The PITA System: Tabling and Answer Subsumption for Reasoning under Uncertainty

Many real world domains require the representation of a measure of uncertainty. The most common such representation is probability, and the combination of probability with logic programs has given rise to the field of Probabilistic Logic Programming (PLP), leading to languages such as the Independent Choice Logic, Logic Programs with Annotated Disjunctions (LPADs), Problog, PRISM and others. These languages share a similar distribution semantics, and methods have been devised to translate programs between these languages. The complexity of computing the probability of queries to these general PLP programs is very high due to the need to combine the probabilities of explanations that may not be exclusive. As one alternative, the PRISM system reduces the complexity of query answering by restricting the form of programs it can evaluate. As an entirely different alternative, Possibilistic Logic Programs adopt a simpler metric of uncertainty than probability. Each of these approaches -- general PLP, restricted PLP, and Possibilistic Logic Programming -- can be useful in different domains depending on the form of uncertainty to be represented, on the form of programs needed to model problems, and on the scale of the problems to be solved. In this paper, we show how the PITA system, which originally supported the general PLP language of LPADs, can also efficiently support restricted PLP and Possibilistic Logic Programs. PITA relies on tabling with answer subsumption and consists of a transformation along with an API for library functions that interface with answer subsumption

Fuzzy to Random Uncertainty Alignment

The objective of this paper is to present new and simple mathematical approach to deal with uncertainty alignment between fuzzy and random data. In particular we present a method to describe fuzzy (possibilistic) distribution in terms of a pair (or more) of related random (probabilistic) events, both fixed and variable. Our approach uses basic properties of both fuzzy and random distributions. We show that the data fuzziness can be viewed as a non uniqueness of related random events. We also show how fuzzy-random consistancy principle can be given precise mathemtaical meaning. Various types of fuzzy distributions are examined, special cases considered, and several numerical examples presented

Uncertainty-wise software anti-patterns detection: A possibilistic evolutionary machine learning approach

Context: Code smells (a.k.a. anti-patterns) are manifestations of poor design solutions that can deteriorate software maintainability and evolution. Research gap: Existing works did not take into account the issue of uncertain class labels, which is an important inherent characteristic of the smells detection problem. More precisely, two human experts may have different degrees of uncertainty about the smelliness of a particular software class not only for the smell detection task but also for the smell type identification one. Unluckily, existing approaches usually reject and/or ignore uncertain data that correspond to software classes (i.e. dataset instances) with uncertain labels. Throwing away and/or disregarding the uncertainty factor could considerably degrade the detection/identification process effectiveness. From a solution approach viewpoint, there is no work in the literature that proposed a method that is able to detect and/or identify code smells while preserving the uncertainty aspect. Objective: The main goal of our research work is to handle the uncertainty factor, issued from human experts, in detecting and/or identifying code smells by proposing an evolutionary approach that is able to deal with anti-patterns classification with uncertain labels. Method: We suggest Bi-ADIPOK, as an effective search-based tool that is capable to tackle the previously mentioned challenge for both detection and identification cases. The proposed method corresponds to an EA (Evolutionary Algorithm) that optimizes a set of detectors encoded as PK-NNs (Possibilistic K-nearest neighbors) based on a bi-level hierarchy, in which the upper level role consists on finding the optimal PK-NNs parameters, while the lower level one is to generate the PK-NNs. A newly fitness function has been proposed fitness function PomAURPC-OVA_dist (Possibilistic modified Area Under Recall Precision Curve One-Versus-All_distance, abbreviated PAURPC_d in this paper). Bi-ADIPOK is able to deal with label uncertainty using some concepts stemming from the Possibility Theory. Furthermore, the PomAURPC-OVA_dist is capable to process the uncertainty issue even with imbalanced data. We notice that Bi-ADIPOK is first built and then validated using a possibilistic base of smell examples that simulates and mimics the subjectivity of software engineers opinions. Results: The statistical analysis of the obtained results on a set of comparative experiments with respect to four relevant state-of-the-art methods shows the merits of our proposal. The obtained detection results demonstrate that, for the uncertain environment, the PomAURPC-OVA_dist of Bi-ADIPOK ranges between 0.902 and 0.932 and its IAC lies between 0.9108 and 0.9407, while for the certain environment, the PomAURPC-OVA_dist lies between 0.928 and 0.955 and the IAC ranges between 0.9477 and 0.9622. Similarly, the identification results, for the uncertain environment, indicate that the PomAURPC-OVA_dist of Bi-ADIPOK varies between 0.8576 and 0.9273 and its IAC is between 0.8693 and 0.9318. For the certain environment, the PomAURPC-OVA_dist lies between 0.8613 and 0.9351 and the IAC values are between 0.8672 and 0.9476. With uncertain data, Bi-ADIPOK can find 35% more code smells than the second best approach (i.e., BLOP). Furthermore, Bi-ADIPOK has succeeded to reduce the number of false alarms (i.e., misclassified smelly instances) by 12%. In addition, our proposed approach can identify 43% more smell types than BLOP and reduces the number of false alarms by 32%. The same results have been obtained for the certain environment, demonstrating Bi-ADIPOK's ability to deal with such environment