Equational zero vector accounting systems, based on duality principles and the double-entry model, were designed as ontological control systems to help prevent and detect fraud and errors inherent in non-equational, single-entry systems. Non-equational systems lend themselves to fraud and errors to a larger degree because the internal control inherent in an equational zero vector system has no ...

The aim of this paper is the study of fuzzy basis and dimensionof fuzzy hypervector spaces. In this regard, first the notions of fuzzy linearindependence and fuzzy basis are introduced and then some related results areobtained. In particular, it is shown that for a large class of fuzzy hypervectorspace the fuzzy basis exist. Finally, dimension of a fuzzy hypervector space isdefined and the basi...

We introduce an abstract general notion of system of equations between terms, called Term Equational System, and develop a sound logical deduction system, called Term Equational Logic, for equational reasoning. Further, we give an analysis of algebraic free constructions that together with an internal completeness result may be used to synthesise complete equational logics. Indeed, as an applic...

The paper presents algebraic and logical developments. From the algebraic viewpoint, we introduce Monadic Equational Systems as an abstract enriched notion of equational presentation. From the logical viewpoint, we provide Equational Metalogic as a general formal deductive system for the derivability of equational consequences. Relating the two, a canonical model theory for Monadic Equational S...

Perfect bases for equational theories are closely related to confluent and finitely terminating term rewrite systems. The two classes have a large overlap, but neither contains the other. The class of perfect bases is recursive. We also investigate a common generalization of both concepts; we call these more general bases normal, and touch the question of their uniqueness. We also give numerous...

Using techniques pioneered by R. McKenzie, we prove that there is no algorithm which, given a finite algebra in a finite language, determines whether the variety (equational class) generated by the algebra has a model companion. In particular, there exists a finite algebra such that the variety it generates has no model companion; this answers a question of Burris and Werner from 1979.

A conditional term rewriting system is called logical if it has the same logical strength as the underlying conditional equational system. In this paper we summarize known logicality results and we present new sufficient conditions for logicality of the important class of oriented conditional term rewriting systems.

This paper contributes to the theory of substructural logics .that are of interest to categorial grammarians. Combining semantic ideas of Hepple [1990] and Mor-rill [1990], proof-theoretic ideas of Venema [1993b; 1993a] and the theory of equational specifications, a class of resource-preserving logics is defined, for which decidability and completeness theorems are established.