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Games and modal mu-calculus [chapter]

Colin Stirling
1996 Lecture Notes in Computer Science  
The resulting 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.  ... 
doi:10.1007/3-540-61042-1_51 fatcat:uid5ycxtq5fv3bxpzyfod6d52i

First-Order Game Logic and Modal Mu-Calculus [article]

Noah Abou El Wafa, André Platzer
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] .  ... 
arXiv:2201.10012v2 fatcat:u3en3eie7fewdm66ueavq7b4sy

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

Thomas Wilke
2001 Bulletin of the Belgian Mathematical Society Simon Stevin  
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.  ...  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.  ... 
doi:10.36045/bbms/1102714178 fatcat:zjl4ze65jja7vobsbjovkphgoe

First-Order Game Logic and Modal Mu-Calculus [article]

Noah Abou El Wafa, André Platzer
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] .  ... 
doi:10.48550/arxiv.2201.10012 fatcat:a5qmvgmna5govea57hgtjqwxci

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

Lauri Hella, Antti Kuusisto, Raine Rönnholm
2020 pre-print
We introduce a new 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.  ... 
doi:10.4204/eptcs.326.6 arXiv:2009.10880v1 fatcat:2c6i7cxk3fbmhibot6yorxewmq

The mu-calculus and Model Checking [chapter]

Julian Bradfield, Igor Walukiewicz
2018 Handbook of Model Checking  
The chapter describes in length the 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  ... 
doi:10.1007/978-3-319-10575-8_26 fatcat:7adhegoggvcjthaa5x5uhfpt24

Recursive Checkonly QVT-R Transformations with General when and where Clauses via the Modal Mu Calculus [chapter]

Julian Bradfield, Perdita Stevens
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 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'.  ... 
doi:10.1007/978-3-642-28872-2_14 fatcat:xt7ud4mzd5bnfcgdvn6kih5lra

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

Julian C. Bradfield
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 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.  ... 
doi:10.7146/brics.v5i53.19499 fatcat:t3btzhwmgvcsreaectbnk36a2q

Fixpoint alternation: arithmetic, transition systems, and the binary tree

J. C. Bradfield
1999 RAIRO - Theoretical Informatics and Applications  
of strict level n 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.  ... 
doi:10.1051/ita:1999122 fatcat:ylhvnxu4fnea3kdz6yutg5xwje

Logics and Games for True Concurrency [article]

Julian Gutierrez
2010 arXiv   pre-print
Such dualities are used to define new 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.  ... 
arXiv:1011.1172v1 fatcat:jmahyvyacffzheloesvuwy25xq

On independence-friendly fixpoint logics

J. C. Bradfield
2004 Philosophia Scientiæ  
We relate it to parity 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.  ... 
doi:10.4000/philosophiascientiae.568 fatcat:vuezjblzpbcadbu6ktxxiq75l4

Model Checking Games for the Quantitative mu-Calculus [article]

Diana Fischer, Erich Grädel, Lukasz Kaiser
2008 arXiv   pre-print
We investigate quantitative extensions of 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.  ... 
arXiv:0802.2871v1 fatcat:lvwg4ryytfebxbgefbbkrj4b3m

HORNSAT, model checking, verification and games [chapter]

Sandeep K. Shukla, Harry B. Hunt, Daniel J. Rosenkrantz
1996 Lecture Notes in Computer Science  
Here we use it to develop model checking algorithms for various fragments of 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.  ... 
doi:10.1007/3-540-61474-5_61 fatcat:kjzqwudy6fb3jbnr3qiozwrqoe

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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