Section: New Results

Reasoning with Imperfect Information and Priorities

Participants : Madalina Croitoru, Jérôme Fortin, Souhila Kaci, Tjitze Rienstra, Rallou Thomopoulos.

In collaboration with: Joël Abecassis (IATE/INRA), Patrice Buche (IATE/INRA), Nir Oren (Univ. of Aberdeen, Scotland), Leon van der Torre (University of Luxembourg) and Nouredine Tamani (post-doc IATE).

This year, we mainly investigated decision support based on argumentations systems and preferences, either in relation with application needs in agronomy or on more fundamental aspects.

Argumentation for Decision Making in Agronomy

Historically, scientific investigations in this axis are guided by applications of our partners in agronomy (IATE laboratory). Part of the work has consisted of analyzing the proposed applications and the techniques they require in order to select appropriate applications with respect to our team project.

In the context of the EcoBioCap project (see Sect.  8.2 ), the different stakeholders have expressed conflicting preferences for the packaging quality. However, when discussing with domain experts they have raised the need for a tool which allows them to highlight a conflict and see the reasons behind it. In order to achieve this goal two steps were taken. First we have instantiated a popular logical argumentation framework (ASPIC+) with a simple preference logic. This allowed the different experts to express arguments about their preferences. We can then extract maximal consistent subsets of preferences by the means of extensions.

• This work was performed in collaboration with the University of Aberdeen (Dr. Nir Oren) and the results were published and presented at the COMMA conference [24] .

Second, a negotiation phase was introduced to the previously described system in order for the domain experts to refine and extend their preferences. This tool was the aim of the master thesis of Patricio Mosse.

• This work was published and presented at the Effost conference [23] , based upon Patricio Mosse's Master Thesis [48] . A detailed journal article reporting on the two steps is under preparation and will be submitted beginning 2013.

Let us mention additional results related to the applications in agronomy on semi-automatic data extraction from web data (tables) [39] , [40] , [41] , data reliability, and the representation and flexible querying of imprecise data with fuzzy sets [42] , [15] . These investigations are complementary to the above mentioned results on argumentation and generally relate to other aspects in the same applicative projects.

Conditional Acceptance Functions

Dung-style abstract argumentation theory centers on argumentation frameworks and acceptance functions. The latter take as input a framework and return sets of labelings. A labeling assigns “in”, “out” or “undecided” to each arguments. Arguments having “in” assignment are acceptable arguments. This methodology however assumes full awareness of the arguments relevant to the evaluation. There are two reasons why this is not satisfactory. Firstly, full awareness is, in general, not a realistic assumption. Second, frameworks have explanatory power, which allows us to reason abductively or counterfactually, but this is lost under the usual semantics. To recover this aspect, we generalized conventional acceptance, and we present the concept of a conditional acceptance function which copes with the dynamics of argumentation frameworks.

• Results published in [28] .

Foundational Aspects of Preferences

Preferences are the backbone of various fields as they naturally arise and play an important role in many real-life decisions. Preferences are fundamental in scientific research frameworks as well as applications. One of the main problems an individual faces when expressing her preferences lies in the number of variables (or attributes or criteria) that she takes into account to evaluate the different outcomes. Indeed, the number of outcomes increases exponentially with the number of variables. Moreover, due to their cognitive limitation, individuals are generally not willing to compare all possible pairs of outcomes or evaluate them individually. These facts have an unfortunate consequence that any preference representation language that is based on the direct assessment of individual preferences over the complete set of outcomes is simply infeasible.

Fortunately, individuals can abstract their preferences. More specifically, instead of providing preferences over outcomes (by pairwise comparison or individual evaluation), they generally express preferences over partial descriptions of outcomes. Often such statements take the form of qualitative comparative preference statements e.g., “I like London more than Paris” and “prefer tea to coffee”. Conditional logics aim at representing such partial descriptions of individual preferences which we refer to as comparative preference statements. They use different completion principles in order to compute a preference relation induced by a set of preference statements. In particular they use various more or less strong semantics to interpret comparative preference statements. So far the main objective in artificial intelligence has been to rank-order the set of outcomes given a set of comparative preference statements and one or several semantics. We addressed this problem from a different angle. We considered a set of postulates studied in preference logics and non-monotonic reasoning which formalize intuition one may have regarding the behavior of preference statements. We analyzed the behavior of the different semantics w.r.t. these postulates. Our analysis gives a complete picture of the behavior of our (five) semantics.

In the last decade, AI researchers have pointed out the existence of two types of information: positive information and negative information. This distinction has also been asserted in cognitive psychology. Distinguishing between these two types of information may be useful in both knowledge and preference representation. In the first case, one distinguishes between situations which are not impossible because they are not ruled out by the available knowledge, and what is possible for sure. In the second case, one distinguishes between what is not rejected and what is really desired. Besides it has been shown that possibility theory is a convenient tool to model and distinguish between these two types of information. Knowledge/Preference representation languages have also been extended to cope with this particular kind of information. Nevertheless despite solid theoretical advances in this topic, the crucial question of “which reading (negative or positive) one should have” remains a real bottleneck. We focused on comparative statements and presented a set of postulates describing different situations one may encounter. We provided a representation theorem describing which sets of postulates are satisfied by which kind of information (negative or positive) and conversely. One can then decide which reading to apply depending on which postulates she privileges.

• Results published in [29] and [30] .

Argumentation for Inconsistency-Tolerant Query Answering (Work in Progress)

Argumentation allows to encode by the means of extensions maximal subsets of the knowledge base which are consistent (given the logic chosen). We are currently investigating the link between different argumentation extensions and the notion of a maximal repair as introduced by [51] , [50] in the context of the positive existential subset of first order logic we are mainly working with. We are then interested in comparing the semantics proposed in the literature for query answering with inconsistent knowledge bases and argumentation reasoning paradigms. This study has been performed jointly with the University of Luxembourg during a research visit during end of November. We plan to submit our results at a conference beginning January.