Graded consequence: an institution theoretic study
نویسندگان
چکیده
منابع مشابه
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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Equivalences and translations between consequence relations abound in logic. The notion of equivalence can be defined syntactically, in terms of translations of formulas, and order-theoretically, in terms of the associated lattices of theories. W. Blok and D. Pigozzi proved in [2] that the two definitions coincide in the case of an algebraizable sentential deductive system. A refined treatment ...
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Fuzzy Logic a la Pavelka has been reintroduced here in terms of consequence relation instead of consequence operator. Metalogical notions like, consistency and inconsistency are proposed as graded notions. The relationship between consequence relation and inconsistency, both fuzzy here, is studied. Another metalogical notion viz., equivalence of two sets of formulae that originates from Tarski ...
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ژورنال
عنوان ژورنال: Soft Computing
سال: 2014
ISSN: 1432-7643,1433-7479
DOI: 10.1007/s00500-014-1231-y