Benthem Theorem
[chapter]

2021
*
Lecture Notes in Computer Science
*

AbstractThe classical van Benthem theorem characterizes modal

doi:10.1007/978-3-030-71995-1_28
fatcat:tjktmyewcrgpdmhyd64xgbvtrq
*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 ...##
###
Expressive Logics for Coinductive Predicates

2020
*
Annual Conference for Computer Science Logic
*

The approach is illustrated

doi:10.4230/lipics.csl.2020.26
dblp:conf/csl/KupkeR20
fatcat:fxdsbiiedrgshgqbeyasc7gina
*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. ...##
###
Observational structures and their logic

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

doi:10.1016/0304-3975(92)90186-j
fatcat:lgdxisxd7jer7fvjzjsvnbtw44
*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. ...##
###
Logical, Metric, and Algorithmic Characterisations of Probabilistic Bisimulation
[article]

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. ...

##
###
Coalgebraic semantics of modal logics: An overview

2011
*
Theoretical Computer Science
*

Coalgebras can be seen

doi:10.1016/j.tcs.2011.04.023
fatcat:ffi53okdkzeqtbyqt5phjdrfaa
*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. ...##
###
Expressive Logics for Coinductive Predicates
[article]

2021
*
arXiv
*
pre-print

The approach is illustrated

arXiv:2006.12465v4
fatcat:idu3sha5yvbntjlc4ihq6tu5a4
*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*. ...##
###
(Metric) Bisimulation Games and Real-Valued Modal Logics for Coalgebras

2018
*
International Conference on Concurrency Theory
*

For this

doi:10.4230/lipics.concur.2018.37
dblp:conf/concur/KonigM18
fatcat:s74ixnbr6vcoxc5ptxqhbpnjgq
*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. ...##
###
Logic-Induced Bisimulations
[article]

2020
*
arXiv
*
pre-print

The main technical result is

arXiv:2008.09238v1
fatcat:yztwjqd5qzd4xobklxdg4w3esy
*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*. ...
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