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Partiality and its dual. (English) Zbl 0988.03012
This paper is worth reading. A number of fundamental logical systems are under consideration, here in their semantical interconnection. The semantical approach explores allowing truth-value assignments to be undetermined or “partial” (no truth values) and overdetermined or “inconsistent” (both truth values), thus returning to an investigation of the four-valued semantics that was initiated by the author in the sixties.

MSC:
03B22 Abstract deductive systems
03B50 Many-valued logic
03B53 Paraconsistent logics
03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
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