This course provides an introduction to the broad and exciting field of substructural logics. We will see how techniques from the different traditions of relevant logic, the Lambek Calculus, linear logic, combinatory logic and modal logic can inform our study of logical consequence. The course will cover proof theory (both natural deduction and Gentzen-style consecution systems), semantics (including Routley-Meyer relational models, operational models, phase spaces and coherence spaces), and decidability and complexity results. The focus will always remain on the applicability of these techniques to different problem domians (from linguistics, computation and philosophy) and the way that different traditions can inform and enrich one another.
The unit will require only a basic understanding of proof theory and semantics for classical propositional logic, though a background in any of linguistics, computation or philosophical logic will benefit any prospective student.
Department of Philosophy