PLEXUS · Philosophical, Logical, and Experimental routes to substructurality

Philosophical, Logical, and Experimental routes to substructurality

OBJECTIVES Classical Logic (the logic devised by Frege at the birth of modern mathematical logic) provides a sharp characterisation of our reasoning in abstract fields like mathematics. However, Classical Logic seems to be inadequate in relation to several phenomena such as vagueness, conditionals or paradoxes. Substructural logics – logics where some structural rule, like weakening, contraction or exchange, can fail – are alternatives to Classical Logic that have attracted a lot of attention by logicians in the last decade. The EU-funded PLEXUS project will study these logics with particular emphasis on "radically substructural logics" – non-transitive and non-reflexive logics. Specifically, PLEXUS will investigate the main philosophical challenges raised by radically substructural logics, their proof-theoretic and model theoretic characterisations and their logico-linguistic applications. The overall goal of PLEXUS is articulated into three main research objectives: Objective 1. Philosophical Foundations: PLEXUS will investigate the major philosophical challenges raised by non-transitive and non-reflexive substructural logics. Objective 2. Logic: PLEXUS will advance knowledge of the field of substructural logics by developing new proof-theoretic and model-theoretic characterizations of radically substructural logics. Objective 3. The Metainferences Inventory & Metainferences Prover: PLEXUS seeks to design and validate a psychometric tool (i.e., the Metainferences Inventory) which would allow us to measure naïve speakers' preferences on different questions about radical substructurality. Complementary to this research, PLEXUS will extend existing techniques of automated reasoning to the logics covered by the project, focusing particularly on the decision of validity for metainferences.

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