Graded consequence: an institution theoretic study

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Graded consequence: an institution theoretic study

We develop a general study of graded consequence (of many-valued logic) in an institution theoretic (in the sense of Goguen and Burstall) 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 multisignature one, in the spirit of institution theory. We co...

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In this paper some basic aspects of the theory of graded consequence are reconsidered, based on many results that appeared since the inception of graded consequences in 1986. Relationships of the notion of graded consequence with the notions of consequence in many-valued and fuzzy logics are discussed. Following this, a detailed study is carried out on the necessary conditions that follow from ...

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M A ⇔df (∀M) [ (∀B ∈ M)(M B) ⇒ M A ]. Thus consequence is transmission of truth from the premisses to the conclusion, where ‘transmission’ is understood in the simple declarative sense of classical implication: if the premisses are true (in a model-theoretic structure), then so is the conclusion. This means in particular that truth is conceptually prior to consequence, as the latter is explaine...

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ژورنال

عنوان ژورنال: Soft Computing

سال: 2014

ISSN: 1432-7643,1433-7479

DOI: 10.1007/s00500-014-1231-y