Souhila Kaci

Bipolar possibility theory in preference modeling: Representation, fusion and optimal solutions

The bipolar view in preference modeling distinguishes between negative and positive preferences. Negative preferences correspond to what is rejected, considered unacceptable, while positive preferences correspond to what is desired. But what is tolerated (i.e., not rejected) is not necessarily desired. Both negative and positive preferences can be a matter of degree. Bipolar preferences can be represented in possibilistic logic by two separate sets of formulas: prioritized constraints, which describe what is more or less tolerated, and weighted positive preferences, expressing what is particularly desirable. The problem of merging multiple-agent preferences in this bipolar framework is then discussed. Negative and positive preferences are handled separately and are combined in distinct ways. Since negative and positive preferences are stated separately, they may be inconsistent, especially in this context of preference fusion. Consistency can be enforced by restricting what is desirable to what is tolerated. After merging, and once the bipolar consistency is restored, the set of preferred solutions can be logically characterized. Preferred solutions should have the highest possible degree of feasibility, and only constraints with low priority may have to be discarded in case of inconsistency inside negative preferences. Moreover, preferred solutions should satisfy important positive preferences when feasible (positive preferences may be also inconsistent). Two types of preferred solutions can be characterized, either in terms of a disjunctive combination of the weighted positive preferences, or in terms of a cardinality-based evaluation.

Possibilistic Merging and Distance-Based Fusion of Propositional Information

The problem of merging multiple sources information is central in many information processing areas such as databases integrating problems, multiple criteria decision making, expert opinion pooling, etc. Recently, several approaches have been proposed to merge propositional bases, or sets of (non-prioritized) goals. These approaches are in general semantically defined. Like in belief revision, they use implicit priorities, generally based on Dalals distance, for merging the propositional bases and return a new propositional base as a result. An immediate consequence of the generation of a propositional base is the impossibility of decomposing and iterating the fusion process in a coherent way with respect to priorities since the underlying ordering is lost. This paper presents a general approach for fusing prioritized bases, both semantically and syntactically, when priorities are represented in the possibilistic logic framework. Different classes of merging operators are considered depending on whether the sources are consistent, conflicting, redundant or independent. We show that the approaches which have been recently proposed for merging propositional bases can be embedded in this setting. The result is then a prioritized base, and hence the process can be coherently decomposed and iterated. Moreover, this encoding provides a syntactic counterpart for the fusion of propositional bases.

Dynamics in Argumentation with Single Extensions: Abstraction Principles and the Grounded Extension

In this paper we consider the dynamics of abstract argumentation in Baroni and Giacomins framework for the evaluation of extension based argumentation semantics. Following Baroni and Giacomin, we do not consider individual approaches, but we define general principles or postulates that individual approaches may satisfy. In particular, we define abstraction principles for the attack relation, and for the arguments in the framework. We illustrate the principles on the grounded extension. In this paper we consider only principles for the single extension case, and leave the multiple extension case to further research.

On the generation of bipolar goals in argumentation-based negotiation

The notion of agent’s goals is crucial in negotiation dialogues. In fact, during a negotiation, each agent tries to make and to accept the offers which satisfy its own goals. Works on negotiation suppose that an agent has a set of fixed goals to pursue. However, it is not shown how these goals are computed and chosen by the agent. Moreover, these works handle one kind of goals: the ones that an agent wants to achieve. Recent studies on psychology claim that goals are bipolar and there are at least two kinds of goals: the positive goals representing what the agent wants to achieve and the negative goals representing what the agent rejects. In this paper, we present an argumentation-based framework which generates the goals of an agent. The framework returns three categories of goals: the positive goals, the negative ones and finally the goals in abeyance.

Logical representation and fusion of prioritized information based on guaranteed possibility measures: application to the distance-based merging of classical bases

In the possibility theory framework, prioritized information can be logically expressed in different formats. The most usual way, used in standard possibilistic logic, is to associate necessity degrees with propositional formulas. This paper considers another representation and fusion of prioritized information using guaranteed possibility measures. Prioritized pieces of information are then represented by sets of weighted formulas, called Δ-knowledge bases, where weights are lower bounds of guaranteed possibility degrees of formulas.We first show that the basic notions of standard possibilistic logic have natural counterparts when dealing with Δ-knowledge bases. In particular we present the inference machinery, and provide syntactic, but semantically meaningful, merging of Δ-knowledge bases. In the second part of the paper, we show that distance-based merging propositional knowledge bases can be naturally encoded using Δ-knowledge bases. Moreover, this encoding is more efficient than the necessity-based encoding of distance-based merging operator.

