Logic Column 15: Coalgebras and Their Logics

This article describes recent work on the topic of specifying properties of transition systems. By giving a suitably abstract description of transition systems as coalgebras, it is possible to derive logics for capturing properties of these transition systems in an elegant way.

[1]  Jan J. M. M. Rutten,et al.  Universal coalgebra: a theory of systems , 2000, Theor. Comput. Sci..

[2]  Bart Jacobs,et al.  Objects and Classes, Co-Algebraically , 1995, Object Orientation with Parallelism and Persistence.

[3]  M. Bonsangue,et al.  Topological Dualities in Semantics , 1996 .

[4]  Robert Goldblatt,et al.  Observational ultraproducts of polynomial coalgebras , 2003, Ann. Pure Appl. Log..

[5]  E. Moggi,et al.  A fully-abstract model for the /spl pi/-calculus , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[6]  Brian A. Davey,et al.  An Introduction to Lattices and Order , 1989 .

[7]  Dirk Pattinson,et al.  An Introduction to the Theory of Coalgebras , 2003 .

[8]  Jan Komenda,et al.  Decentralized supervisory control with coalgebra , 2003, 2003 European Control Conference (ECC).

[9]  Dirk Pattinson Expressive Logics for Coalgebras via Terminal Sequence Induction , 2004, Notre Dame J. Formal Log..

[10]  Samson Abramsky,et al.  A Domain Equation for Bisimulation , 1991, Inf. Comput..

[11]  Farhad Arbab,et al.  A Coinductive Calculus of Component Connectors , 2002, WADT.

[12]  Bart Jacobs,et al.  Duality Beyond Sober Spaces: Topological Spaces and Observation Frames , 1995, Theor. Comput. Sci..

[13]  Marcelo P Fiore,et al.  Topology via Logic , 1999 .

[14]  R. Goldblatt Metamathematics of modal logic , 1974, Bulletin of the Australian Mathematical Society.

[15]  Stefan Milius,et al.  The Category Theoretic Solution of Recursive Program Schemes , 2005, CALCO.

[16]  Jan J. M. M. Rutten,et al.  Automata and Coinduction (An Exercise in Coalgebra) , 1998, CONCUR.

[17]  Bart Jacobs,et al.  The Coalgebraic Class Specification Language CCSL , 2001, J. Univers. Comput. Sci..

[18]  Erik P. de Vink,et al.  Bisimulation for Probabilistic Transition Systems: A Coalgebraic Approach , 1997, Theor. Comput. Sci..

[19]  Alexander Kurz,et al.  Operations and equations for coalgebras , 2005, Mathematical Structures in Computer Science.

[20]  Grant Palmer,et al.  Objects and Classes , 2004 .

[21]  Stefan Friedrich,et al.  Topology , 2019, Arch. Formal Proofs.

[22]  M. Stone The theory of representations for Boolean algebras , 1936 .

[23]  Samson Abramsky,et al.  Domain Theory in Logical Form , 1991, LICS.

[24]  Alexander Kurz A Co-Variety-Theorem for Modal Logic , 1998, Advances in Modal Logic.

[25]  Bart Jacobs,et al.  The LOOP Compiler for Java and JML , 2001, TACAS.

[26]  Jan J. M. M. Rutten,et al.  A tutorial on coinductive stream calculus and signal flow graphs , 2005, Theor. Comput. Sci..

[27]  Marcello M. Bonsangue,et al.  Pi-Calculus in Logical Form , 2007, 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007).

[28]  Gordon D. Plotkin,et al.  Towards a mathematical operational semantics , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.

[29]  Samson Abramsky,et al.  Domain theory , 1995, LICS 1995.

[30]  Robert Goldblatt,et al.  A modal proof theory for final polynomial coalgebras , 2006, Theoretical Computer Science.

[31]  A. Tarski,et al.  Boolean Algebras with Operators. Part I , 1951 .

[32]  Martin Rö,et al.  From modal logic to terminal coalgebras , 2001, Theor. Comput. Sci..

[33]  Erik P. de Vink,et al.  A hierarchy of probabilistic system types , 2003, CMCS.

[34]  Erik P. de Vink,et al.  Control flow semantics , 1996 .

[35]  Yde Venema,et al.  Closure properties of coalgebra automata , 2005, 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05).

[36]  F. Bartels,et al.  On Generalised Coinduction and Probabilistic Specification Formats , 2004 .

