Graded consequence: an institution theoretic study (abstract)
We develop a general study of graded consequence (of many-valued
logic) in an institution theoretic (in the sense of Goguen and
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
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.
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