Safa Yahi

JELIA Conference 2010 Conference Paper

Bridging Possibilistic Conditional Knowledge Bases and Partially Ordered Bases

• Salem Benferhat
• Sylvain Lagrue
• Safa Yahi

Abstract Possibilistic logic offers a unified framework for revising prioritized pieces of information and for reasoning with conditional knowledge bases. A conditional assertion of the form ”generally, if α is true then β is true” is interpreted as a constraint expressing that the possibility degree of having \(\alpha \land \beta\) being true is greater than the possibility degree of having \(\alpha \land \neg \beta\) being true. Recently, an important extension of possibilistic logic has been proposed to deal with partially pre-ordered bases in order to avoid comparing unrelated pieces of information. This paper establishes relationships between reasoning from partially pre-ordered bases and reasoning from conditional knowledge bases. It contains two important contributions. The first contribution consists in identifying conditions under which a partially ordered belief base can be encoded as a set of conditional assertions, and conversely. In particular, we provide the correspondences between the concept of compatible possibility distributions used for conditional assertions and the one of compatible prioritized bases used for partially pre-ordered bases. The second important contribution of this paper consists in providing the computational complexity of reasoning with partially pre-ordered bases using the well-known possibilistic and inclusion-based policies.

KR Conference 2008 Conference Paper

A Lexicographic Inference for Partially Preordered Belief Bases

• Safa Yahi
• Salem Benferhat
• Sylvain Lagrue
• Mariette Sérayet
• Odile Papini

Coherence-based approaches are quite popular to reason under inconsistency. Most of them are defined with respect to totally preordered belief bases such as the lexicographic inference which is known to have desirable properties from theoretical, practical and psychological points of view. However, partially preordered belief bases offer much more flexibility to represent efficiently incomplete knowledge and to avoid comparing unrelated pieces of information. In this paper, we propose a lexicographic inference for partially preordered belief bases that extends the classical one. On one hand, we define a natural inference relation which consists in applying classical lexicographic inference from all compatible totally preordered belief bases. On the other hand, we propose a novel cardinality-based preorder between consistent subbases. This cardinality-based preorder can be indifferently applied on partially or totally preordered belief bases. Then, applying classical inference on the preferred consistent subbases, according to this preorder, provides another lexicographic inference relation for partially preordered belief bases. Interestingly enough, we show that these two inference relations are equivalent. Lastly, a semantic characterization of these two equivalent definitions is provided.

IJCAI Conference 2007 Conference Paper

• Salem Benferhat
• Safa Yahi
• Habiba Drias

Developing efficient approaches for reasoning under inconsistency is an important issue in many applications. Several methods have been proposed to compile, possibly inconsistent, weighted or stratified bases. This paper focuses on the well-known linear order and possibilistic logic strategies. It provides a way for compiling a stratified belief base in order to be able to process inference from it in polynomial time. The resulting extra compilation cost is very low. In particular, the number of additional variables, that are added to original stratified bases, corresponds exactly to the number of priority levels existing in the base. Moreover, our compilation approach allows an efficient computation of weighted possibilistic conclusions and possibilistic conditioning.