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zpravodaj ČSKI - leden 2010 [ pdf ]
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datum: 20.1.2010 v 9:00
název: Paraconsistent Semantics for Pavelka Style Fuzzy Sentential Logics
přednášející: Esko Turunen (University of Tampere)
místo konání: UI, 2.patro, místnost č.318

souhrn: The root of this work is on the one hand in Belnap's four valued paraconsistent logic, and on the other hand on Pavelka's pápera further developed by Turunen. We do not introduce a new non-classical logic but, based on a related study of Perny and Tsoukas, we introdukce paraconsistent semantics of Pavelka style fuzzy sentential logic. Restricted to Lukasiewicz t-norm, our approach and the approach of Perny and Tsoukias partly overlap; the main difference lies in the interpretation of the logical connectives 'implication and 'negation'. The essential mathematical tool is a one-one correspondence between evidence couples and evidence matrices that holds in all injective MV-algebras. Evidence couples associate to each atomic formula p two values a and b that can be interpreted as the degrees of pros and cons for p, respectively. Four values t, f, k, u, interpreted as the degrees of the truth, falsehood, contradiction and unknowness of p, respectively, can then be calculated by means of a and b and finally, the degrees of the truth, falsehood, contradiction and unknowness of any well formed formula alpha are available. The obtained logic is Pavelka style fuzzy sentential logic. In such an approach truth and falsehood are not each others complements.