The shortest axioms of the implicational calculus.
نویسندگان
چکیده
منابع مشابه
Single Axioms in the Implicational Propositional Calculus
A class of challenge problems derived from a first-order encoding of the implicational propositional calculus is presented.
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It has long been an open question whether the formula XCB = EpEEEpqErqr is, with the rules of substitution and detachment, a single axiom for the classical equivalential calculus. This paper answers that question affirmatively, thus completing a search for all such eleven-symbol single axioms that began seventy
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Shortest possible axiomatizations for the implicational fragments of the modal logics S4 and S5 are reported. Among these axiomatizations is included a shortest single axiom for implicational S4—which to our knowledge is the first reported single axiom for that system—and several new shortest single axioms for implicational S5. A variety of automated reasoning strategies were essential to our d...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1968
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1093893523