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Paraconsistent First-Order Logic with infinite hierarchy levels of contradiction $LP^#_{omega}$. Axiomatical system $HST^#_{omega}$, as paraconsistent generalization of Hrbacek set theory HST

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 Added by Jaykov Foukzon
 Publication date 2020
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and research's language is English




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In this paper paraconsistent first-order logic LP^{#}_{omega} with infinite hierarchy levels of contradiction is proposed. Corresponding paraconsistent set theory KSth^{#}_{omega} is discussed.Axiomatical system HST^{#}_{omega} as paraconsistent generalization of Hrbacek set theory HST is considered.



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193 - Jaykov Foukzon 2009
In this paper paraconsistent second order arithmetic Z#2 with unrestricted comprehension scheme is proposed. We outline the development of certain portions of paraconsistent mathematics within paraconsistent second order arithmetic Z#2.In particular we defined infinite hierarchy Berrys and Richards inconsistent numbers as elements of the paraconsistent field R^#.
In this paper the 3-valued paraconsistent first-order logic QCiore is studied from the point of view of Model Theory. The semantics for QCiore is given by partial structures, which are first-order structures in which each n-ary predicate R is interpreted as a triple of paiwise disjoint sets of n-uples representing, respectively, the set of tuples which actually belong to R, the set of tuples which actually do not belong to R, and the set of tuples whose status is dubious or contradictory. Partial structures were proposed in 1986 by I. Mikenberg, N. da Costa and R. Chuaqui for the theory of quasi-truth (or pragmatic truth). In 2014, partial structures were studied by M. Coniglio and L. Silvestrini for a 3-valued paraconsistent first-order logic called LPT1, whose 3-valued propositional fragment is equivalent to da Costa-DOtavianos logic J3. This approach is adapted in this paper to QCiore, and some important results of classical Model Theory such as Robinsons joint consistency theorem, amalgamation and interpolation are obtained. Although we focus on QCiore, this framework can be adapted to other 3-valued first-order logics.
122 - C. A. Middelburg 2020
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354 - Jaykov Foukzon 2015
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