Partial implication semantics in the context of a background theory has been introduced to formalize partial goal satisfaction in the context of beliefs. In this paper, we introduce strong partial implication prohibiting redundancies and weak partial implication allowing side effects, we study their semantic as well as complexity properties, and we apply the three notions of partial implication...

We argue that the usual trace-based notions of implication and equivalence for linear temporal logics are too strong and should be complemented by the weaker notions of open implication and open equivalence. Although open implication is harder to compute, it can be used to advantage both in model checking and in synthesis. We study the difference between trace-based equivalence and open equival...

At least also introduces an implication of speaker ignorance ([9, 1, 12, 19]). (1) conveys that the speaker is uncertain about the exact number of cooks Al hired. In one view, pioneered by Büring ([1]), this ignorance implication is a Gricean Quantity implicature. Büring proposes to capitalize on a striking similarity between at least and disjunction. Just like 1, 3 below lacks the upper-boundi...

Lukasiewicz implication algebras are the {→, 1}-subreducts of MV algebras. They are the algebraic counterpart of SuperLukasiewicz Implicational Logics. We give a description of free Lukasiewicz implication algebras in the context of McNaughton functions. More precisely, we show that the |X|-free Lukasiewicz implication algebra is isomorphic to ⋃ x∈X [xθ) for a certain congruence θ over the |X|-...

A quasi-implication algebra is introduced as an algebraic counterpart of an implication reduct of propositional logic having noninvolutory negation (e.g. intuitionistic logic). We show that every pseudocomplemented semilattice induces a quasi-implication algebra (but not conversely). On the other hand, a more general algebra, a so-called pseudocomplemented q-semilattice is introduced and a mutu...

(Abstract) In this paper, we propose a new method for discovering hidden information from large-scale transaction databases by considering a property of cofactor implication. Cofactor implication is an extension or generalization of symmetric itemsets, which has been presented recently. Here we discuss the meaning of cofactor implication for the data mining applications, and show an efficient a...

objective(s): several researchers have reported the relationship between infertility in male and varicocele for so many years but the implication of varicocele in female patients is remains elusive. here, we aim to examine the effects of unilateral varicose ovarian vein on antioxidant capacity and oocyte quality of rat ovary after the experimental creation of varicocele in female rats. material...

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...

This dissertation introduces a path constraint language and investigates its associated implication and finite implication problems. This path constraint language has proven useful in a variety of database contexts, ranging from semistructured data as found for instance on the Web, to structured data such as data in object-oriented databases. It is capable of expressing natural integrity constr...

In this work we solve the following problem: Characterize the subclasses of implication algebras that can be axiomatized by sentences of the form 89! ^ p = q. In the process we obtain a representation result for …nite implication algebras, and as a by-product of our solution a number of interesting classes of implication algebras arise. We also obtain a characterization of the congruence permut...