An Introduction to Fuzzy Propositional Calculus Using Proofs from Assumptions
The subject of this paper is fuzzy propositional calculus. The proposed approach is related to the basic fuzzy propositional logics, i.e. to each of the following three most important such systems (in short: BL): Łukasiewicz’s, Gödel’s, and product logic. The logical calculi considered here are based on a system of rules that define the methods used in proofs from assumptions. To simplify the considered proofs some set of laws called also ‘primitive rules’ is next introduced. It was shown that any fuzzy propositional formula provable under Hájek’s axioms of the logic BL is also provable under the above-proposed approach.
KeywordsFuzzy Logic Propositional Variable Axiomatic Approach Indirect Proof Truth Degree
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