Database preferences queries: a possibilistic logic approach with symbolic priorities

The paper presents a new approach to database preferences queries, where preferences are represented in a possibilistic logic manner, using symbolic weights. The symbolic weights may be processed without assessing their precise value, which leaves the freedom for the user to not specify any priority among the preferences. The user may also enforce a (partial) ordering between them, if necessary. The approach can be related to the processing of fuzzy queries whose components are conditionally weighted in terms of importance. Here, importance levels are symbolically processed, and refinements of both Pareto ordering and minimum ordering are used. The representational power of the proposed setting is stressed, while the approach is compared with database Best operator-like methods and with the CP-net approach developed in artificial intelligence. The paper also provides a structured and rather broad overview of the different lines of research in the literature dealing with the handling of preferences in database queries.

Fusion of possibilistic knowledge bases from a postulate point of view

This paper proposes a postulate-based analysis of the fusion of possibilistic logic bases which are made of pieces of information expressing knowledge associated with certainty degrees. We propose two main sets of postulates: one only focuses on plausible conclusions, while the other considers both plausible conclusions and the certainty degrees associated with them. For each rational postulate, the class of operators that it satisfies is identified. The existence of weights associated with the pieces of information considerably enriches the postulates-based analysis, and leads to a refined classification of combination operators.

Reasoning with various kinds of preferences: logic, non-monotonicity, and algorithms

As systems dealing with preferences become more sophisticated, it becomes essential to deal with various kinds of preference statements and their interaction. We introduce a non-monotonic logic distinguishing sixteen kinds of preferences, ranging from strict to loose and from careful to opportunistic, and two kinds of ways to deal with uncertainty, either optimistically or pessimistically. The classification of the various kinds of preferences is inspired by a hypothetical agent comparing the two alternatives of a preference statement. The optimistic and pessimistic way of dealing with uncertainty correspond on the one hand to considering either the best or the worst states in the comparison of the two alternatives of a preference statement, and on the other hand to the calculation of least or most specific “distinguished” preference orders from a set of preference statements. We show that each way to calculate distinguished preference orders is compatible with eight kinds of preferences, in the sense that it calculates a unique distinguished preference order for a set of such preference statements, and we provide efficient algorithms that calculate these unique distinguished preference orders. In general, optimistic kinds of preferences are compatible with optimism in calculating distinguished preference orders, and pessimistic kinds of preferences are compatible with pessimism in calculating distinguished preference orders. However, these two sets of eight kinds of preferences are not exclusive, such that some kinds of preferences can be used in both ways to calculate distinguished preference orders, and other kinds of preferences cannot be used in either of them. We also consider the merging of optimistically and pessimistically constructed distinguished preferences orders.

Algorithms for a nonmonotonic logic of preferences

In this paper we introduce and study a nonmonotonic logic to reason about various kinds of preferences. We introduce preference types to choose among these kinds of preferences, based on an agent interpretation. We study ways to calculate “distinguished” preference orders from preferences, and show when these distinguished preference orders are unique. We define algorithms to calculate the distinguished preference orders.

Database preference queries--a possibilistic logic approach with symbolic priorities

The paper presents a new approach to database preference queries, where preferences are represented in a possibilistic logic manner, using symbolic weights. The symbolic weights may be processed without assessing their precise value, which leaves the freedom for the user to not specify any priority among the preferences. The user may also enforce a (partial) ordering between them, if necessary. The approach can be related to the processing of fuzzy queries whose components are conditionally weighted in terms of importance. In this paper, importance levels are symbolically processed, and refinements of both Pareto ordering and minimum ordering are used. The representational power of the proposed setting is stressed, while the approach is compared with database Best operator-like methods and with the CP-net approach developed in artificial intelligence. The paper also provides a structured and rather broad overview of the different lines of research in the literature dealing with the handling of preferences in database queries.