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Games and modal mu-calculus
[chapter]

1996
*
Lecture Notes in Computer Science
*

The resulting

doi:10.1007/3-540-61042-1_51
fatcat:uid5ycxtq5fv3bxpzyfod6d52i
*games*have signi cance, we believe, within*and*outside of concurrency theory. ... For this purpose we also de ne second-order propositional*modal*logic to contrast xed points*and*second-order quanti ers. ... Acknowledgement: Thanks to Faron Moller*and*Perdita Stevens for comments on an earlier draft. ...##
###
First-Order Game Logic and Modal Mu-Calculus
[article]

2022
*
arXiv
*
pre-print

*mu*-

*calculus*, the

*modal*

*mu*-

*calculus*for hybrid systems. ... This paper investigates first-order

*game*logic

*and*first-order

*modal*

*mu*-

*calculus*, which extend their propositional

*modal*logic counterparts with first-order

*modalities*of interpreted effects such as variable ... General connections between

*modal*-

*calculus*

*and*

*games*have been observed [10] , but

*modal*-

*calculus*is inexpressible in

*game*logic in the propositional case [2] . ...

##
###
Alternating tree automata, parity games, and modal {$\mu$}-calculus

2001
*
Bulletin of the Belgian Mathematical Society Simon Stevin
*

A coherent exposition of the connection of alternating tree automata

doi:10.36045/bbms/1102714178
fatcat:zjl4ze65jja7vobsbjovkphgoe
*and**modal*µ-*calculus*is given, advocating an automaton model specifically tailored for working with*modal*µ-*calculus*. ... A coherent exposition of the connection of alternating tree automata*and**modal*µ-*calculus*is given, advocating an automaton model specifically tailored for working with*modal*µ-*calculus*. ...*Modal*µ-*Calculus**Modal*µ-*calculus*is*modal*logic augmented by operators for least*and*greatest fixed points. ...##
###
First-Order Game Logic and Modal Mu-Calculus
[article]

2022

*mu*-

*calculus*, the

*modal*

*mu*-

*calculus*for hybrid systems. ... This paper investigates first-order

*game*logic

*and*first-order

*modal*

*mu*-

*calculus*, which extend their propositional

*modal*logic counterparts with first-order

*modalities*of interpreted effects such as variable ... General connections between

*modal*-

*calculus*

*and*

*games*have been observed [10] , but

*modal*-

*calculus*is inexpressible in

*game*logic in the propositional case [2] . ...

##
###
Bounded Game-Theoretic Semantics for Modal Mu-Calculus and Some Variants
[article]

2020
pre-print

We introduce a new

doi:10.4204/eptcs.326.6
arXiv:2009.10880v1
fatcat:2c6i7cxk3fbmhibot6yorxewmq
*game*-theoretic semantics (GTS) for the*modal**mu*-*calculus*. ... The novel*games*offer alternative approaches to various constructions in the framework of the*mu*-*calculus*. ... The work of Raine Rnnholm was partially supported by Jenny*and*Antti Wihuri Foundation. We thank the anonymous referees for comments*and*additional references. ...##
###
The mu-calculus and Model Checking
[chapter]

2018
*
Handbook of Model Checking
*

The chapter describes in length the

doi:10.1007/978-3-319-10575-8_26
fatcat:7adhegoggvcjthaa5x5uhfpt24
*game*characterization of the semantics of the*mu*-*calculus*. ... Then it develops the notion of*modal*automaton: an automaton-based model behind the*mu*-*calculus*. ... model-checking*and*automata emptiness, 18 model-checking via*games*, 16, 18 model-checking:*mu*-*calculus*, 18 monadic second-order logic, 36 MSOL, 36 MSOL relation to the*mu*-*calculus*, 37*mu*-*calculus*, 2*mu*-*calculus*...##
###
Recursive Checkonly QVT-R Transformations with General when and where Clauses via the Modal Mu Calculus
[chapter]

2012
*
Lecture Notes in Computer Science
*

In this paper we show how to interpret checkonly QVT-R -or any future model transformation language structured similarly -in the

doi:10.1007/978-3-642-28872-2_14
fatcat:xt7ud4mzd5bnfcgdvn6kih5lra
*modal**mu**calculus**and*use its well-understood model-checking*game*to lift ... We demonstrate*and*justify a corresponding extension to the rules of the QVT-R*game*. ... The first author is partly supported by UK EPSRC grant EP/G012962/1 'Solving Parity*Games**and**Mu*-Calculi'. ...##
###
Page 4447 of Mathematical Reviews Vol. , Issue 99g
[page]