[37]  Bart Jacobs,et al.  Many-Sorted Coalgebraic Modal Logic: a Model-theoretic Study , 2001, RAIRO Theor. Informatics Appl..

[38]  Erik P. de Vink,et al.  Bisimulation for Probabilistic Transition Systems: A Coalgebraic Approach , 1999, Theor. Comput. Sci..

[39]  Bartek Klin The Least Fibred Lifting and the Expressivity of Coalgebraic Modal Logic , 2005, CALCO.

[40]  Samson Abramsky,et al.  A Cook's Tour of the Finitary Non-Well-Founded Sets , 2011, We Will Show Them!.

[41]  S. Shelah,et al.  Annals of Pure and Applied Logic , 1991 .

[42]  Markus Roggenbach,et al.  Algebraic-coalgebraic specification in CoCasl , 2006, J. Log. Algebraic Methods Program..

[43]  M. de Rijke,et al.  Modal Logic , 2001, Cambridge Tracts in Theoretical Computer Science.

[44]  Marcello M. Bonsangue,et al.  Duality for Logics of Transition Systems , 2005, FoSSaCS.

[45]  Jan J. M. M. Rutten Coinductive Counting with Weighted Automata , 2003, J. Autom. Lang. Comb..

[46]  Helle Hvid Hansen,et al.  A Coalgebraic Perspective on Monotone Modal Logic , 2004, CMCS.

[47]  B. Jacobs,et al.  A tutorial on (co)algebras and (co)induction , 1997 .

[48]  Chris Brink,et al.  A paradigm for program semantics - power structures and duality , 2001, Studies in logic, language and information.

[49]  I. Stark,et al.  A fully abstract domain model for the /spl pi/-calculus , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[50]  Alexander Kurz,et al.  Ultrafilter Extensions for Coalgebras , 2005, CALCO.

[51]  Erwin Engeler,et al.  Languages with expressions of infinite length , 1966 .

[52]  Lawrence S. Moss,et al.  Coalgebraic Logic , 1999, Ann. Pure Appl. Log..

[53]  Marcello M. Bonsangue,et al.  Presenting Functors by Operations and Equations , 2006, FoSSaCS.

[54]  Dirk Pattinson,et al.  Coalgebraic modal logic: soundness, completeness and decidability of local consequence , 2003, Theor. Comput. Sci..

[55]  Corina Cîrstea On Expressivity and Compositionality in Logics for Coalgebras , 2003, CMCS.

[56]  Lutz Schröder,et al.  Expressivity of coalgebraic modal logic: The limits and beyond , 2008, Theor. Comput. Sci..

[57]  Yde Venema Automata and fixed point logic: A coalgebraic perspective , 2006, Inf. Comput..

[58]  Peter Aczel,et al.  Non-well-founded sets , 1988, CSLI lecture notes series.

[59]  Martín Hötzel Escardó,et al.  Synthetic Topology: of Data Types and Classical Spaces , 2004, DTMPP.

[60]  Alexander Kurz,et al.  Specifying Coalgebras with Modal Logic , 1998, CMCS.

[61]  Bartek Klin,et al.  An Abstract Coalgebraic Approach to Process Equivalence for Well-Behaved Operational Semantics , 2004 .

[62]  Samson Abramsky,et al.  Handbook of logic in computer science. , 1992 .

[63]  Corina Cîrstea,et al.  Modular Construction of Modal Logics , 2004, CONCUR.

[64]  Horst Reichel,et al.  An approach to object semantics based on terminal co-algebras , 1995, Mathematical Structures in Computer Science.

[65]  H. Gumm Elements Of The General Theory Of Coalgebras , 1999 .

[66]  Yde Venema,et al.  Stone Coalgebras , 2004, CMCS.

[67]  Alessandra Palmigiano,et al.  A coalgebraic view on positive modal logic , 2004, Theor. Comput. Sci..

[68]  A. Tarski,et al.  Boolean Algebras with Operators , 1952 .

[69]  Alexander Kurz,et al.  Algebraic Semantics for Coalgebraic Logics , 2004, CMCS.

[70]  Hans-Jörg Schek,et al.  Object Orientation with Parallelism and Persistence , 1996 .

[71]  Lawrence S. Moss,et al.  Final coalgebras for functors on measurable spaces , 2006, Inf. Comput..