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Completeness for Coalgebraic Fixpoint Logic

Sebastian Enqvist, Fatemeh Seifan, Yde Venema, Marc Herbstritt
2016 Annual Conference for Computer Science Logic  
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

Sebastian Enqvist, Fatemeh Seifan, Yde Venema, F Seifan@uva, Nl
2016 19 Leibniz International Proceedings in Informatics Schloss Dagstuhl-Leibniz-Zentrum für Informatik   unpublished
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

Clemens Kupke, Dirk Pattinson
2011 Theoretical Computer Science  
, 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]

Corina Cîrstea
2014 Lecture Notes in Computer Science  
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]

Samson Abramsky, Jonathan Zvesper
2010 arXiv   pre-print
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]

Samson Abramsky, Jonathan Zvesper
2012 Lecture Notes in Computer Science  
-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]

Daniel Hausmann, Lutz Schröder
2019 Green Chemistry and Sustainable Technology  
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]

Corina Cîrstea, Clemens Kupke, Dirk Pattinson
2009 Lecture Notes in Computer Science  
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

Daniel Hausmann, Lutz Schröder, Michael Wagner
2019 International Conference on Concurrency Theory  
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]

Daniel Hausmann, Lutz Schröder
2019 arXiv   pre-print
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]

Daniel Gorín, Lutz Schröder
2014 arXiv   pre-print
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

Corina Cirstea, Marc Herbstritt
2015 Conference on Algebra and Coalgebra in Computer Science  
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]

Daniel Hausmann, Lutz Schröder
2020 arXiv   pre-print
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

Corina Cirstea
2013 Electronic Proceedings in Theoretical Computer Science  
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  
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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