TY - JOUR AB - Non-deterministic Multiple-valued Structures Arnon Avron and Iddo Lev 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. Characterisations of some Preferential Paraconsistent Consequence Relations Jonathan Ben-Naim The theory of preferential consequence relations has been investigated extensive ly in the classical context, where copies of classical valuations serve as the terms of the preference relation. The first purpose of the present paper is to extend the theory to preferential consequence relations in certain three/four-valued co ntexts, well-known as the paraconsistent logics and . We give characterizations of several families of preferential consequence relations TI - Forthcoming Papers JF - Journal of Logic and Computation DO - 10.1093/logcom/exi023 DA - 2005-04-01 UR - https://www.deepdyve.com/lp/oxford-university-press/forthcoming-papers-QSsmtOOAz3 SP - 239 EP - 240 VL - 15 IS - 2 DP - DeepDyve ER -