出版社：Philosophy Department, University of Melbourne
摘要：The plurivalent logics considered in Graham Priest's recent paper of that name can be thought of as logics determined by matrices (in the `logical ma- trix' sense) whose underlying algebras are power algebras (a.k.a. complex algebras, or `globals'), where the power algebra of a given algebra has as elements subsets of the universe of the given algebra, and the power matrix of a given matrix has has the power algebra of the latter's algebra as its underlying algebra, with its designated elements being selected in a natu- ral way on the basis of those of the given matrix. The present discussion stresses the continuity of Priest's work on the question of which matrices determine consequence relations (for propositional logics) which remain un- aected on passage to the consequence relation determined by the power matrix of the given matrix with the corresponding (long-settled) question in equational logic as to which identities holding in an algebra continue to hold in its power algebra. Both questions are sensitive to a decision as to whether or not to include the empty set as an element of the power algebra, and our main fo cus will be on the contrast, when it is included, between the power matrix semantics (derived from the two-element Boolean matrix) and the four-valued DunnBelnap semantics for rst-degree entailment (à la Anderson and Belnap) in terms of sets of classical values (subsets of {T, F }, that is), in which the empty set gures in a somewhat dierent way, as Priest had remarked his 1984 study, `Hyper-contradictions', in which what we are calling the power matrix construction rst appeared
