In his well-known paper \How computer should think" ((Be77b]) Belnap argues that four valued semantics is a very suitable setting for computerized reasoning. In this paper we vindicate this thesis by showing that the logical role that the four-valued structure has among Ginsberg's well-known bilattices is similar to the role that the two-valued algebra has among Boolean algebras. Speciically, w...

Axiomatic bases of admissible rules are obtained for fragments of the substructural logic R-mingle. In particular, it is shown that a “modus-ponens-like” rule introduced by Arnon Avron forms a basis for the admissible rules of its implication and implication-fusion fragments, while a basis for the admissible rules of the full multiplicative fragment requires an additional countably infinite set...

Logical systems with classical negation and means for sentential or propositional self-reference involve, in some way, paradoxical statements such as the liar. However, the paradox disappears if one replaces classical by an appropriate non-classical negation such as a paraconsistent one (no paradox arises if the liar is both true and false). We consider a non-Fregean logic which is a revised an...