Applying Answer Set Programming with Fuzzy Membership Functions: a Case Study

Human reasoning often operates through qualitative concepts expressed by linguistic labels such as high, low, expensive, or cheap, whose interpretation depends on context and is usually vague, despite being rooted in numerical data. This paper explores a novel fuzzy-logic-based qualitative extension of Answer Set Programming (ASP) to bridge numerical information and qualitative reasoning. The underlying language, formally introduced in a separate work, provides a principled framework that avoids rigid thresholds and supports robust reasoning under vagueness. Focusing on a representative use case, we illustrate how the framework integrates numerically grounded inputs (such as outputs of machine learning models) with symbolic reasoning over qualitative labels. Key features, including learning-based membership functions and semantically enriched predicates, enable the combination of expert knowledge, contextual factors, and subjective interpretations within a unified declarative setting.

Reconstruction Error-based Anomaly Detection with Few Outlying Examples

Reconstruction error-based neural architectures constitute a classical deep learning approach to anomaly detection which has shown great performances. It consists in training an Autoencoder to reconstruct a set of examples deemed to represent the normality and then to point out as anomalies those data that show a sufficiently large reconstruction error. Unfortunately, these architectures often become able to well reconstruct also the anomalies in the data. This phenomenon is more evident when there are anomalies in the training set. In particular when these anomalies are labeled, a setting called semi-supervised, the best way to train Autoencoders is to ignore anomalies and minimize the reconstruction error on normal data. The goal of this work is to investigate approaches to allow reconstruction error-based architectures to instruct the model to put known anomalies outside of the domain description of the normal data. Specifically, our strategy exploits a limited number of anomalous examples to increase the contrast between the reconstruction error associated with normal examples and those associated with both known and unknown anomalies, thus enhancing anomaly detection performances. The experiments show that this new procedure achieves better performances than the standard Autoencoder approach and the main deep learning techniques for semi-supervised anomaly detection.