Title: Constructive and Intermediate Fuzzy Logics

Abstract: We present recent work developing relational semantics for Fuzzy / substructural logics. This work takes algebraic representation results of residuated lattices and extracts a generalisation of Kripke’s Famous semantics for Intuitionistic logic and extensions (alias Intermediate logics), to fuzzy analogues such as GBLewf (aka Intuitionistic Lukasiewicz logic) and Hajek’s BL. Our current work looks at a couple of special cases which are particularly interesting, namely Intuitionistic Lukasiewicz logic with Weak Excluded Middle and what we term Fuzzy Smetanovich logic. The non-fuzzy variants of these systems have connections to logic programming and computability theory, raising questions about what a fuzzy theory of computability look like.

Bio: Dr Andrew Lewis-Smith obtained his doctorate in Computer Science from the Theoretical Computer Science Research Group at the Queen Mary University of London. He then held a few postdoctoral positions before becoming University Teaching Associate at the University of Sheffield, followed by Lecturer at the University of the West of Scotland and now Middlesex. Dr Lewis-Smith has supervised both MSc and BSc students, taught at King’s College London and QMUL in Mathematics, Computer Science and Neuroscience programmes, conducted research across several disciplines and various technical work on contracts at KCL and QMUL whilst PhD student (and afterward). He is a core member of the London Logic Forum.

(This talk is a joint event with the SETA Research Group)