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A rational number can be naturally presented by an arithmetic computation (AC): a sequence of elementary arithmetic operations starting from a fixed constant, say 1. The asymptotic complexity issues of such a representation are studied e.g.…
Artificial Intelligence (AI) approaches to problem-solving and decision-making are becoming more and more complex, leading to a decrease in the understandability of solutions. The European Union's new General Data Protection Regulation…
Over the last two decades, propositional satisfiability (SAT) has become one of the most successful and widely applied techniques for the solution of NP-complete problems. The aim of this paper is to investigate theoretically how Sat can be…
While in recent years machine learning (ML) based approaches have been the popular approach in developing end-to-end question answering systems, such systems often struggle when additional knowledge is needed to correctly answer the…
Disjunctive Answer Set Programming is a powerful declarative programming paradigm with complexity beyond NP. Identifying classes of programs for which the consistency problem is in NP is of interest from the theoretical standpoint and can…
Answer Set Programming (ASP) is nowadays a dominant rule-based knowledge representation tool. Though existing ASP variants enjoy efficient implementations, generating an answer set remains intractable. The goal of this research is to define…
As the practical use of answer set programming (ASP) has grown with the development of efficient solvers, we expect a growing interest in extensions of ASP as their semantics stabilize and solvers supporting them mature. Epistemic…
Open Answer Set Programming (OASP) is an undecidable framework for integrating ontologies and rules. Although several decidable fragments of OASP have been identified, few reasoning procedures exist. In this article, we provide a sound,…
Answer set programming (ASP) and planning are two widely used paradigms for solving logic programs with declarative programming. In both cases, the quality of the input programs has a major influence on the quality and performance of the…
We compare two recent extensions of the answer set (stable model) semantics of logic programs. One of them, due to Lifschitz, Tang and Turner, allows the bodies and heads of rules to contain nested expressions. The other, due to Niemela and…
Answer Set Programming (ASP), a well-known declarative logic programming paradigm, has recently found practical application in Process Mining. In particular, ASP has been used to model tasks involving declarative specifications of business…
It is expected that progress toward true artificial intelligence will be achieved through the emergence of a system that integrates representation learning and complex reasoning (LeCun et al. 2015). In response to this prediction, research…
Answer Set Programming (ASP) is a well-known problem-solving formalism in computational logic. Nowadays, ASP is used in many real world scenarios thanks to ASP solvers. Standard evaluation of ASP programs suffers from an intrinsic…
Encoding finite linear CSPs as Boolean formulas and solving them by using modern SAT solvers has proven to be highly effective, as exemplified by the award-winning sugar system. We here develop an alternative approach based on ASP. This…
Answer Set Programming (ASP) is one of the major declarative programming paradigms in the area of logic programming and non-monotonic reasoning. Despite that ASP features a simple syntax and an intuitive semantics, errors are common during…
Extending ASP with constraints (CASP) enhances its expressiveness and performance. This extension is not straightforward as the grounding phase, present in most ASP systems, removes variables and the links among them, and also causes a…
Possibilistic logic programs (poss-programs) under stable models are a major variant of answer set programming (ASP). While its semantics (possibilistic stable models) and properties have been well investigated, the problem of inductive…
Neural symbolic processing aims to combine the generalization of logical learning approaches and the performance of neural networks. The Neural Theorem Proving (NTP) model by Rocktaschel et al (2017) learns embeddings for concepts and…
Cognitive theories for reasoning are about understanding how humans come to conclusions from a set of premises. Starting from hypothetical thoughts, we are interested which are the implications behind basic everyday language and how do we…
We introduce a stepping methodology for answer-set programming (ASP) that allows for debugging answer-set programs and is based on the stepwise application of rules. Similar to debugging in imperative languages, where the behaviour of a…