INSTYTUT MATEMATYKI
Uniwersytet Śląski
40-007 Katowice, ul. Bankowa 14

tel/fax (032) 2582976
e-mail:im@ux2.math.us.edu.pl


Wojciech Dzik

 

 
MODAL LOGIC, AUTOMATA and. LANGUAGES

 Modal logics and temporal logics, algebraic models (Boolean algebras with operators) and relatinal models (Kripke models),  duality between them.

Automata and languages  Finite state  automata. Minimal automata.  Characterizations of regular languages: Kleene theorem, Myhill –Nerode theorem. 
Remarks on formal languages
. Regular languages. Context-free languages and grammars. Chomsky normal forms. Pushdown automata. Chomsky hierarchy.
Co-algebras: Kripke frames and Automata 

 References:
P. Blackburn, M. de Rijke, Y. Venema, Modal Logic, (Cambridge: Cambridge University Press: 2001)
P. Blackburn, Johan van Benthem, and Frank Wolter, Handbook of Modal Logic, 
Dordrecht: Elsevier: 2006,  in Internet: http://www.csc.liv.ac.uk/~frank/MLHandbook/
K. Devlin,  Goodbye, Descartes,
The End of Logic and the Search for a New Cosmology of the Mind,  John Wiley & Sons, 1997, (In Polish - Żegnaj, Kartezjuszu: rozstanie z logiką  …, Wa-wa 1999)
J. E. Hopcroft, J.D. Ullman „Wprowadzenie do teorii automatów, języków i obliczeń.
PWN Warszawa 1994
K. Swirydowicz, Podstawy Logiki Modalnej,  Wydawnictwo UAM, Poznań 2004,

Lectures in  Finland

"Algebraic and logical methods for computer science"University of Turku,Finland, Department of Information Technology
September 2009
"Galois Connections and Modal Logics"
University of Turku,Finland, Department of Information Technology
March 2010


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