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 ...

This paper deals with the problem of searching basic properties for robust implication operators in fuzzy control. We use the word “robust” in the sense of good average behavior in different applications and in combination with different defuzzification methods. We study the behavior of the two main families of implication operators in the fuzzy control inference process. These two families are...

Inductive Logic Programming (ILP) deals with inducing clausal theories from examples basically through generalization or specialization. The specialization and generalization operators used are mainly based on three generality orderings subsumption, implication and implication relative to background knowledge. Implication is stronger than subsumption, but relative implication is more powerful b...

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.

Given an implication function I defined on the finite chain L = {0, ..., n}, a method for extending I to the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers contained in L (denoted by A1 ) is given. The resulting extension is in fact a fuzzy implication on A1 preserving some boundary properties. Moreover, if the initial implication I is an S, QL or D-implicat...

In this paper, we introduce the notionofWajsberg implicative ideal(WI-ideal)of lattice Wajsberg algebra.Further, we definelattice H-Wajsberg algebra, implication homomorphismand lattice implication homomorphism oflattice Wajsberg algebra. Finally, we give kernel of implication homomorphism and obtain some oftheir properties.

All generalisations within logic involve inverting implication. Yet, ever since Plotkin's work in the early 1970's methods of generalising rst-order clauses have involved inverting the clausal subsumption relationship. However , even Plotkin realised that this approach was incomplete. Since inversion of subsumption is central to many Inductive Logic Programming approaches, this form of incomple...

In order to investigate a many valued logical system whose proportional value is given in a lattice, in 1993 Y. Xu [12] first established the lattice implication algebra by combining lattice and implication algebra, and explored many useful structures. The ideal theory serves a vital function for the development of lattice implication algebras. Y. Xu, Y.B. Jun and E.H. Roh [6] introduced the no...

Due to the shortage of rough impHcation in [4] ~ [6], rough set and rough implication operators are redefined by using interval structure in [7], the shortages have been e improved. We have investigated the characteristics of the rough implication, and also point out that the good logic property of the rough implication in [7]. In this paper, we will study the algebraic properties of the rough ...