This is an exposition of Lambek’s strengthening and generalization of the deduction theorem in categories related to intuitionistic propositional logic. Essential notions of category theory are introduced so as to yield a simple reformulation of Lambek’s Functional Completeness Theorem, from which its main consequences can be readily drawn. The connections of the theoremwith combinatory logic, ...

This study aims to examine the approaches of people involved in mathematics education and logic to the role played by learning mathematics in the development of general deductive reasoning. The data source includes 21 individual semistructured interviews. Analysis based on the Grounded Theory method identified three distinct groups of interviewees with relation to views of (a) the meaning of de...

There are many ways in which the query answering process for deductive databases may be optimised. At the heart of many of these methods is some form of constraint on the variables of the query, so that facts which are not relevant to the query are not computed. In this paper we show how fold/unfold transformations may be used to propagate some forms of constraint which are not captured by tech...

In this paper, we will report on the experience of building a successful industrial application using the LDL++ deductive database as part of the technology transfer process to our sponsor company, Eastman Chemical Company. We will describe the nature of the problems faced by Eastman Chemical Company and show how the LDL++ deductive database technology helps to build an Intelligent Information ...

In a nested relational or complex object database, nested tuples and sets are used to represent real world objects. For various reasons, such tuples and sets can be partial or complete. In this paper, we discuss how to support them in deductive databases. In particular, we present a deductive database language RLOG II that supports partial and complete tuples and sets based on Relationlog. This...

A pair of deductive systems (S,S’) is Leibniz-linked when S’ is an extension of S and on every algebra there is a map sending each filter of S to a filter of S’ with the same Leibniz congruence. We study this generalization to arbitrary deductive systems of the notion of the strong version of a protoalgebraic deductive system, studied in earlier papers, and of some results recently found for pa...

There are currently increased efforts to make proof central to school mathematics throughout the grades. Yet, realizing this goal is not easy, as it requires that students master several abilities. In this article, we focus on one such ability, namely, the ability for deductive reasoning. We first offer a conceptualization of proof, which we use to delineate our focus on deductive reasoning. We...

We investigate a Web information structuring mechanism called lightweight deductive databases. Lightweight deductive databases enable more sophisticated automated searching, extraction, and processing, and can facilitate agent-based programming. We also explore how these deductive databases bene t from being distributed on the Web.

The notions of bipolar fuzzy hyper MV-subalgebras, (weak) bipolar fuzzy hyper MV-deductive system and precisely weak bipolar fuzzy hyper MV-deductive system are introduced, and their relations are investigated. Characterizations of bipolar fuzzy hyper MV-subalgebras and weak bipolar fuzzy hyper MV-deductive systems are provided.