Possibilistic states of information are fuzzy sets of possible worlds. They constitute a complete lattice, which can be endowed with a monoidal operation (a t-norm) to produce a quantal. An algebraic semantics is presented which links possibilistic formulae with information states, and gives a natural interpretation of logical connectives as operations on fuzzy sets. Due to the quantal structure of information states, we obtain a system which shares several features with (exponential-free) intuitionistic linear logic. Soundness and completeness are proved, parametrically on the choice of the t-norm operation.

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. 1

Several qualitative notions of epistemic dependence between propositions are studied. They are closely related to the ordinal notion of conditional possibility. What this paper proposes is a systematic investigation of how the fact of learning a new piece of evidence individually affects previous beliefs. Namely a new piece of information A can either leave a previous belief untouched, or cancel it from the set of accepted beliefs, or even refute it. On the contrary, A can justify a new belief, not previously held, or fail to justify it. We provide axiomatizations of epistemic independence and relevance and show the close links between qualitative independence and the theory of belief change. It turns out that qualitative independence and AGM belief change operations have the same expressive power. Lastly, it is briefly suggested how qualitative independence can be applied to plausible reasoning. 1. Introduction It has been known for some time that the AGM revision th...

We present a truth-functional semantics for necessity-valued logics, based on the forcing technique. We interpret possibility distributions (which correspond to necessity measures) as informational states, and introduce a suitable language (basically, an extension of classical logic, similar to Pavelka’s language). Then we define the relation of “forcing ” between an informational state and a formula, meaning that the state contains enough information to support the validity of the formula. The subsequent step is the definition of a many-valued truth-functional semantics, by simply taking the truth value of a formula to be the set of all informational states that force the truth of the formula. A proof system in sequent calculus form is provided, and validity and completeness theorems are proved. 1

We present a formal method for data fusion, based on possibilistic logic. The method has been applied to a real-world problem of noisy sensor-data fusion: the position estimation of an autonomous mobile robot navigating in an approximately and partially known office environment using a topological map. Each place in the map is characterized by a set of logical formulae axiomatizing both symbolic knowledge and uncertain information from the sensors. At each time instant during navigation, the necessity for each place is calculated using a function generated by a proof system based on sequent calculus. Several test runs using a real robot have shown the adequacy of the approach in interpreting and disambiguating the information coming from independent perceptual sources, in combination with symbolic knowledge.

this paper, we start from the intuition that an event C is independent of another event A when one's opinion about C is not affected by learning A. Then 2 D. DUBOIS, L. FARI NAS DEL CERRO, A. HERZIG AND H. PRADE

We present a formal method, based on possibilistic logic, to fuse uncertain sensory information. The basic concepts underlying the approach are summarized and discussed. The method has been applied to a real-world problem of noisy sensor-data fusion: the position estimation of an autonomous mobile robot navigating in an approximately and partially known o#ce environment, using a topological map. Each place in the map is characterized by a set of logical formulae axiomatizing both abstract knowledge and uncertain information from the sensors. At each time instant during navigation, the necessity value for each place is calculated using a purely syntactical method, based on sequent calculus. Several test runs on a real robot have evidenced the adequacy of the approach in interpreting and disambiguating the information coming from independent perceptual sources, in combination with abstract knowledge. Keywords: Reasoning with Uncertainty, Possibilistic Logic, Sequent Calculus, Sensor Fus...

We present n , a multi-agent epistemic logic where each agent can perform uncertain (possibilistic) reasoning. The original feature of this logic is the presence of a distributed belief operator, with the purpose of merging the belief of different agents. Unlike the corresponding operator in the categorical (non-uncertain) case, our distributed belief operator accumulates support for the same fact coming from different agents. This means that opinions shared by different agents can be combined into a stronger distributed belief. This feature is useful in problems like pooling expert opinions and combining information from multiple unreliable sources. We provide a possible worlds semantics and an axiomatic calculus for our logic, and prove soundness, completeness and decidability results. We hint at some possible applications n in the conclusions.