Implication graphs are used to solve the test generation, redundancy identification, synthesis, and verification problems of digital circuits. We propose a new “oring” node structure to represent partial implications in a graph. The oring node is the contrapositive of the previously used “anding” node. The addition of a single oring node in the implication graph of a Boolean gate eliminates the...

The role of topological De Morgan algebra in the theory of rough sets is investigated. The rough implication operator is introduced in strong topological rough algebra that is a generalization of classical rough algebra and a topological De Morgan algebra. Several related issues are discussed. First, the two application directions of topological De Morgan algebras in rough set theory are descri...

The implication problem is to test whether a given set of independencies logically implies another independency. This problem is crucial in the design of a probabilistic reasoning system. We advocate that Bayesian networks are a generalization of standard relational databases. On the contrary, it has been suggested that Bayesian networks are different from the relational databases because the i...

This paper discusses the generalization of deenite Horn programs beyond the ordering of logical implication. Since the seminal paper on generalization of clauses based on subsumption, there are various extensions in this area. Especially in inductive logic programming(ILP), people are using various methods that approximate logical implication, such as inverse resolution(IR), relative least gene...

If we know that an implication A ! B is to some extent true, and if we know that a statement A is true \to some extent", i.e., if we know that the statement m(A) is true, for some logical modiier m (\approximately", \slightly", etc.), then we can conclude that B is also true to some extent, i.e., that m 0 (B) is true for some logical modiier m 0. Thus, every fuzzy implication deenes a mapping f...

It has long been assumed that using the deictic motion verb come to describe a motion event involves taking the perspective of an individual located at the destination of the motion event (Fillmore 1966). I argue that this perspective-taking is built into the meaning of come, drawing on novel data concerning what I call the “anchoring implication” of come. This is the implication that a particu...

Full hierarchical dependencies (FHDs) constitute a large class of relational dependencies. A relation exhibits an FHD precisely when it can be decomposed into at least two of its projections without loss of information. Therefore, FHDs generalise multivalued dependencies (MVDs) in which case the number of these projections is precisely two. The implication of FHDs has been defined in the contex...

We discuss paradoxes of implication in the setting of a proof-conditional theory of meaning for logical constants. We argue that a proper logic of implication should be not only relevant, but also constructive and nonmonotonic. This leads us to select as a plausible candidate LL, a fragment of linear logic which differs from R in that it rejects both contraction and

In this paper, we deal with soft lattice implication algebras based on fuzzy sets. Using the concepts of fuzzy (implicative) filters, (∈,∈∨q)fuzzy (implicative) filters and (∈,∈∨q)-fuzzy (implicative) filters, some characterizations for ∈-soft sets and q-soft sets to be (implicative) filteristic soft lattice implication algebras are established.

Intuitionistic Fuzzy Sets (IFS) are defined as pairs of mutually orthogonal fuzzy sets. We discuss this approach from an algebraic point of view. As a result we characterize two implication operators on the collection of IFS, which on a particular subset of IFS behave as a Lukasiewicz and a Gödel implication.