Plausibility logic

Abstract

This is an effort towards an abstract presentation of the formal properties of the way we tend to jump to conclusions from less than fully convincing information. In [6], such properties were presented as families of binary relations between propositional formulas, i.e., built out of preexisting propositional logic. Though the family of cumulative relations is easily amenable to an abstract presentation that does not use the propositional connectives, as was noticed in [8] and [9], no such presentation is known for the more attractive family of preferential relations. Plausibility Logic is a step towards such an abstract presentation. It enables the definition of connectives: each connective is defined by introduction rules only. It provides a nonmonotonic presentation of the Gentzen's consequence relation of classical logic. But, no representation theorem is known for Plausibility Logic and it does not enjoy Cut Elimination.

Some results contained here have been obtained since the Conference oral presentation. This work was partially supported by grant 351/89 from the Basic Research Foundation, Israel Academy of Sciences and Humanities and by the Jean and Helene Alfassa fund for research in Artificial Intelligence. Part of this work was performed while the author was visiting the Laboratoire d'Informatique Théorique et de Programmation, Université Paris 6.