1999
*
Mathematical Reviews
*

This paper solves a long-standing open question regarding the interplay between the syntax

*and*the semantics of the*modal**mu*-*calculus*. ... The*calculus*in question results from extending positive*modal*logic by the least*and*greatest fixed point operators. ...##
###
Fixpoint Alternation: Arithmetic, Transition Systems, and the Binary Tree

1998
*
BRICS Report Series
*

We provide an elementary proof of the fixpoint alternation<br />hierarchy in arithmetic, which in turn allows us to simplify the proof of the

doi:10.7146/brics.v5i53.19499
fatcat:t3btzhwmgvcsreaectbnk36a2q
*modal**mu*-*calculus*alternation hierarchy. ... Preliminaries*Modal**mu*-*calculus*We assume some familiarity with the*modal**mu*-*calculus*, so in this section we give brief definitions to establish notations*and*conventions. ... examples of strict level n*modal**mu*-*calculus*formulae. ...##
###
Fixpoint alternation: arithmetic, transition systems, and the binary tree

1999
*
RAIRO - Theoretical Informatics and Applications
*

of strict level n

doi:10.1051/ita:1999122
fatcat:ylhvnxu4fnea3kdz6yutg5xwje
*modal**mu*-*calculus*formulae. ... PRÉLIMINAIRES*MODAL**MU*-*CALCULUS*We assume some familiarity with the*modal**mu*-*calculus*, so in this section we give brief définitions to establish notations*and*conventions. ...##
###
Logics and Games for True Concurrency
[article]

2010
*
arXiv
*
pre-print

Such dualities are used to define new

arXiv:1011.1172v1
fatcat:jmahyvyacffzheloesvuwy25xq
*mu*-calculi*and*logic*games*for the analysis of concurrent systems with partial order semantics. ... Since these*mu*-calculi*and*logic*games*generalise well-known fixpoint logics*and**game*-theoretic decision procedures for concurrent systems with interleaving semantics, the results herein give some of the ... Fixpoints*and*the*Modal**Mu*-*Calculus*. ...##
###
On independence-friendly fixpoint logics

2004
*
Philosophia Scientiæ
*

We relate it to parity

doi:10.4000/philosophiascientiae.568
fatcat:vuezjblzpbcadbu6ktxxiq75l4
*games*of imperfect information,*and*show its application to defining independence-friendly*modal**mu*-calculi. ... Nous la relions aux jeux de paritéà information imparfaite, et nous montrons une applicationà la définition d'un*mu*-calcul*modal*fait pour l'indépendance. ...*mu*-*calculus*, a popular*and*interesting temporal logic -see [Bradfield & Stirling 2001] for an introductory survey of*modal**mu*-*calculus*. ...##
###
Model Checking Games for the Quantitative mu-Calculus
[article]

2008
*
arXiv
*
pre-print

We investigate quantitative extensions of

arXiv:0802.2871v1
fatcat:lvwg4ryytfebxbgefbbkrj4b3m
*modal*logic*and*the*modal**mu*-*calculus*,*and*study the question whether the tight connection between logic*and**games*can be lifted from the qualitative logics to ... , the values of quantitative parity*games*are definable in the quantitative*mu*-*calculus*. ... logic ML, the temporal logics LTL*and*CTL,*and*the*modal*µ-*calculus*L µ , to quantitative formalisms. ...##
###
HORNSAT, model checking, verification and games
[chapter]

1996
*
Lecture Notes in Computer Science
*

Here we use it to develop model checking algorithms for various fragments of

doi:10.1007/3-540-61474-5_61
fatcat:kjzqwudy6fb3jbnr3qiozwrqoe
*modal**mu*-*calculus*. ... This general methodology leads naturally to algorithms, that are local [25, 19] , on the fly [28, 11, 13, 5]*and*incremental [24] . ... Ravi,*and*Moshe Vardi for helpful discussions. ...##
###
Page 1303 of Mathematical Reviews Vol. , Issue 96c
[page]

1996
*
Mathematical Reviews
*

*mu*-

*calculus*

*and*Biichi tree automata. ... The

*modal*

*mu*-

*calculus*is a logical formalism obtained by ex- 03D Recursion theory 96c:03086 tending propositional

*modal*logic by operators of the least

*and*the greatest fixed points. ...

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