منابع مشابه
Complete Lattices Represent Complete Heyting Algebras (or: Quantum Logic with an Intuitionistic Implication)
Via the introduction of (infinitary) disjunctions on any complete lattice while inheriting the meet as a conjunction, we construct a bijective correspondence (up to isomorphism) between complete lattices L and complete Heyting algebras DI(L) equipped with a so called disjunctive join dense closure operator RL. If L is itself a complete Heyting algebra then DI(L) ∼= L and RL = idDI(L). Ortholatt...
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Quantum implication algebras without complementation are formulated with the same axioms for all five quantum implications. Previous formulations of orthoimplication, orthomodular implication , and quasi-implication algebras are analysed and put in perspective to each other and our results.
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is obvious, and then what always hold in the Mamdani's case is the equivalence (p 2 q ! r) = (p ! r) ^ (q ! r): (14) Consequently, if I is a Mamdani–Larsen's implication (8) never holds, but (14) is always true. IV. CONCLUSION After remembering the four main types of implications used in Fuzzy Logic, the equality [p ^ q ! r] = [(p ! r) _ (q ! r)] (*) is analyzed bot in complemented lattices and...
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In this paper we propose to enrich the four-valued modal logic associated to Monteiro’s Tetravalent modal algebras (TMAs) with a deductive implication, that is, such that the Deduction Meta–theorem holds in the resulting logic. All this lead us to establish some new connections between TMAs, symmetric (or involutive) Boolean algebras, and modal algebras for extensions of S5, as well as their lo...
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We study the positive fragment of a system of partial logic which has been developed by Ackermann in the course of his typefree foundation of mathematics. One of the prominent features of this system is its implication, which has been supplied with a deductive interpretation according to which A ! B expresses that B is derivable from A. The first section provides Ackermann’s original Hilbert-st...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1979
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1093882792