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Completeness for Coalgebraic Fixpoint Logic
2016
Annual Conference for Computer Science Logic
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Here we address the completeness question for this coalgebraic fixpoint logic µML T . ...
Note that a complete axiomatisation M for basic coalgebraic modal logic, i.e., the logic µML T without the fixpoint operators, was given in [9] . ...
The authors would like to thank the anonymous referees for many useful comments. ...
doi:10.4230/lipics.csl.2016.7
dblp:conf/csl/EnqvistSV16
fatcat:3tcuqtw74jbrxkheocbyhixtu4
Completeness for Coalgebraic Fixpoint Logic
2016
19 Leibniz International Proceedings in Informatics Schloss Dagstuhl-Leibniz-Zentrum für Informatik
unpublished
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It consists of a complete axiomatization for Moss' modality, extended with Kozen's axiom and rule for the fixpoint operators. ...
We introduce an axiomatization for the coalgebraic fixed point logic which was introduced by Venema as a generalization, based on Moss' coalgebraic modality, of the well-known modal mu-calculus. ...
The authors would like to thank the anonymous referees for many useful comments. ...
fatcat:kajlm7bvzjgbfb4myjve5wjc64
Coalgebraic semantics of modal logics: An overview
2011
Theoretical Computer Science
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, expressiveness and complexity in these settings, both for basic languages as well as a number of extensions, such as hybrid languages and fixpoints. ...
Coalgebras can be seen as a natural abstraction of Kripke frames. In the same sense, coalgebraic logics are generalised modal logics. ...
Acknowledgements We thank our colleagues in the field for many lively discussions and the editors of this volume for their continued patience. ...
doi:10.1016/j.tcs.2011.04.023
fatcat:ffi53okdkzeqtbyqt5phjdrfaa
A Coalgebraic Approach to Linear-Time Logics
[chapter]
2014
Lecture Notes in Computer Science
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We extend recent work on defining linear-time behaviour for state-based systems with branching, and propose modal and fixpoint logics for specifying linear-time temporal properties of states in such systems ...
This yields logics for reasoning about quantitative aspects of linear-time behaviour. ...
-We define modal and fixpoint linear-time logics for coalgebras with branching, and provide an alternative relational semantics for these logics that is amenable to model checking. ...
doi:10.1007/978-3-642-54830-7_28
fatcat:fqvo6h7m2ffhletcnnkz5u7wpi
From Lawvere to Brandenburger-Keisler: interactive forms of diagonalization and self-reference
[article]
2010
arXiv
pre-print
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We also outline a general approach to the construction of assumption complete models. ...
We recast it as a fixpoint result, which can be carried out in any regular category, and show how it can be reduced to a relational form of the one-person diagonal argument due to Lawvere. ...
-We analyze the exact logical resources required for our fixpoint version of the BK argument, and show that it can be carried out in regular logic, the fragment of first-order logic comprising sequents ...
arXiv:1006.0992v1
fatcat:zyqsr4etfvgp3adg5dwele7qu4
From Lawvere to Brandenburger-Keisler: Interactive Forms of Diagonalization and Self-reference
[chapter]
2012
Lecture Notes in Computer Science
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-We analyze the exact logical resources required for our fixpoint version of the BK argument, and show that it can be carried out in regular logic, the fragment of first-order logic comprising sequents ...
Powerful general methods are available for finding such fixpoints, as solutions of domain equations [5] or final coalgebras [21] . ...
doi:10.1007/978-3-642-32784-1_1
fatcat:76atx6whdjfplexegqjgnq7ofe
Optimal Satisfiability Checking for Arithmetic $$\mu $$ -Calculi
[chapter]
2019
Green Chemistry and Sustainable Technology
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The coalgebraic µ-calculus provides a generic semantic framework for fixpoint logics with branching types beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. ...
logic, roughly described as the nesting-free next-step fragment of the logic. ...
Soundness and completeness of the algorithm are proved in Sect. 5.
The Coalgebraic µ-Calculus We recall basic definitions in coalgebraic logic [29, 34] and the coalgebraic μcalculus [4] . ...
doi:10.1007/978-3-030-17127-8_16
dblp:conf/fossacs/HausmannS19
fatcat:a532tjzygzez5ctwmsohietthu
EXPTIME Tableaux for the Coalgebraic μ-Calculus
[chapter]
2009
Lecture Notes in Computer Science
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logic with fixpoints. ...
In this paper, we introduce the coalgebraic µ-calculus, an extension of the general (coalgebraic) framework with fixpoint operators. ...
