An algebraic semantics for possibilistic logic

Authors:
Luca Boldrin;Claudio Sossai
Affiliations:
Dept. of Pure and Applied Math., University of Padova, Padova, PD, Italy;Ladseb, CNR, Padova, PD, Italy
Venue:
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Year:
1995

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Abstract

The first contribution of this paper is the presentation of a Pavelka-like formulation of possibilistic logic in which the language is naturally enriched by two connectives which represent negation (¬) and a new type of conjunction (⊗). The space of truth values for this logic is the lattice of possibility functions, that, from an algebraic point of view, forms a quantal. A second contribution comes from the understanding of the new conjunction as the combination of tokens of information coming from different sources, which makes our language "dynamic". A Gentzen calculus is presented, which is proved sound and complete with respect to the given semantics. The problem of truth functionality is discussed in this context.