Non-deterministic Multi-valued Logics--A Tutorial

Non-deterministic multi-valued matrices (Nmatrices) are a new, fruitful and quickly expanding field of research first introduced a few years ago. Since then it has been rapidly developing towards a foundational logical theory and has found numerous applications. The novelty of Nmatrices is in extending the usual many-valued algebraic semantics of logical systems by importing the idea of non-deterministic computations, and allowing the truthvalue of a formula to be chosen non-deterministically out of a given set of options. Nmatrices have proved to be a powerful tool, the use of which preserves all the advantages of ordinary many-valued matrices, but is applicable to a much wider range of logics. Indeed, there are many useful (propositional) non-classical logics, which have no finite multi-valued characteristic matrices, but do have finite Nmatrices, and thus are decidable. In this tutorial we introduce the reader to the concept of Nmatrices, and demonstrate their usefulness by pro...

• Type: Conference
• Year: 2010
• Where: ISMVL
• Authors: Arnon Avron, Anna Zamansky
• Keywords: Foundational Logical Theory, Hardware, ISMVL 2010, Many-valued Algebraic Semantics, Non-deterministic Multi-valued Matrices