The modal logic of continuous functions on cantor space

The modal logic of continuous functions on cantor space

Let L be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality and a temporal modality , understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language L by interpreting L in dynamic topological systems, i.e. ordered pairs 〈X, f 〉, where X is a topological space and f is a continuous function on X. Artemov...

The modal logic of continuous functions on the rational numbers

Let L ◦ be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality and a temporal modality ◦, understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language L ◦ by interpreting L ◦ in dynamic topological systems, i.e., ordered pairs 〈X, f 〉, where X is a topological space and f is a continuous function on X ...

Propositional logic of continuous transformations in Cantor space

A well-known axiomatization of the basic notions of general topology in the form of propositional logic S4 was given by McKinsey and (for mathematically more interesting spaces like real line, real plane etc.) by McKinsey and Tarski. If only open sets are considered instead of arbitrary sets, one gets intuitionistic logic. L.E.J. Brower (of fixed point theorem) who created the background for th...

On the modal logic of the iterated Cantor derivative and finitary operations on topological spaces

where Ω is an ordinal (or the class of ordinals) and F is a family of (unary or finitary) operations on a topological space. The natural semantics is as follows: the modality 〈α〉 is interpreted by the αth iteration of the Cantor derivative, while the modalities 〈F 〉 and (F−1) are interpreted by the image and the preimage of the operation F . We describe logics in this language that are sound w....

On images of continuous functions from a compact manifold to Euclidean space