Neighborhood models generalize the well-known relational models, or Kripke models, for
modal logic. Although the idea underlying neighborhood models is implicit in the seminal …

Spectral spaces are a class of topological spaces. They are a tool linking algebraic
structures, in a very wide sense, with geometry. They were invented to give a functional …

In 6 it is shown that if we interpret modal diamond as the derived set operator of a
topological space (the so-called d-semantics), then the modal logic of all topological spaces …

Both early analytic philosophy and the branch of mathematics now known as topology were
gestated and born in the early part of the 20th century. It is not well recognized that there …

In this chapter we overview the main structures of epistemic and doxastic logic. We start by
discussing the most celebrated models for epistemic logic, ie, epistemic Kripke structures …

This volume is dedicated to Leo Esakia's contributions to the theory of modal and
intuitionistic systems. Leo Esakia was one of the pioneers in develo** duality theory for …

The finite model property (FMP) in weakly transitive tense logics is explored. Let S=[wK t 4, K
t 4] be the interval of tense logics between wK t 4 and K t 4. We introduce the modal formula t …

In this chapter we study modal logics of topological spaces in the combined language with
the derivational modality and the difference modality. We give axiomatizations and prove …

Abstract The McKinsey axiom (M)□◊ p→◊□ p has a local first-order correspondent on the
class of all weakly transitive frames WT. It globally corresponds to Lemmon's condition (m∞) …

We prove that each countable rooted K4-frame is a d-morphic image of a subspace of the
space Q of rational numbers. From this we derive that each modal logic over K4 …