Logic of Bipartite Truth with Uncertainty Dimension

Grigoriev, O.M.

Автор: Grigoriev O.M.
Журнал: Journal of Applied Logics - IfCoLoG Journal of Logics and their Applications
Том: 6
Номер: 2
Год издания: 2019
Издательство: College Publications
Местоположение издательства: United States
Первая страница: 291
Последняя страница: 319
Аннотация: This research continues the studies of a system of two-dimensional truth values equipped with a pair of unary negation-like operations and their logics. The basic ideas of this approach historically were first presented in [11] and thoroughly investigated further in [18, 19]. According to the methodology of [11, 18, 19] a truth value consists of a pair of entities each representing a certain aspect of “being true” or “being false” property, eg. ontological and epistemic aspects, as assumed in papers cited above. The basic set of two-dimensional truth values constitutes a four-element diamond-shaped lattice endowed with the pair of unary operations which give rise to the corresponding propositional connectives, so called semi-negations, on syntactical level. Intuitively these semi-negation affects only one of the coordinates of a truth value, thus only partially transforming information which a particular truth value encodes. In this paper we extend the initial structure of the truth values adding uncertainty dimensions in each position of a pair thereby obtaining a nine-element distributive lattice. We present an axiomatization for the logic of this semantic structure along with correctness and completeness proofs. Then we abstract away from the finite semantic structures and explore relational semantics for the same logic but without distribution laws. We use an approach related to the methods of [16, 1, 3, 10].
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Logic of Bipartite Truth with Uncertainty Dimensionстатья

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