Weak Completeness of Coalgebraic Dynamic Logics

Hansen, Helle Hvid; Kupke, Clemens

doi:10.4204/eptcs.191.9

Cited by 8 publications

(7 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore we believe that our game logic automata have the potential to help us understand a wider class of automata for families of dynamic logics such as coalgebraic dynamic logics [14] or many-valued dynamic logics as described in [21] or for a combination of these frameworks.…”

Section: Resultsmentioning

confidence: 99%

Parity Games and Automata for Game Logic

Hansen

Kupke

Marti

et al. 2018

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Abstract. Parikh's game logic is a PDL-like fixpoint logic interpreted on monotone neighbourhood frames that represent the strategic power of players in determined two-player games. Game logic translates into a fragment of the monotone µ-calculus, which in turn is expressively equivalent to monotone modal automata. Parity games and automata are important tools for dealing with the combinatorial complexity of nested fixpoints in modal fixpoint logics, such as the modal µ-calculus. In this paper, we (1) discuss the semantics a of game logic over neighbourhood structures in terms of parity games, and (2) use these games to obtain an automata-theoretic characterisation of the fragment of the monotone µ-calculus that corresponds to game logic. Our proof makes extensive use of structures that we call syntax graphs that combine the ease-of-use of syntax trees of formulas with the flexibility and succinctness of automata. They are essentially a graph-based view of the alternating tree automata that were introduced by Wilke in the study of modal µ-calculus.

show abstract

Section: Resultsmentioning

confidence: 99%

Parity Games and Automata for Game Logic

Hansen

Kupke

Marti

et al. 2018

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…Over multirelational models, intersection of the accessibility relations corresponds to pointwise intersection of neighbourhood sets. 20 In sum, monotonic models (using the exact semantic clause), arbitrary models (using the monotonic semantic clause), and multirelational models (using the multi-relational semantic clause) can all be used to interpret the same logic of pooling modalities.…”

Section: The Monotonic Semantic Clausementioning

confidence: 99%

“…[33,38]. In [20,21], operations on monotonic neighbourhood models are studied from an abstract, algebraic viewpoint, giving rise to highly generic completeness results. 6 However, notwithstanding these important achievements, the counterpart of intersections of accessibility relations for neighbourhood semantics is largely unknown.…”

Section: Introductionmentioning

confidence: 99%

Pooling Modalities and Pointwise Intersection: Semantics, Expressivity, and Dynamics

Putte

Klein

2022

J Philos Logic

View full text Add to dashboard Cite

We study classical modal logics with pooling modalities, i.e. unary modal operators that allow one to express properties of sets obtained by the pointwise intersection of neighbourhoods. We discuss salient properties of these modalities, situate the logics in the broader area of modal logics (with a particular focus on relational semantics), establish key properties concerning their expressive power, discuss dynamic extensions of these logics and provide reduction axioms for the latter.

show abstract

“…More generally, we believe this approach can be used to provide cut-free complete proof systems for coalgebraic µcalculi [20], [21], and for coalgebraic dynamic logics [22]. Also, there are many fragments of the modal µ-calculus that could be studied by similar techniques.…”

Section: B Future Researchmentioning

confidence: 99%

Completeness for Game Logic

Enqvist

Hansen²,

Kupke

et al. 2019

2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

Self Cite

View full text Add to dashboard Cite

Game logic was introduced by Rohit Parikh in the 1980s as a generalisation of propositional dynamic logic (PDL) for reasoning about outcomes that players can force in determined 2-player games. Semantically, the generalisation from programs to games is mirrored by moving from Kripke models to monotone neighbourhood models. Parikh proposed a natural PDL-style Hilbert system which was easily proved to be sound, but its completeness has thus far remained an open problem.In this paper, we introduce a cut-free sequent calculus for game logic, and two cut-free sequent calculi that manipulate annotated formulas, one for game logic and one for the monotone µ-calculus, the variant of the polymodal µ-calculus where the semantics is given by monotone neighbourhood models instead of Kripke structures. We show these systems are sound and complete, and that completeness of Parikh's axiomatization follows. Our approach builds on recent ideas and results by Afshari & Leigh (LICS 2017) in that we obtain completeness via a sequence of proof transformations between the systems. A crucial ingredient is a validity-preserving translation from game logic to the monotone µ-calculus.

show abstract

Weak Completeness of Coalgebraic Dynamic Logics

Cited by 8 publications

References 20 publications

Parity Games and Automata for Game Logic

Parity Games and Automata for Game Logic

Pooling Modalities and Pointwise Intersection: Semantics, Expressivity, and Dynamics

Completeness for Game Logic

Contact Info

Product

Resources

About