A Heyting algebra is a distributive lattice with implication and a dual $BCK$-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras between dual $BCK$-algebras. We define notions of $i$-invariant and $m$-invariant on dual $BCK$-semilattices and prove that a Heyting semilattice is equiva...

The main condition of the differently implicational inferencealgorithm is reconsidered from a contrary direction, which motivatesa new fuzzy inference strategy, called the double fuzzyimplications-based restriction inference algorithm. New restrictioninference principle is proposed, which improves the principle of thefull implication restriction inference algorithm. Furthermore,focusing on the ...

The aim of the present paper is to analyze the complexity of strict implication (together with falsum, conjunction and disjunction). We prove that Ladner’s Theorem remains valid when we restrict the language to the strict implication fragment, and that the same holds for Hemaspaandra’s Theorem. As a consequence we have that the validity problem for most standard normal modal logics is the same ...

The implication problem for saturated conditional independence statements is studied in the presence of fixed and undetermined sets of incomplete random variables. Here, random variables are termed incomplete since they admit missing data. Two different notions of implication arise. In the classic notion of V -implication, a statement is implied jointly by a set of statements and a fixed set V ...

will is the basis and foundation of contracts and possessions; almost without which no contract and possession can take the religious and legal affects. heart is the place of will, and because will has a high dignity, it cannot attributed to any matter unless it is declared and manifested. silence is one of the means of interpretation of the will. it, like utterance, scribe, deed and gesture, h...

The implication problem for saturated conditional independence statements is studied in the presence of fixed and undetermined sets of incomplete random variables. Here, random variables are termed incomplete since they admit missing data. Two different notions of implication arise. In the classic notion of V -implication, a statement is implied jointly by a set of statements and a fixed set V ...

At first, George Boole introduced conditional propositions as the basis for better development of propositional logic. A compound statement composed two atomic statements (antecedent and consequent) by connective 'if—then' is called For example: "If it raining, then roads are wet". Here first this proposition, 'It raining,' antecedent, second, 'the wet,' consequent. The material in which false ...

In the area of inductive learning, generalization is a main operation, and the usual deenition of induction is based on logical implication. Recently there has been a rising interest in clausal representation of knowledge in machine learning. Almost all inductive learning systems that perform generalization of clauses use the relation-subsumption instead of implication. The main reason is that ...