A MODAL LOGIC FOR HYPOTHESIS THEORY

Article type: Research Article

Authors: Schwind, Camilla | Siegel, Pierre

Affiliations: G.I.A., Faculté des Sciences de Luminy, 163, Avenue de Luminy, Case 901, 13288 Marseille, Cedex 9, France | LIUP Université de Provence, 3 pl Victor Hugo, Case G, 13331 Marseille, Cedex 3, France

Abstract: Hypothesis theory for nonmonotonic reasoning expresses notions of hypotheses and of known information. In this paper, we define these notions in the framework of a new modal system with two modalities, one for exprressing known information and the other for expressing possible hypotheses. A complete characterization of the new logic is given in terms of Kripke semantics. Moreover, our logic allows to characterize completely default logic, including a necessary and sufficient criterium for the existence and the non-existence of extensions. We also present a notion of nonmonotonic inference which is cumulative.

DOI: 10.3233/FI-1994-21125

Journal: Fundamenta Informaticae, vol. 21, no. 1-2, pp. 89-101, 1994