What is modal logic

General Topology-I

The Art and Science of Negotiation

Handbook of logic in computer science.

What do you do to start reading dimension theory? Searching the book that you love to read first or find an interesting book that will make you want to read? Everybody has difference with their reason of reading a book. Actuary, reading habit must be from earlier. Many people may be love to read, but not a book. It's not fault. Someone will be bored to open the thick book with small words to read. In more, this is the real condition. So do happen probably with this dimension theory.

Aspects of topology: On dimension theory

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Lattices of intermediate and cylindric modal logics

We introduce pairwise Stone spaces as a bitopological generalisation of Stone spaces – the duals of Boolean algebras – and show that they are exactly the bitopological duals of bounded distributive lattices. The category PStone of pairwise Stone spaces is isomorphic to the category Spec of spectral spaces and to the category Pries of Priestley spaces. In fact, the isomorphism of Spec and Pries is most naturally seen through PStone by first establishing that Pries is isomorphic to PStone, and then showing that PStone is isomorphic to Spec. We provide the bitopological and spectral descriptions of many algebraic concepts important in the study of distributive lattices. We also give new bitopological and spectral dualities for Heyting algebras, thereby providing two new alternatives to Esakia's duality.

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Bitopological duality for distributive lattices and heyting algebras

Algebras axiomatized entirely by rank 1 axioms are algebras for a functor and thus the free algebras can be obtained by a direct limit process. Dually, the final coalgebras can be obtained by an inverse limit process. In order to explore the limits of this method we look at Heyting algebras which have mixed rank 0-1 axiomatizations. We will see that Heyting algebras are special in that they are almost rank 1 axiomatized and can be handled by a slight variant of the rank 1 coalgebraic methods.

Finitely generated free Heyting algebras via Birkhoff duality and coalgebra

We introduce a new topological semantics for evidence, evidence-based justifications, belief and knowledge. This setting builds on the evidence model framework of van Benthem and Pacuit, as well as our own previous work on a topological semantics for Stalnaker's doxastic-epistemic axioms. We prove completeness, decidability and finite model property for the associated logics, and we apply this setting to analyze key issues in Epistemology: "no false lemma" Gettier examples, misleading defeaters, and undefeated justification versus undefeated belief.

Justified Belief and the Topology of Evidence

Algebras axiomatized entirely by rank 1 axioms are algebras for a functor and
thus the free algebras can be obtained by a direct limit process. Dually, the
final coalgebras can be obtained by an inverse limit process. In order to
explore the limits of this method we look at Heyting algebras which have mixed
rank 0-1 axiomatizations. We will see that Heyting algebras are special in that
they are almost rank 1 axiomatized and can be handled by a slight variant of
the rank 1 coalgebraic methods.

Nick Bezhanishvili

Papers

Lattices of intermediate and cylindric modal logics

Bitopological duality for distributive lattices and heyting algebras

Finitely generated free Heyting algebras via Birkhoff duality and coalgebra

Justified Belief and the Topology of Evidence

Finitely generated free Heyting algebras via Birkhoff duality and coalgebra