Logic and Computation introductory course:
Non-deterministic Multi-valued Logics.
Non-deterministic multi-valued logics is a recent natural generalization of ordinary multi-valued logics which has been inspired by the idea of non-deterministic computation from Computer Science. In this course we introduce the basic concepts and results related to both ordinary multi-valued logics and their non-deterministic generalizations. We then demonstrate the usefulness of the non-deterministic approach by providing semantics for thousands of non-classical logics, in particular paraconsistent logics, fuzzy logics and other logics for reasoning under uncertainty. Another application which will be described is the construction and characterization of analytic proof systems for a variety of logics, including classical and intuitionistic logics (the relevant proof theoretical concepts will be described in the course). Another application which will be dealt with in the course using the tool of non-deterministic logics is a complete mathematical solution to the famous philosophical "Tonk" problem. The course assumes only a basic background in formal logic.