An Algebraic Semantics for Possibilistic Logic
This work provides a theoretical foundation for possibilistic logic, which is incremental in extending existing algebraic frameworks for handling uncertainty in AI and logic.
The paper tackles the problem of formalizing possibilistic logic by introducing a Pavelka-like formulation with enriched connectives and a semantics based on possibility functions, resulting in a sound and complete Gentzen calculus and discussion of truth functionality.
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 (eg) and a new type of conjunction (otimes). 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.