Research Perspectives for Logic and Deduction

Abstract

The article is meant to be kind of the author's manifesto for the role of logic and deduction within Intellectics. Based on a brief analysis of this role the paper presents a number of proposals for future scienti c research along the various dimensions in the space of logical explorations. These dimensions include the range of possible applications including modelling intelligent behavior, the grounding of logic in some semantic context, the choice of an appropriate logic from the great variety of alternatives, then the choice of an appropriate formal system for representing the chosen logic, and nally the issue of developing the most e cient search strategies. Among the proposals is a conjecture concerning the treatment of cuts in proof search.

Deductive Reasoning Systems

“…This is an advantage since this transformation in general introduces redundancy thus increasing the search space. On the contrary, the given formula may even be reduced by factoring, making it more nonnormal, possibly resulting in (much) shorter proofs and less proof search (Bibel, 2006).…”

Early History and Perspectives of Automated Deduction

“…The author has outlined his credo for the field of AD only recently in the article [Bib06]. We will therefore not repeat these arguments here again except for a few additions especially with respect to the issues discussed in the previous sections.…”

“…One particularly important example is the cut rule which has never been taken care of in any running system except for its very limited consideration in SETHEO. The author has stated a conjecture in [Bib06] which would open a way for its treatment. Another example concerns a refined treatment of variables as already discussed in [Bib87] which has just been worked out in more details in [AW07].…”