Artificial Intelligence
Fundamenta Informaticae - Topics in Logic, Philosophy and Foundations of Mathematics and Computer Science. In Recognition of Professor Andrzej Grzegorczyk
Uniform Interpolation, Bisimulation Quantifiers, and Fixed Points
Logic, Language, and Computation
Uniform Interpolation by Resolution in Modal Logic
JELIA '08 Proceedings of the 11th European conference on Logics in Artificial Intelligence
Free Heyting algebras: revisited
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Connecting many-sorted structures and theories through adjoint functions
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Löb's logic meets the µ-calculus
Processes, Terms and Cycles
Fundamenta Informaticae - Topics in Logic, Philosophy and Foundations of Mathematics and Computer Science. In Recognition of Professor Andrzej Grzegorczyk
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This book investigates propositional intuitionistic and modal logics from an entirely new point of view, covering quite recent and sometimes yet unpublished results. It mainly deals with the structure of the category of finitely presented Heyting and modal algebras, relating it both with proof theoretic and model theoretic facts: existence of model completions, amalgamability, Beth definability, interpretability of second order quantifiers and uniform interpolation, definability of dual connectives like difference, projectivity, etc. are among the numerous topics which are covered. Dualities and sheaf representations are the main techniques in the book, together with Ehrenfeucht-Fraiss games and bounded bisimulations. The categorical instruments employed are rich, but a specific extended Appendix explains to the reader all concepts used in the text, starting from the very basic definitions to what is needed from topos theory. Audience: The book is addressed to a large spectrum of professional logicians, from such different areas as modal logics, categorical and algebraic logic, model theory and universal algebra.