algorithms  
Editorial Special Issue on Logic-Based Artificial Intelligence  
[PERSON]  
Department of Mathematics and Computer Science, University of Calabria, Arcavacata, 87036 Rende, Italy; [EMAIL_ADDRESS]  
Since its inception, research in the field of _Artificial Intelligence_ (AI) has had a fundamentally logical approach; therefore, discussions have taken place to establish a way of distinguishing symbolic AI from sub-symbolic AI, basing the approach instead on the statistical approaches typical of _machine learning_, _deep learning_ or _Bayesian networks_. The logical-symbolic approach was dominant from 1956, the year in which the term AI was proposed by [PERSON], until the mid-nineteen seventies. However, when the overambitious expectations, such as that of reaching a _General AI_ within a few years, were not met, the decrease in funding led to the first AI Winter. In the early nineteen eighties, however, we witnessed a new springtime due to the commercially profitable idea of _expert systems_, capable of allowing the simulation of the knowledge of experts in a certain field through techniques of knowledge representation and automatic reasoning. However, even the expert systems had a short life and from 1988 onwards there was a new and longer AI Winter. Despite this, Symbolic AI remained the dominant paradigm until the mid-1990s, when the sub-symbolic approaches of machine learning began to re-emerge, but without unlocking the winter season. It would take until 2012 for the new spring of AI. This occurred thanks to sub-symbolic approaches through neural networks and so-called _deep learning_, which were able to implement their potential thanks to the ever-increasing amount of data available (_Big Data_). The results achieved by statistical approaches to AI led many in the academic community to think that logical theories could be totally abandoned and that the only fundamental aspect was a sufficiently large amount of data. However, the presence of bias in AI systems and the inability to provide explanations of decisions made through such systems showed the intrinsic limitations of purely statistical approaches and resulted in a pressing call to make AI systems explainable. This heralded _Explainable AI_ (XAI), showing at least the need for a hybrid approach, symbolic and sub-symbolic, at the same time, to develop an AI system capable of interacting satisfactorily with humans. The irrepressible human need to understand the reason for a certain response, action or decision thus brings the logical-symbolic approach back to the center of research; however, this was never abandoned by AI researchers, even in the coldest periods both for the whole AI and for Symbolic AI. In particular, since the 1980s, _logic programming_ has proven to be fundamental for solving computationally complex problems in AI. Problems are translated into a set of facts and rules, i.e., into a theory or logical program with a particular syntax and semantics. It is a declarative and non-procedural programming, allowing the developer to identify the logical structure of the starting problem, so that the logical models of the program will correspond to the possible solutions of the studied problem. Over the years, several families of logic programming languages have been developed, including _Prolog, Datalog_ and _Answer Set Programming_ (ASP), which will be referred to in the articles of this Special Issue. ASP has shown considerable potential in the modeling of NP-hard problems and, thanks to the development of increasingly efficient ASP-solvers such as DLV and Clasp, creating concrete resolution in real situations. Among the most significant applications in recent years can be found, for example, in the use of ASP in nuclear engineering, healthcare, business, and robotics. A classic example of the ability of ASP to model complex problems is given by the so-called _3-coloring problem_ known to be NP-complete.