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Searching for the roots of non-contradiction and excluded-middle. (English) Zbl 1019.03049
The authors discuss standard propositional formulas which are counted as formalizations of the principles of non-contradiction and of excluded middle. Their aim is to discuss under rather weak algebraic assumptions the truth-value structure conditions under which these formulas become valid or equivalent. Their basic structure is a nonempty set equipped with a transitive binary relation $$R$$, modeling entailment, and a unary operation that has to be $$R$$-reversing, hence a structure which subsumes, e.g., orthomodular and De Morgan lattices.

##### MSC:
 03G25 Other algebras related to logic 03B52 Fuzzy logic; logic of vagueness