Here, we improve on this situation, not by providing a new complexity result for a specific fixpoint logic, but by providing a generic and uniform treatment of modal fixpoint logics on the basis of coalgebraic ...
doi:10.1007/978-3-642-04027-6_15
fatcat:tdqe46nv6jdp3p6s2sfxu2tjpu
Game-Based Local Model Checking for the Coalgebraic mu-Calculus
2019
International Conference on Concurrency Theory
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The coalgebraic µ-calculus is a generic framework for fixpoint logics with varying branching types that subsumes, besides the standard relational µ-calculus, such diverse logics as the graded µ-calculus ...
In the present work, we give a local model checking algorithm for the coalgebraic µ-calculus using a coalgebraic variant of parity games that runs, under mild assumptions on the complexity of the so-called ...
As a unifying framework for such fixpoint logics beyond relational semantics, the coalgebraic µ-calculus [6] has emerged. ...
doi:10.4230/lipics.concur.2019.35
dblp:conf/concur/HausmannS19
fatcat:2b4524tktjchhkr3v2aybi6qq4
Optimal Satisfiability Checking for Arithmetic μ-Calculi
[article]
2019
arXiv
pre-print
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The coalgebraic μ-calculus provides a generic semantic framework for fixpoint logics with branching types beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. ...
^2) on minimum model size for satisfiable formulas for all coalgebraic μ-calculi, where n is the size of the formula and k its alternation depth. ...
The coalgebraic µ-calculus [4] caters for fixpoint logics within this framework, and essentially covers all mentioned (two-valued) examples as instances. ...
arXiv:1901.04893v1
fatcat:kd5upgd6avev3kdofjxpab4y6y
Subsumption Checking in Conjunctive Coalgebraic Fixpoint Logics
[article]
2014
arXiv
pre-print
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Apart from recovering known results for description logics such as EL and FL0, we obtain new ones for conjunctive fragments of relational and non-relational modal logics with greatest fixpoints. ...
We work in the framework of coalgebraic logic as a unifying semantic setting. ...
Acknowledgments The authors wish to thank Carsten Lutz for useful discussions, and Erwin R. Catesbeiana for unsolicited remarks regarding the absence of unsatisfiable formulas in EL. ...
arXiv:1401.6359v5
fatcat:trxo5hf4a5ec7bk7smprdgwa5y
Canonical Coalgebraic Linear Time Logics
2015
Conference on Algebra and Coalgebra in Computer Science
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We extend earlier work on linear time fixpoint logics for coalgebras with branching, by showing how propositional operators arising from the choice of branching monad can be canonically added to these ...
Another contribution of our work is a reformulation of fixpoint semantics, which applies to any coalgebraic modal logic whose semantics arises from a one-step semantics. ...
A canonical, modular approach to defining maximal (including infinite) traces for coalgebras with branching was proposed in [1] , and linear time coalgebraic fixpoint logics that match this notion of ...
doi:10.4230/lipics.calco.2015.66
dblp:conf/calco/Cirstea15
fatcat:6swfor7dx5cxjjxbi2b4nmsyxe
Quasipolynomial Computation of Nested Fixpoints
[article]
2020
arXiv
pre-print
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While this result is of clear interest in itself, we focus in particular on applications to modal fixpoint logics and games beyond relational semantics. ...
via nested fixpoints of functions that differ substantially from the function for parity games but still can be computed in quasipolynomial time; our result hence implies that model checking for these ...
ambient fixpoint logic of concurrent dynamic logic [49] and Parikh's game logic [46] . ...
arXiv:1907.07020v4
fatcat:k6rhwkj3pbdndp5dffscpaisdu
From Branching to Linear Time, Coalgebraically
2013
Electronic Proceedings in Theoretical Computer Science
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account of the linear-time behaviour of a state in such a coalgebra. ...
We consider state-based systems modelled as coalgebras whose type incorporates branching, and show that by suitably adapting the definition of coalgebraic bisimulation, one obtains a general and uniform ...
[25, Theorem 2.12] ) that for T = P (in which case Rel C,Z is complete lattice), restricting to a finite-state P • F -coalgebra (C, γ) and a finitestate F -coalgebra (D, δ) results in the greatest fixpoint ...
doi:10.4204/eptcs.126.2
fatcat:qcjyc5vvnfgzfpybpc2j67euim
Special Issue: Fixpoints in Computer Science 2000
2002
Journal of Logic and Computation
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For -continuous endofunctors of Set an ordering of a final coalgebra Ì is exhibited which makes Ì a CPO. ...
A major result concerning Temporal Logics (Ì Ä ) is Kamp's theorem which states that the temporal logic over the pair of modalities ÙÒØ Ð Ò since is expressively complete for the first-order fragment of ...
However, whereas least fixpoint semantics works well for SLD-refutations (i.e. is sound and complete), there is no satisfactory (i.e. complete) fixpoint semantics for infinite derivations. ...
doi:10.1093/logcom/12.1.211
fatcat:yowegpu725gxpbpi7eabhc6caa
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