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Non-deterministic Multi-valued Logics--A Tutorial

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2 Author(s)
Arnon Avron ; Sch. of Comput. Sci., Tel-Aviv Univ., Ramat-Aviv, Israel ; Anna Zamansky

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 truth-value 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 providing modular non-deterministic semantics for a well-known family of logics for reasoning under uncertainty.

Published in:

2010 40th IEEE International Symposium on Multiple-Valued Logic

Date of Conference:

26-28 May 2010