Possibilistic logic is a well-known logic for reasoning under uncertainty, which is based on the idea that the epistemic state of an agent can be modeled by assigning to each possible world a degree of possibility, taken from a totally ordered, but essentially qualitative scale. Recently, a generalization has been proposed that extends possibilistic logic to a meta-epistemic logic, endowing it with the capability of reasoning about epistemic states, rather than merely constraining them. In this paper, we further develop this generalized possibilistic logic (GPL). We introduce an axiomatization showing that GPL is a fragment of a graded version of the modal logic KD, and we prove soundness and completeness w.r.t. a semantics in terms of possibility distributions. Next, we reveal a close link between the well-known stable model semantics for logic programming and the notion of minimally specific models in GPL. More generally, we analyze the relationship between the equilibrium logic of Pearce and GPL, showing that GPL can essentially be seen as a generalization of equilibrium logic, although its notion of minimal specificity is slightly more demanding than the notion of minimality underlying equilibrium logic.

Possibilistic logic is the most popular approach to represent and reason with uncertain and partially inconsistent knowledge. Regarding normal forms, the encoding of real-world problems does usually not result in a clausal formula and although a possibility nonclausal formula is theoretically equivalent to some possibilistic clausal formula [26, 22], approaches needing clausal form transformations are practically infeasible or have experimentally shown to be highly inefficient as discussed below. Two kinds of clausal form transformation are known: (1) one is based on the repetitive application of the distributive laws to the input non-clausal formula until a logically equivalent clausal formula is obtained; and (2) the other transformation, Tsetin-transformation [59], is based on recursively substituting sub-formulas in the input non-clausal formula by fresh literals until obtaining an equi-satisfiable, but not equivalent, clausal formula.

Boolean games are a game-theoretic framework in which propositional logic is used to describe agents’ goals. In this paper we investigate how agents in Boolean games can reach an efficient and fair outcome through a simple negotiation protocol. We are particularly interested in settings where agents only have incomplete knowledge about the preferences of others. After explaining how generalized possibilistic logic can be used to compactly encode such knowledge, we analyze how a lack of knowledge affects the agreement outcome. In particular, we show how knowledgeable agents can obtain a more desirable outcome than others.

In this paper an approach to automated deduction under uncertainty,based on possibilistic logic, is proposed ; for that purpose we deal with clauses weighted by a degree which is a lower bound of a necessity or a possibility measure, according to the nature of the uncertainty. Two resolution rules are used for coping with the different situations, and the refutation method can be generalized. Besides the lower bounds are allowed to be functions of variables involved in the clause, which gives hypothetical reasoning capabilities. The relation between our approach and the idea of minimizing abnormality is briefly discussed. In case where only lower bounds of necessity measures are involved, a semantics is proposed, in which the completeness of the extended resolution principle is proved. Moreover deduction from a partially inconsistent knowledge base can be managed in this approach and displays some form of non-monotonicity.

A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The proposed semantics is based on fuzzy sets of interpretations. It is tolerant to partial inconsistency. Satisfiability is extended from interpretations to fuzzy sets of interpretations, each fuzzy set representing a possibility distribution describing what is known about the state of the world. A possibilistic knowledge base is then viewed as a set of possibility distributions that satisfy it. The refutation method of automated deduction in possibilistic logic, based on previously introduced generalized resolution principle is proved to be sound and complete with respect to the proposed semantics, including the case of partial inconsistency.

Many AI synthesis problems such as planning or scheduling may be modelized as constraint satisfaction problems (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all given constraints between these variables. However, for many real tasks such as job-shop scheduling, time-table scheduling, design?, all these constraints have not the same significance and have not to be necessarily satisfied. A first distinction can be made between hard constraints, which every solution should satisfy and soft constraints, whose satisfaction has not to be certain. In this paper, we formalize the notion of possibilistic constraint satisfaction problems that allows the modeling of uncertainly satisfied constraints. We use a possibility distribution over labelings to represent respective possibilities of each labeling. Necessity-valued constraints allow a simple expression of the respective certainty degrees of each constraint. The main advantage of our approach is its integration in the CSP technical framework. Most classical techniques, such as Backtracking (BT), arcconsistency enforcing (AC) or Forward Checking have been extended to handle possibilistics CSP and are effectively implemented. The utility of our approach is demonstrated on a simple design problem.

Possibilistic logic has been proposed as a numerical formalism for reasoning with uncertainty. There has been interest in developing qualitative accounts of possibility, as well as an explanation of the relationship between possibility and modal logics. We present two modal logics that can be used to represent and reason with qualitative statements of possibility and necessity. Within this modal framework, we are able to identify interesting relationships between possibilistic logic, beliefs and conditionals. In particular, the most natural conditional definable via possibilistic means for default reasoning is identical to Pearl's conditional for e-semantics.

This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation taking into account the existence of consistent arguments in favor of a conclusion and the absence of consistent arguments in favor of its contrary, is particularly investigated. Flat knowledge bases, i.e. without any priority between their elements, as well as prioritized ones where some elements are considered as more strongly entrenched than others are studied under different consequence relations. Lastly a paraconsistent-like treatment of prioritized knowledge bases is proposed, where both the level of entrenchment and the level of paraconsistency attached to a formula are propagated. The priority levels are handled in the framework of possibility theory.

This paper discusses belief revision under uncertain inputs in the framework of possibility theory. Revision can be based on two possible definitions of the conditioning operation, one based on min operator which requires a purely ordinal scale only, and another based on product, for which a richer structure is needed, and which is a particular case of Dempster's rule of conditioning. Besides, revision under uncertain inputs can be understood in two different ways depending on whether the input is viewed, or not, as a constraint to enforce. Moreover, it is shown that M.A. Williams' transmutations, originally defined in the setting of Spohn's functions, can be captured in this framework, as well as Boutilier's natural revision.

This paper addresses the problem of merging uncertain information in the framework of possibilistic logic. It presents several syntactic combination rules to merge possibilistic knowledge bases, provided by different sources, into a new possibilistic knowledge base. These combination rules are first described at the meta-level outside the language of possibilistic logic. Next, an extension of possibilistic logic, where the combination rules are inside the language, is proposed. A proof system in a sequent form, which is sound and complete with respect to the possibilistic logic semantics, is given.