Induction of Interpretable Possibilistic Logic Theories from Relational Data

The field of Statistical Relational Learning (SRL) is concerned with learning probabilistic models from relational data. Learned SRL models are typically represented using some kind of weighted logical formulas, which make them considerably more interpretable than those obtained by e.g. neural networks. In practice, however, these models are often still difficult to interpret correctly, as they can contain many formulas that interact in non-trivial ways and weights do not always have an intuitive meaning. To address this, we propose a new SRL method which uses possibilistic logic to encode relational models. Learned models are then essentially stratified classical theories, which explicitly encode what can be derived with a given level of certainty. Compared to Markov Logic Networks (MLNs), our method is faster and produces considerably more interpretable models.Comment: Longer version of a paper appearing in IJCAI 201

A psychological study of bipolarity in the possibilistic framework

The expression "bipolar information" denotes the fact that positive and negative information are not processed in the same way. This study aimed at testing the psychological plausibility of the possibilistic treatment of bipolar information. Rather than testing empirically some predictions derived from possibility theory, we tested whether the possibilistic representation of bipolarity allows understanding previously unexplained psychological data. Psychological works related to Human hypothesis testing furnished the task for this study, namely, the "2-4-6 rule discovery task". Based on an analysis of the status ("impossible", "guaranteed possible", "non impossible") of the states of the world ruled out or allowed by positive or negative pieces of information, we found that the so-called "positive test strategy" (previously seen as irrational) produces on the whole information less uncertain than the concurrent so-called "negative test strategy" (previously seen as the normative one). Further works on the same line of research are pointed out

Anytime Algorithms for Solving Possibilistic MDPs and Hybrid MDPs

The ability of an agent to make quick, rational decisions in an uncertain environment is paramount for its applicability in realistic settings. Markov Decision Processes (MDP) provide such a framework, but can only model uncertainty that can be expressed as probabilities. Possibilistic counterparts of MDPs allow to model imprecise beliefs, yet they cannot accurately represent probabilistic sources of uncertainty and they lack the efficient online solvers found in the probabilistic MDP community. In this paper we advance the state of the art in three important ways. Firstly, we propose the first online planner for possibilistic MDP by adapting the Monte-Carlo Tree Search (MCTS) algorithm. A key component is the development of efficient search structures to sample possibility distributions based on the DPY transformation as introduced by Dubois, Prade, and Yager. Secondly, we introduce a hybrid MDP model that allows us to express both possibilistic and probabilistic uncertainty, where the hybrid model is a proper extension of both probabilistic and possibilistic MDPs. Thirdly, we demonstrate that MCTS algorithms can readily be applied to solve such hybrid models. © Springer International Publishing Switzerland 2016.This work is partially funded by EPSRC PACES project (Ref: EP/J012149/1).Peer Reviewe

Lexicographic Inference for Partially Ordered Belief Bases

International audienceCoherence-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 con- sists 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 the second inference is covered by the first one. Lastly, a semantic characterization of these two definitions is provided

Formalisation and logical properties of the maximal ideal recursive semantics for weighted defeasible logic programming

Possibilistic defeasible logic programming (P-DeLP) is a logic programming framework which combines features from argumentation theory and logic programming, in which defeasible rules are attached with weights expressing their relative belief or preference strength. In P-DeLP,a conclusion succeeds if there exists an argument that entails the conclusion and this argument is found to be undefeated by a warrant procedure that systematically explores the universe of arguments in order to present an exhaustive synthesis of the relevant chains of pros and cons for the given conclusion. Recently, we have proposed a new warrant recursive semantics for P-DeLP, called Recursive P-DeLP (RP-DeLP for short), based on the claim that the acceptance of an argument should imply also the acceptance of all its sub-arguments which reflect the different premises on which the argument is based. This paper explores the relationship between the exhaustive dialectical analysis-based semantics of P-DeLP and the recursive-based semantics of RP-DeLP, and analyses a non-monotonic inference operator for RP-DeLP which models the expansion of a given program by adding new weighted facts associated with warranted conclusions. Given the recursive-based semantics of RP-DeLP, we have also implemented an argumentation framework for RP-DeLP that is able to compute not only the output of warranted and blocked conclusions, but also explain the reasons behind the status of each conclusion. We have developed this framework as a stand-alone application with a simple text-based input/output interface to be able to use it as part of other artificial intelligence systemsThis research was partially supported by the Spanish projects EdeTRI (TIN2012-39348-C02-01) and AT (CONSOLIDER- INGENIO 2010, CSD2007-00022)