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An institutional approach to positive coalgebraic logic

Adriana Balan, Alexander Kurz, Jiří Velebil
2015 Journal of Logic and Computation  
Velebil An institutional approach to positive coalgebraic logic WADT2014 The institution of Set-coalgebraic logic Sentences -The natural transformation δ provides one-step semantics -To pass to the global  ...  Velebil An institutional approach to positive coalgebraic logic WADT2014 The institution of Set-coalgebraic logic Satisfaction relation -T -model (coalgebra) X c −→ TX -L-algebra of subsets LPX δ −→ PT  ...  Poset-functors and their coalgebras T : Poset → Poset locally monotone functor T -coalgebras Partially ordered set of states X = (X , ≤) Examples -ordered automata: X → X A × 2, with A the (discrete) input  ... 
doi:10.1093/logcom/exv074 fatcat:knrtahnj7jgybmxayswhkjzaw4

Logics Admitting Final Semantics [chapter]

Alexander Kurz
2002 Lecture Notes in Computer Science  
A logic for coalgebras is said to admit nal semantics i | up to some technical requirements|all de nable classes contain a fully abstract nal coalgebra.  ...  It is shown that a logic admits nal semantics i the formulas of the logic are preserved under coproducts (disjoint unions) and quotients (homomorphic images).  ...  Acknowledgements I am indebted to Alexandru Baltag for suggesting to consider logics with a global diamond, to Tobias Schr oder for his example showing that a Kripke model admitting no non-trivial endomorphisms  ... 
doi:10.1007/3-540-45931-6_17 fatcat:ndk5qa4rhzbazg5cb4p5j3l67a

An institution of modal logics for coalgebras

Corina Cıˆrstea
2006 The Journal of Logic and Algebraic Programming  
The resulting logical framework is shown to be an institution, whose specifications and specification morphisms admit final and respectively cofree models. 4 The category-theoretic definition of relations  ...  as monic spans is used here. 5 For C = Set S , such an endofunctor can be used to specify the structure associated to an S-indexed collection of coalgebraic types. 6 Each such γ provides a particular  ...  Acknowlegements The author is grateful to the two anonymous referees for their valuable comments and suggestions.  ... 
doi:10.1016/j.jlap.2005.09.004 fatcat:t4ckpapfp5cohh43uak66yhgfe

Fibred Coalgebraic Logic and Quantum Protocols

Daniel Marsden
2014 Electronic Proceedings in Theoretical Computer Science  
We extend the semantics of coalgebraic logic to this setting, and prove that this extension respects behavioural equivalence.  ...  We show how properties of the semantics of modalities are preserved under composition operations, and then apply the calculational aspect of our logic to produce an expressive set of modalities for reasoning  ...  Acknowledgements I would like to thank Andreas Döring and Samson Abramsky for their feedback and suggestions.  ... 
doi:10.4204/eptcs.171.9 fatcat:2flur2wl2befxidk7hoitrsjw4

Modal Logic for Rewriting Theories

Dirk Pattinson
2000 Electronical Notes in Theoretical Computer Science  
This allows us on the one hand to use "off the shelf" logics for coalgebras to specify and, on the other hand, to verify properties of rewriting programs and to obtain results about the expressive power  ...  We view models of rewrite theories enriched with observations coalgebraically.  ...  Differing from [17, 5] , the approach we propose is based on coalgebraic modal logic.  ... 
doi:10.1016/s1571-0661(05)80145-8 fatcat:qrnt2zzfrfhm7ggtwglhsvcm3q

Institutionalising Many-Sorted Coalgebraic Modal Logic

Corina Cîrstea
2002 Electronical Notes in Theoretical Computer Science  
4] describes a modal logic for coalgebras of certain polynomial endofunctors on Set. This logic is here generalised to endofunctors on categories of sorted sets.  ...  The structure of the endofunctors considered is then exploited in order to define ways of moving from (coalgebras of) one endofunctor to (coalgebras of) another, and to equip them with translations between  ...  Acknowledgements The author would like to thank the anonymous referees for their comments and suggestions.  ... 
doi:10.1016/s1571-0661(04)80359-1 fatcat:gylsbajqrzhl7borqkavuscr7i

A coalgebraic equational approach to specifying observational structures

Corina Cı̂rstea
2002 Theoretical Computer Science  
A coalgebraic, equational approach to the speciÿcation of observational structures allowing for a choice in the result type of observations is presented.  ...  Finally, the approach is extended in order to account for the availability of a ÿxed data universe in the speciÿcation of such structures.  ...  Acknowledgements The author wishes to thank Andrea Corradini for a useful discussion on an earlier version of this paper, and the two anonymous referees for their valuable comments.  ... 
doi:10.1016/s0304-3975(01)00020-2 fatcat:lm4etvphwnd75o6dxolf5diohu

