This position paper considers several existing relational database rule languages with a focus on exploring the fundamental di erences between deductive and active databases. We nd that deductive and active databases do not form two discernible classes, but rather they delineate two ends of a spectrum of database rule languages. We claim that this spectrum also corresponds to a notion of abstra...

Traditional deductive systems work with sentences of symbols. Even in newer systems that also reason from diagrams sentential representations still play a major role. The work here explores deductive systems that use only picture-like representations. Machinery functionally equivalent to variables, quantifiers, substitution, unification, and binding are defined based on a model of deductive cha...

We present in this paper both a novel theoretically well-founded framework for integrating the treatment of advanced update and rule enforcement problems in deductive databases and the architecture of a new deductive database management system based upon such a framework. Our results extend the query-processing and basic updating functionalities provided by current deductive database systems wi...

According to Frege’s principle the denotation of a sentence coincides with its truthvalue. The principle is investigated within the context of abstract algebraic logic, and it is shown that taken together with the deduction theorem it characterizes intuitionistic logic in a certain strong sense. A 2nd-order matrix is an algebra together with an algebraic closed set system on its universe. A ded...

Deductive retrieval and deductive synthesis are two conceptually closely related software development methods which apply theorem proving techniques to support the construction of correct programs. In this paper, we describe an integration of both methods which combines their complementary benefits and alleviates some of their drawbacks. The core of our integration is an algorithm which automat...