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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We describe a method for obtaining classical logic from intuitionistic logic which does not depend on any proof system, and show that by applying it to the most important implicational relevance logics we get relevance logics with nice semantical and proof-theoretical properties. Semantically all these logics are sound and strongly complete relative to classes of structures in which all element...
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Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $mathscr{B}$ (resp. $varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with $mathscr{B}$ (resp. $varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbase...
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Implicational bases are objects of interest in formal concept analysis and its applications. Unfortunately, even the smallest base, the Duquenne-Guigues base, has an exponential size in the worst case. In this paper, we use results on the average number of minimal transversals in random hypergraphs to show that the base of proper premises is, on average, of quasi-polynomial size.
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Completion is a general paradigm for applying inferences to generate a canonical presentation of a logical theory, or to semi-decide the validity of theorems, or to answer queries. We investigate what canonicity means for implicational systems that are axiomatizations of Moore families – or, equivalently, of propositional Horn theories. We build a correspondence between implicational systems an...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1975
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1093891887