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Validity Measurement in Some Propositional Logics
Author(s) -
Boričić Branislav
Publication year - 1997
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19970430410
Subject(s) - propositional variable , mathematics , well formed formula , propositional calculus , axiom , zeroth order logic , completeness (order theory) , t norm fuzzy logics , propositional formula , intermediate logic , discrete mathematics , calculus (dental) , gödel's completeness theorem , atomic formula , measure (data warehouse) , algebra over a field , pure mathematics , computer science , theoretical computer science , description logic , artificial intelligence , multimodal logic , data mining , fuzzy set , medicine , mathematical analysis , geometry , dentistry , membership function , fuzzy logic
The language of the propositional calculus is extended by two families of propositional probability operators, inductively applicable to the formulae, and the set of all formulae provable in an arbitrary superintuitionistic propositional logic is extended by the probability measure axioms concerning those probability operators. A logical system obtained in such a way, similar to a kind of polymodal logic, makes possible to express a probability measure of truthfulness of any formula. The paper contains a description of the Kripke‐type possible worlds semantics covering the considered logical systems, being followed by the corresponding completeness results.