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An important problem in the management of knowledge-based systems is the handling of inconsistency. Inconsistency may appear because the knowledge may come from different sources of information. To solve this problem, two kinds of

Possibilistic logic provides a convenient tool for dealing with inconsistency and handling uncertainty. In this paper, we propose possibilistic description logics as an extension of description logics. We give semantics and syntax of possibilistic description logics. We then define two inference services in possibilistic description logics. Since possibilistic inference suffers from the drowning problem, we consider a drowning-free variant of possibilistic inference, called linear order inference. Finally, we implement the algorithms for inference services in possibilistic description logics using KAON2 reasoner.

Abstract. Possibilistic logic provides a convenient tool for dealing with inconsistency and handling uncertainty. In this paper, we propose possibilistic description logics (DLs) as an extension of description logics. We give semantics and syntax of possibilistic description logics. Two kinds of inference services are considered in our logics and algorithms are provided for them. These algorithms are implemented using KAON2 reasoner. 1

Abstract. Inconsistency handling is a central problem in many knowledge representation fields, such as belief revision, belief merging. Many approaches have been proposed to handle inconsistency in ontologies. In this paper, we propose a stratification-based approach for inconsistency handling in description logics (DLs), a family of ontology languages. This approach consists of two steps. In the first step, we obtain a preference relation on the axioms in the DL knowledge base using an algorithm. Then two existing approaches in first-order logic are adapted to resolve conflicting information in the stratified DL knowledge base. 1

In this paper, we propose an adaptive approach to merging possibilistic knowledge bases that deploys multiple operators instead of a single operator in the merging process. The merging approach consists of two steps: one is called the splitting step and the other is called the combination step. The splitting step splits each knowledge base into two subbases and then in the second step, di#erent classes of subbases are combined using di#erent operators. Our approach is applied to knowledge bases which are self-consistent and the result of merging is also a consistent knowledge base. Two operators are proposed based on two di#erent splitting methods. Both operators result in a possibilistic knowledge base which contains more information than that obtained by the t-conorm (such as the maximum) based merging methods. In the flat case, one of the operators provides a good alternative to syntax-based merging operators in classical logic.

Abstract — This paper describes the use of syntactical data fusion to computing possibilistic qualitative decisions. More precisely qualitative possibilistic decisions can be viewed as a data fusion problem of two particular possibility distributions (or possibilistic knowledge bases): the first one representing the beliefs of an agent and the second one representing the qualitative utility. The proposed algorithm computes a pessimistic optimal decisions based on data fusion techniques. We show that the computation of optimal decisions is equivalent to computing an inconsistency degree of possibilistic bases representing the fusion of agent’s beliefs and agent’s preferences.

Linear constraints occur naturally in many reasoning problems and the information that they represent is often uncertain. There is a difficulty in applying AI uncertainty formalisms to this situation, as their representation of the underlying logic, either as a mutually exclusive and exhaustive set of possibilities, or with a propositional or a predicate logic, is inappropriate (or at least unhelpful). To overcome this difficulty, we express reasoning with linear constraints as a logic, and develop the formalisms based on this different underlying logic. We focus in particular on a possibilistic logic representation of uncertain linear constraints, a lattice-valued possibilistic logic, an assumption-based reasoning formalism and a Dempster-Shafer representation, proving some fundamental results for these extended systems. Our results on extending uncertainty formalisms also apply to a very general class of underlying monotonic logics. Key words: possibilistic logic, lattice-valued possibilistic logic, Dempster-Shafer theory, assumption-based reasoning, linear constraints, spatial and temporal reasoning 1

Abstract — This paper proposes a first comparative study of the expressive power of two approaches to the representation of preferences: the conditional preferences networks (CP-nets) and a logical preference representation framework, namely the possibilistic logic. It is shown that possibilistic logic, using a method for handling symbolic priority weights, can always provide complete preorders compatible with the partial CPnet order. Although CP-nets provide an intuitive appealing setting for expressing preferences, possibilistic logic appears to be somewhat more flexible for that purpose. I.

Possibilistic logic is a well-known framework for dealing with uncertainty and reasoning under inconsistent knowledge bases. Standard possibilistic logic expressions are propositional logic formulas associated with positive real degrees belonging to [0,1]. However, in practice it may be difficult for an expert to provide exact degrees associated with formulas of a knowledge base. This paper proposes a flexible representation of uncertain information where the weights associated with formulas are in the form of intervals. We first study a framework for reasoning with interval-based possibilistic knowledge bases by extending main concepts of possibilistic logic such as the ones of necessity and possibility measures. We then provide a characterization of an interval-based possibilistic logic base by means of a concept of compatible standard possibilistic logic bases. We show that intervalbased possibilistic logic extends possibilistic logic in the case where all intervals are singletons. Lastly, we provide computational complexity results of deriving plausible conclusions from interval-based possibilistic bases and we show that the flexibility in representing uncertain information is handled without extra computational costs.