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.

Deductive verification provides a powerful tool to show functional properties of a given program. However, in practice, many properties of interest link several program calls. This is for instance the case for non-interference, continuity and monotony. Other examples relate sequences of function calls, for instance to show that decrypting an encrypted message with the appropriate key gives back...

Our current understanding about the AS level topology of the Internet is based on measurements and inductive-type models which set up rules describing the behavior (node and edge dynamics) of the individual ASes and generalize the consequences of these individual actions for the complete AS ecosystem using induction. In this paper we suggest a third, deductive approach in which we have premises...

In three case studies on notions of fuzzy logic and fuzzy set theory (Dubois–Prade’s gradual elements, the entropy of a fuzzy set, and aggregation operators), the paper exemplifies methodological differences between traditional and deductive fuzzy logic. While traditional fuzzy logic admits various interpretations of membership degrees, deductive fuzzy logic always interprets them as degrees of...

Modern fact databases contain abundant data classified through several classifications. Typically users must consult these classifications in separate manuals or files thus making their effective use difficult. Contemporary database systems do little to support deductive use of classifications. In this paper we show how deductive data management techniques can be applied to the utilization of d...

This article begins with an account of logic, and of how logicians formulate formal rules of inference for the sentential calculus, which hinges on analogs of negation and the connectives if, or, and and. It considers the various ways in which computer scientists have written programs to prove the validity of inferences in this and other domains. Finally, it outlines the principal psychological...

We present several results concerning deductive completeness of the simply typed λcalculus with constants and equational axioms. First, we prove deductive completeness of the calculus with respect to standard semantics for axioms containing neither free nor bound occurrences of higher-order variables. Using this result, we analyze some fundamental deductive and semantic properties of axiomatic ...