Ratnakirti's ‘Ksanikatva-anumana’ and Topological Logic ‘system TL1’

Dynamic Topological Logic

Dynamic Topological Logic provides a context for studying the confluence of the topological semantics for S4, based on topological spaces rather than Kripke frames; topological dynamics; and temporal logic. In the topological semantics for S4, 2 is interpreted as topological interior: thus S4 can be understood as the logic of topological spaces. Topological dynamics studies the asymptotic prope...

Topological Semantics of Justification Logic

Games for Topological Fixpoint Logic

Topological fixpoint logics are a family of logics that admits topological models and where the fixpoint operators are defined with respect to the topological interpretations. Here we consider a topological fixpoint logic for relational structures based on Stone spaces, where the fixpoint operators are interpreted via clopen sets. We develop a game-theoretic semantics for this logic. First we i...

Topological Reasoning and The Logic of Knowledge

What are fields of mathematics, such as probability theory, point-set topology, and combinatorics, about? When asked this, a mathematician is likely to answer that the field is about various mathematical concepts, or about the consequences of some axioms or other. Although this answer would be adequate for many purposes, it misses a deeper answer that areas of mathematics can be seen as reposit...

Twenty Years of Topological Logic

Topological logics are formal systems for representing and manipulating information about the topological relationships between objects in space. Over the past two decades, these logics have been the subject of intensive research in Artificial Intelligence, under the general rubric of Qualitative Spatial Reasoning. This chapter sets out the mathematical foundations of topological logics, and su...