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p-Adic valued logical calculi in simulations of the slime mould behaviour

Andrew Schumann

Journal of Applied Non-Classical Logics 25 (2):125-139 (2015)

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(1 other version)A p-adic probability logic.Angelina Ilić-Stepić, Zoran Ognjanović, Nebojša Ikodinović & Aleksandar Perović - 2012 - Mathematical Logic Quarterly 58 (4):263-280.details In this article we present a p-adic valued probabilistic logic equation image which is a complete and decidable extension of classical propositional logic. The key feature of equation image lies in ability to formally express boundaries of probability values of classical formulas in the field equation image of p-adic numbers via classical connectives and modal-like operators of the form Kr, ρ. Namely, equation image is designed in such a way that the elementary probability sentences Kr, ρα actually do have their (...) Download Export citation Bookmark 4 citations
(1 other version)A p‐adic probability logic.Angelina Ilić-Stepić, Zoran Ognjanović, Nebojša Ikodinović & Aleksandar Perović - 2012 - Mathematical Logic Quarterly 58 (4-5):263-280.details In this article we present a p-adic valued probabilistic logic equation image which is a complete and decidable extension of classical propositional logic. The key feature of equation image lies in ability to formally express boundaries of probability values of classical formulas in the field equation image of p-adic numbers via classical connectives and modal-like operators of the form Kr, ρ. Namely, equation image is designed in such a way that the elementary probability sentences Kr, ρα actually do have their (...) Download Export citation Bookmark 4 citations
Systematic construction of natural deduction systems for many-valued logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1993 - In Unknown (ed.), Proceedings of The Twenty-Third International Symposium on Multiple-Valued Logic, 1993. IEEE Press. pp. 208-213.details A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness, and normal-form theorems for natural deduction systems. Download Export citation Bookmark 14 citations
Non-Archimedean fuzzy and probability logic.Andrew Schumann - 2008 - Journal of Applied Non-Classical Logics 18 (1):29-48.details In this paper the non-Archimedean multiple-validity is proposed for basic fuzzy logic BL∀∞ that is built as an ω-order extension of the logic BL∀. Probabilities are defined on the class of fuzzy subsets and, as a result, for the first time the non-Archimedean valued probability logic is constructed on the base of BL∀∞. Download Export citation Bookmark 8 citations
Toward Theory of p-adic Valued Probabilities.Andrei Khrennikov - 2008 - Studies in Logic, Grammar and Rhetoric 14 (27).details Download Export citation Bookmark 3 citations
Logics for Reasoning About Processes of Thinking with Information Coded by p-adic Numbers.Angelina Ilić Stepić & Zoran Ognjanović - 2015 - Studia Logica 103 (1):145-174.details In this paper we present two types of logics and \ ) where certain p-adic functions are associated to propositional formulas. Logics of the former type are p-adic valued probability logics. In each of these logics we use probability formulas K r,ρ α and D ρ α,β which enable us to make sentences of the form “the probability of α belongs to the p-adic ball with the center r and the radius ρ”, and “the p-adic distance between the probabilities of (...) Download Export citation Bookmark 2 citations
Non-Archimedean valued predicate logic.Andrew Schumann - 2007 - Bulletin of the Section of Logic 36 (1/2):67-78.details Download Export citation Bookmark 1 citation

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