Non-deterministic multiple-valued structures

Arnon Avron*, Iddo Lev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

151 Scopus citations

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.

Original languageEnglish
Pages (from-to)241-261
Number of pages21
JournalJournal of Logic and Computation
Volume15
Issue number3
DOIs
StatePublished - Jun 2005

Funding

FundersFunder number
Israel Academy of Sciences and Humanities
Israel Science Foundation

    Keywords

    • Automated reasoning
    • Compactness
    • Decidability
    • Multi-valued logics
    • Non-determinism
    • Paraconsistent reasoning
    • Uncertainty

    Fingerprint

    Dive into the research topics of 'Non-deterministic multiple-valued structures'. Together they form a unique fingerprint.

    Cite this