For nite convergent term-rewriting systems it is shown that the equational unii-cation problem is recursively independent of the equational matching problem, the word matching problem, and the 2 nd-order equational matching problem. Apart from the latter these results are derived by considering term-rewriting systems on signatures that contain unary function symbols only (that is, string-rewrit...

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

In this note we settle a question posed by Hobby and McKenzie in [2] on the nature of locally finite equational classes which satisfy some nontrivial congruence identity. We settle problem #14 from [2] by exhibiting a locally finite equational class V which omits types 1 and 5 and which satisfies some non-trivial congruence identity, but which contains a finite algebra having a type 4 minimal s...

By an equational theory we mean a set of equations from some fixed language which is closed with respect to logical consequences. We regard equations as universal sentences whose quantifierfree parts are equations between terms. In our notation, we suppress the universal quantifiers. Once a language has been fixed, the collection of all equational theories for that language is a lattice ordered...

For a class of fuzzy metric spaces (in the sense of George and Veeramani) with an H-type t-norm,  we present a method to construct a metric on a  fuzzy metric space. The induced metric space shares many important properties with the given fuzzy metric space.  Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some probl...

In this paper a method is proposed to compute typical objects for the classes in the scheme of a fuzzy object oriented database. Typical objects are considered as "representatives" of a fuzzy majority of the class instances. The instances of a class are represented in a topological space and the typical object is derived as "closest" to the fuzzy majority of the class instances.

We provide a Lawvere-style definition for partial theories, extending the classical notion of equational theory by allowing partially defined operations. As in case, our is syntactic: we use an appropriate class string diagrams as terms. This allows reasoning about models theory. demonstrate expressivity such theories considering number examples, including combinatory algebras and cartesian clo...