TY - GEN
T1 - Non-deterministic multi-valued logics - A tutorial
AU - Avron, Arnon
AU - Zamansky, Anna
PY - 2010
Y1 - 2010
N2 - Non-deterministic multi-valued matrices (Nmatri-ces) 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.
AB - Non-deterministic multi-valued matrices (Nmatri-ces) 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.
UR - http://www.scopus.com/inward/record.url?scp=77955319878&partnerID=8YFLogxK
U2 - 10.1109/ISMVL.2010.18
DO - 10.1109/ISMVL.2010.18
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AN - SCOPUS:77955319878
SN - 9780769540245
T3 - Proceedings of The International Symposium on Multiple-Valued Logic
SP - 53
EP - 60
BT - ISMVL 2010 - 40th IEEE International Symposium on Multiple-Valued Logic
T2 - 40th IEEE International Symposium on Multiple-Valued Logic, ISMVL 2010
Y2 - 26 May 2010 through 28 May 2010
ER -