Section: New Results

Reasoning with Inconsistency

Participants : Meghyn Bienvenu, Pierre Bisquert, Patrice Buche, Abdelraouf Hecham, Madalina Croitoru, Jérôme Fortin, Rallou Thomopoulos, Bruno Yun.

When reasoning about inconsistent logical KBs, one has to deploy reasoning mechanisms that do not follow the classical logical inference. This is due to the fact that, in classical logic, falsum implies everything. Alternative reasoning techniques are therefore needed in order to make sense of such KBs. In this section we present our results using two main classes of such techniques: defeasible reasoning and maxi-consistent reasoning.

Defeasible Reasoning

Defeasible reasoning is used to evaluate claims or statements in an inconsistent setting where the rules encoding the ontological knowledge may contradict each other. Unfortunately, there is no universally valid way to reason defeasibly. An inherent characteristic of defeasible reasoning is its systematic reliance on a set of intuitions and rules of thumb, which have been long debated between logicians. For example, could an information derived from a contested claim be used to contest another claim (i.e., ambiguity handling)? Could “chains” of reasoning for the same claim be combined to defend against challenging statements (i.e., team defeat)? Is circular reasoning allowed? Etc. We got interested in the task of a data engineer looking to select what existing tool to use to perform defeasible reasoning. To this end we proposed the first benchmark in the literature for first-order logic defeasible reasoning tools profiling and showed how to use the proposed benchmark in order to categorize existing tools based on their semantics (e.g. ambiguity handling), logical language (e.g. existential rules) and expressiveness (e.g. priorities) [25]. Furthermore, we proposed a new logical formalism called Statement Graphs (SGs) that captures the state-of-the-art defeasible reasoning features via a flexible labelling function [24].

Maxi-Consistent Reasoning

We now consider reasoning with inconsistent knowledge bases, when making the assumption that the ontological knowledge (here expressed by rules) is reliable, hence inconsistencies come from the data (or factbase), which may contradict ontological knowledge. We consider maximally consistent subsets of the factbase as the basis for inference (in short, “maxi-consistent” reasoning).

Repair semantics. One of the main challenges of reasoning with inconsistency is handling the inherent inconsistency that might occur amongst independently built data sources partially describing the same knowledge of interest. Inconsistency-tolerant semantics consider all maximally consistent subsets of a factbase, called repairs, that they manipulate using a modifier of these repairs (e.g. saturating them by the rules) and an inference strategy (e.g. answers have to be found in all repairs). However, using all repairs might be inappropriate for certain applications that would rather focus on particular data sources. For instance, when considering more reliable sources (i.e., sensor information, provenance data etc.) one could focus on repairs using mostly facts from such sources. When there is no given preference order on sources, we propose to use an intrinsic preference on facts based on their participation in inconsistencies, which generates a preference of repairs (i.e., those that contain less controversial facts are preferred). This led us to define a novel framework that takes into consideration the inconsistency on the facts and restricts the set of repairs to the “best” with respect to inconsistency values. We showed the significance and the practical interest of our approach using the real data collected in the framework of the Pack4Fresh project for reducing food wastes. During this project, we collected data using an online poll from a set of professionals of the food industry, including wholesalers, quality managers, floorwalkers and warehouse managers, about food packagings and their characteristics. The framework was able to rank the repairs efficiently and the results were then analysed and evaluated by experts from the packaging industry [35].

Argumentation. Argumentation is a reasoning under inconsistency technique, that allows to build arguments and attacks over an inconsistent data. The arguments represent the various inferences one can make. The attacks capture the inconsistency between the different pieces of knowledge. The set of arguments and the corresponding set of attacks is referred to as an argumentation framework (AF). AFs are visually represented using a directed graph where the nodes represent the arguments and the directed edges the attacks between the arguments. Classically, reasoning with argumentation systems consists of finding the maximal sets of arguments that (1) are not attacking each other and (2) defend themselves (as a group) from all incoming attacks. Such sets are called extensions.

Argumentation as a reasoning method over logic knowledge bases has the added value of providing better explanations to users than classical methods. However, one drawback of logic based argumentation frameworks is the large number of arguments generated. We provided a methodology for filtering semantically redundant arguments adapted for knowledge bases without rules or knowledge bases with rules. In the first case of knowledge bases without rules, we use the observation that free facts (i.e., facts that are not touched by any negative constraints) induce an exponential growth on the argumentation graph without any impact on its underlying structure. Therefore, we first generate the argumentation graph corresponding to the knowledge base without the free facts and then redo the whole graph including the arguments of the free facts in an efficient manner. In the second case, of the knowledge bases with rules, we introduce a new structure for the arguments and the attacks. In this new structure, we have significantly less arguments [28] (extended in [31]).

Furthermore, we provided a tool called Dagger that allows a knowledge engineer to (1) input a KB in a commonly used format and then (2) generate, (3) visualise or (4) export the argumentation graph [30]. Using the tool we were able to provide the first benchmark of logic based argumentation graphs in the litterature [32].

An alternative to the extension based semantics explained above are the ranking based semantics used mainly in the case where arguments are seen as abstract entities (and not necessarily logic derivation). There is a difference in the output format between these two approaches: when using a ranking based semantics, the output is a ranking on the arguments; in the case of extension based semantics, the output is a set of extensions. While the ranking and the scores (which are present in many ranking based semantics) allow to better assess the acceptability degree of each individual argument, the question “what are the different points of view of the argumentation framework?” stays unanswered when using a ranking based semantics. We have proposed a modular framework that is generic enough to be able to accommodate various application scenarios. In this case, one important property of the framework lies in its versatility and its capacity to yield different results according to various instantiations [33].