|Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||Logics for Reasoning About Processes of Thinking with Information Coded by p-adic Numbers||Journal:||Studia Logica||Issue:||1||First page:||145||Last page:||174||Issue Date:||1-Jan-2015||Rank:||M22||ISSN:||0039-3215||DOI:||10.1007/s11225-014-9552-5||Abstract:||
In this paper we present two types of logics (denoted LDQp and LthinkingZp) 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 α and β is less than or equal to ρ”, respectively. Logics of the later type formalize processes of thinking where information are coded by p-adic numbers. We use the same operators as above, but in this formalism K r,ρ α means “the p-adic code of the information α belongs to the p-adic ball with the center r and the radius ρ”, while D ρ α,β means “the p-adic distance between codes of α and β are less than or equal to ρ”. The corresponding strongly complete axiom systems are presented and decidability of the satisfiability problem for each logic is proved.
|Keywords:||Coding information | P-adic | Probability logic||Publisher:||Springer Link||Project:||Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education
Representations of logical structures and formal languages and their application in computing
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