@article{10beaffa952a44f4b081c25899d908ad,
title = "Non-deterministic multiple-valued structures",
abstract = "The ordinary concept of a multiple-valued matrix is generalized by introducing non-deterministic matrices (Nmatrices), in which non-deterministic computations of truth-values are allowed. It is shown that some important logics for reasoning under uncertainty can be characterized by finite Nmatrices (and so they are decidable), although they have only infinite characteristic ordinary (deterministic) matrices. A generalized compactness theorem that applies to all finite Nmatrices is then proved. Finally, a strong connection is established between the admissibility of the cut rule in canonical Gentzen-type propositional systems, non-triviality of such systems, and the existence of sound and complete non-deterministic two-valued semantics for them. This connection is used for providing a complete solution for the old 'Tonk' problem of Prior.",
keywords = "Automated reasoning, Compactness, Decidability, Multi-valued logics, Non-determinism, Paraconsistent reasoning, Uncertainty",
author = "Arnon Avron and Iddo Lev",
note = "Funding Information: This research was supported by The Israel Science Foundation founded by The Israel Academy of Sciences and Humanities.",
year = "2005",
month = jun,
doi = "10.1093/logcom/exi001",
language = "אנגלית",
volume = "15",
pages = "241--261",
journal = "Journal of Logic and Computation",
issn = "0955-792X",
publisher = "Oxford University Press",
number = "3",
}