TitleA logic for reasoning about coherent conditional probability: a modal fuzzy logic approach
Publication TypeConference Paper
Year of Publication2004
AuthorsMarchioni E, Godo L
Conference Name9th European Conference on Logics in Artificial Intelligence, JELIA 2004
EditionAlferes, J.J. and Leite, J.
Conference LocationLisbon, Portugal
Date Published27/09/2004
ISBN Number978-3-540-23242-1

In this paper we define a logic to reason about coherent conditional probability, in the sense of de Finetti. Under this view, a conditional probability P(•|•) is a primitive notion that applies over conditional events of the form “\varphi given \psi”, where ψis not the impossible event. Our approach exploits an idea already used by Hájek and colleagues to define a logic for (unconditional) probability in the frame of fuzzy logics. Namely, in our logic for each pair of classical propositions ? and ?, we take the probability of the conditional event “? given ?”, ?|? for short, as the truth-value of the (fuzzy) modal proposition P(?|?), read as “?|? is probable”. Based on this idea we define a fuzzy modal logic FCP(??), built up over the many-valued logic ?? ½ (a logic which combines the well-known Lukasiewicz and Product fuzzy logics), which is shown to be complete with respect to the class of probabilistic Kripke structures induced by coherent conditional probabilities. Finally, we show that checking coherence of a probability assessment to an arbitrary family of conditional events is tantamount to checking consistency of a suitable defined theory over the logic FCP(??).