Automata and Algebras in Categories
Automata and Algebras in Categories
Coalgebraic modal logic of finite rank
Mathematical Structures in Computer Science
PSPACE Bounds for Rank-1 Modal Logics
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Free modal algebras: a coalgebraic perspective
CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
The goldblatt-thomason theorem for coalgebras
CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
Beyond rank 1: algebraic semantics and finite models for coalgebraic logics
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Distributive lattice-structured ontologies
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Sheaves, Games, and Model Completions: A Categorical Approach to Nonclassical Propositional Logics
Sheaves, Games, and Model Completions: A Categorical Approach to Nonclassical Propositional Logics
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We use coalgebraic methods to describe finitely generated free Heyting algebras. Heyting algebras are axiomatized by rank 0-1 axioms. In the process of constructing free Heyting algebras we first apply existing methods to weak Heyting algebras--the rank 1 reducts of Heyting algebras--and then adjust them to the mixed rank 0-1 axioms. On the negative side, our work shows that one cannot use arbitrary axiomatizations in this approach. Also, the adjustments made for the mixed rank axioms are not just purely equational, but rely on properties of implication as a residual. On the other hand, the duality and coalgebra perspectives do allow us, in the case of Heyting algebras, to derive Ghilardi's (Ghilardi, 1992) powerful representation of finitely generated free Heyting algebras in a simple, transparent, and modular way using Birkhoff duality for finite distributive lattices.