Parametric Connectives in Disjunctive Logic Programming

Disjunctive Logic Programming (\DLP) is an advanced formalism for Knowledge Representation and Reasoning (KRR). \DLP is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class \SigmaP{2} (\NP^{\NP}). Importantly, the \DLP encodings are often simple and natural. In this paper, we single out some limitations of \DLP for KRR, which cannot naturally express problems where the size of the disjunction is not known ``a priori'' (like N-Coloring), but it is part of the input. To overcome these limitations, we further enhance the knowledge modelling abilities of \DLP, by extending this language by {\em Parametric Connectives (OR and AND)}. These connectives allow us to represent compactly the disjunction/conjunction of a set of atoms having a given property. We formally define the semantics of the new language, named $DLP^{\bigvee,\bigwedge}$ and we show the usefulness of the new constructs on relevant knowledge-based problems. We address implementation issues and discuss related works

A Machine Learning guided Rewriting Approach for ASP Logic Programs

Answer Set Programming (ASP) is a declarative logic formalism that allows to encode computational problems via logic programs. Despite the declarative nature of the formalism, some advanced expertise is required, in general, for designing an ASP encoding that can be efficiently evaluated by an actual ASP system. A common way for trying to reduce the burden of manually tweaking an ASP program consists in automatically rewriting the input encoding according to suitable techniques, for producing alternative, yet semantically equivalent, ASP programs. However, rewriting does not always grant benefits in terms of performance; hence, proper means are needed for predicting their effects with this respect. In this paper we describe an approach based on Machine Learning (ML) to automatically decide whether to rewrite. In particular, given an ASP program and a set of input facts, our approach chooses whether and how to rewrite input rules based on a set of features measuring their structural properties and domain information. To this end, a Multilayer Perceptrons model has then been trained to guide the ASP grounder I-DLV on rewriting input rules. We report and discuss the results of an experimental evaluation over a prototypical implementation.Comment: In Proceedings ICLP 2020, arXiv:2009.0915

Data Augmentation: a Combined Inductive-Deductive Approach featuring Answer Set Programming

Although the availability of a large amount of data is usually given for granted, there are relevant scenarios where this is not the case; for instance, in the biomedical/healthcare domain, some applications require to build huge datasets of proper images, but the acquisition of such images is often hard for different reasons (e.g., accessibility, costs, pathology-related variability), thus causing limited and usually imbalanced datasets. Hence, the need for synthesizing photo-realistic images via advanced Data Augmentation techniques is crucial. In this paper we propose a hybrid inductive-deductive approach to the problem; in particular, starting from a limited set of real labeled images, the proposed framework makes use of logic programs for declaratively specifying the structure of new images, that is guaranteed to comply with both a set of constraints coming from the domain knowledge and some specific desiderata. The resulting labeled images undergo a dedicated process based on Deep Learning in charge of creating photo-realistic images that comply with the generated label