Observational logic, constructor-based logic, and their duality

Michel Bidoit, Rolf Hennicker, Alexander Kurz
2003 Theoretical Computer Science  
In this paper we ÿrst reconsider the observational logic institution which provides a logical framework for dealing with observability.  ...  Then we develop in a completely analogous way the constructor-based logic institution which formalizes a novel treatment of reachability.  ...  To justify that our constructor-based approach indeed yields an institution the order of arguments is completely analogous to the one used in Section 2 for the observational logic institution.  ... 
doi:10.1016/s0304-3975(02)00865-4 fatcat:mcemmgzykbewbm5zlkh6arkcxe

Complementation of Coalgebra Automata [chapter]

Christian Kissig, Yde Venema
2009 Lecture Notes in Computer Science  
Our construction works for automata operating on coalgebras for an arbitrary standard set functor which preserves weak pullbacks and restricts to finite sets.  ...  This coalgebraic perspective on automata lays foundation to a universal theory of automata operating on infinite models of computation.  ...  We are grateful to Alessandra Palmigiano and one of the anonymous reviewers for suggesting a simplification of a definition, and to the anonymous reviewers in general for their comments.  ... 
doi:10.1007/978-3-642-03741-2_7 fatcat:rtildjippnbxxnqnberkyeolwy

Page 2324 of Mathematical Reviews Vol. , Issue 2002D [page]

2002 Mathematical Reviews  
“This work puts forward an application of intuitionistic modal logic that exploits the model-theoretic strength of the constructive approach.  ...  Then it is shown that this result specializes to Moss’ coalgebraic logic (with propositional variables added) and to in- finitary modal logic: the modally definable classes of Kripke frames are those closed  ... 

Coalgebraic theories of sequences in PVS

U Hensel
1999 Journal of Logic and Computation  
Hopefully, it will help to convey the view that coalgebraic data types should form an intrinsic part of (future) languages for programming and reasoning.  ...  Therefore, some suggestions for an appropriate syntax for coalgebraic datatypes are included.  ...  Acknowledgements We thank Marco Devillers and David Gri oen for stimulating discussions, and for pushing us to substantiate our claims about the suitability of the coalgebraic approach.  ... 
doi:10.1093/logcom/9.4.463 fatcat:kdp6sm3dezgtdi76bckrrlauaa

A modal proof theory for final polynomial coalgebras

David Friggens, Robert Goldblatt
2006 Theoretical Computer Science  
An infinitary proof theory is developed for modal logics whose models are coalgebras of polynomial functors on the category of sets.  ...  The canonical model method from modal logic is adapted to construct a final coalgebra for any polynomial functor.  ...  Acknowledgements The authors acknowledge support from a Logic and Computation programme funded by the New Zealand Institute of Mathematics and its Applications, and thank the referees for their helpful  ... 
doi:10.1016/j.tcs.2005.11.041 fatcat:ts6bjtp6kbca3lb4gdlkevealu

Completeness of the finitary Moss logic

Clemens Kupke, Alexander Kurz, Yde Venema
2008 Advances in Modal Logic  
We give a sound and complete derivation system for the valid formulas in the finitary version of Moss' coalgebraic logic, for coalgebras of arbitrary type.  ...  The research programme of Coalgebraic Logic is to extend this uniform approach to logics for specifying and reasoning about the behavior of coalgebras.  ...  The main idea of the completeness proof is based on the Stone duality approach to coalgebraic logic and, as a byproduct, we also see how Moss' language fits into this approach.  ... 
dblp:conf/aiml/KupkeKV08 fatcat:62e7uh22zzambno3b2j5x3eu7a

Algebraic–coalgebraic specification in CoCasl

Till Mossakowski, Lutz Schröder, Markus Roggenbach, Horst Reichel
2006 The Journal of Logic and Algebraic Programming  
Moreover, it provides syntactic sugar for an observer-indexed modal logic that allows e.g. expressing fairness properties.  ...  CoCasl allows the nested combination of algebraic datatypes and coalgebraic process types.  ...  Acknowledgements The authors would like to thank the participants of an informal CoCasl and observability meeting, Hubert Baumeister, Michel Bidoit, Rolf Hennicker, Bernd Krieg-Brückner, Don Sannella,  ... 
doi:10.1016/j.jlap.2005.09.006 fatcat:okuywxa2cjcpji2san2ozfnjfi

Algebraic-Coalgebraic Specification in CoCasl [chapter]

Till Mossakowski, Horst Reichel, Markus Roggenbach, Lutz Schröder
2003 Lecture Notes in Computer Science  
Moreover, it provides syntactic sugar for an observer-indexed modal logic that allows e.g. expressing fairness properties.  ...  CoCasl allows the nested combination of algebraic datatypes and coalgebraic process types.  ...  Acknowledgements The authors would like to thank the participants of an informal CoCasl and observability meeting, Hubert Baumeister, Michel Bidoit, Rolf Hennicker, Bernd Krieg-Brückner, Don Sannella,  ... 
doi:10.1007/978-3-540-40020-2_22 fatcat:rwzoyted2bhcbks3kqc6p7pk6q
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