A modal analysis of possibility theory
In this paper we study possibility theory from the point of view of modal logic. Our first and main result is that the logic of qualitative possibility is nothing else than Lewis's conditional logic VN. Second, we propose a multi-modal logic able to support possibility theory. Some connexions between these formalisms are stressed.
Unable to display preview. Download preview PDF.
- D. Dubois (1986), Belief Structures, Possibility Theory, Decomposables Confidence Measures on finite sets. Computer and Arti. Intell, vol 5, Nℴ 5 pp 403–417.Google Scholar
- D. Dubois, H. Prade (1988), Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York.Google Scholar
- P. Gärdenfors, D. Makinson (1991), Nonmonotonic Inference based on Expectation Ordering. Manuscript.Google Scholar
- D. Makinson (1991), letter, march 1991.Google Scholar
- G. E. Hughes, M. J. Cresswell (1968), An Introduction to Modal Logic. Methuen & Co.Google Scholar
- D. K. Lewis (1973), Counterfactuals. Harvard University Press.Google Scholar
- D. Scott (1964), Measurement structures and linear inequalities. Jounal of Mathematical Psychology, Vol. 1, 233–247.Google Scholar
- K.Segerberg (1971), Qualitative probability in a modal setting. In: Proc. of the Second Scandinavian Logic Symposium (ed. J. E. Fenstad), North Holland.Google Scholar