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

M3 - Conference contribution

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 -