We deal with the fragment of modal logic consisting of implications of formulas built up from
the variables and the constant 'true'by conjunction and diamonds only. The weaker …

A dynamical system is a pair (X,f), where X is a topological space and f:X→X is continuous.
Kremer observed that the language of propositional linear temporal logic can be interpreted …

Several interesting applications of provability logic in proof theory made use of a polymodal
logic GLP due to Giorgi Japaridze. This system, although decidable, is not very easy to …

Provability logic concerns the study of modality\Box□ as provability in formal systems such
as Peano Arithmetic. A natural, albeit quite surprising, topological interpretation of provability …

We introduce the logics GLP Λ, a generalization of Japaridze's polymodal provability logic
GLP ω where Λ is any linearly ordered set representing a hierarchy of provability operators …

We study the transfinite sequence of topologies on the ordinal numbers that is obtained
through successive closure under Cantor's derivative operator on sets of ordinals, starting …

For any ordinal Λ, we can define a polymodal logic GLPΛ, with a modality [ξ] for each ξ< Λ.
These represent provability predicates of increasing strength. Although GLPΛ has no Kripke …

For each $ n\in\mathbb {N} $, let $[n]\phi $ mean" the sentence $\phi $ is true in all $\Sigma_
{n+ 1} $-correct transitive sets." Assuming G\" odel's axiom $ V= L $, we prove the following …

Provability logics are modal or polymodal systems designed for modeling the behavior of
Gödel's provability predicate and its natural extensions. If Λ is any ordinal, the Gödel-Löb …

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 …