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Graded consequence: an institution theoretic study. (English) Zbl 1388.03068

Summary: We develop a general study of graded consequence (of many-valued logic) in an institution theoretic (in the sense of J. A. Goguen and R. M. Burstall [Lect. Notes Comput. Sci. 164, 221–256 (1984; Zbl 0543.68021)]) style. This means both syntax and semantics are considered fully abstract, as well as the satisfaction between them. Our approach contrasts to other approaches on many-valued logic in that it is a multi-signature one, in the spirit of institution theory. We consider graded consequence at three different conceptual levels: entailment, semantic, and closure operators, and explore several interpretations between them. We also study logical connectors and quantifiers both at the entailment and semantic level, compactness and soundness properties.

MSC:

03G30 Categorical logic, topoi
03B50 Many-valued logic

Citations:

Zbl 0543.68021
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References:

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