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Connecting bilattice theory with multivalued logic

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Genito D., Gerla G.

Logic and Logical Philosophy

2014

vol. 23

issue 1

15–45

This is an exploratory paper whose aim is to investigate the potentialities of bilattice theory for an adequate definition of the deduction apparatus for multi-valued logic. We argue that bilattice theory enables us to obtain a nice extension of the graded approach to fuzzy logic. To give an example, a completeness theorem for a logic based on Boolean algebras is proved.

Vagueness and Formal Fuzzy Logic: Some Criticisms

75%

Gerla G.

Logic and Logical Philosophy

2017

vol. 26

issue 4

431–460

In the common man reasoning the presence of vague predicates is pervasive and under the name “fuzzy logic in narrow sense” or “formal fuzzy logic” there are a series of attempts to formalize such a kind of phenomenon. This paper is devoted to discussing the limits of these attempts both from a technical point of view and with respect the original and principal task: to define a mathematical model of the vagueness. For example, one argues that, since vagueness is necessarily connected with the intuition of the continuum, we have to look at the order-based topology of the interval [0,1] and not at the discrete topology of the set {0,1}. In accordance, in switching from classical logic to a logic for the vague predicates, we cannot avoid the use of the basic notions of real analysis as, for example, the ones of “approximation“, “convergence“, “continuity“. In accordance, instead of defining the compactness of the logical consequence operator and of the deduction operator in terms of finiteness, we have to define it in terms of continuity. Also, the effectiveness of the deduction apparatus has to be defined by using the tools of constructive real analysis and not the one of recursive arithmetic. This means that decidability and semi-decidability have to be defined by involving effective limit processes and not by finite steps stopping processes.

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2 Logic and Logical Philosophy

2 Gerla G.

1 Genito D.

1 2017

1 2014

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Connecting bilattice theory with multivalued logic

Vagueness and Formal Fuzzy Logic: Some Criticisms