The 3-coloring problem is the problem used to decide whether a given graph, formed by nodes and edges, can be colored by using three colors (namely, red, blue and green), in such a way that each pair of adjacent nodes is colored by two different colors. The knowledge about a graph can be modeled through a set of facts of the following form: \(node(1\dots n)\) (a set of \(n\) nodes) and \(edge(i,j)\), whenever there is an edge from node \(i\) to node \(j\). Now, the problem can be easily solved by guessing a possible coloration of the nodes:  
\[colored(X,red)\mid colored(X,green)\mid colored(X,blue)\gets node(X)\]  
where symbol \(|\) is similar to classical logical disjunction (\(\vee\)) but imposes a minimization of the selected atoms. Thus, in this case, the rule is satisfied by choosing exactly one atom. Hence, the problem is solved by forcing the following to be false: there is an edge from node \(X\) to node \(Y\), such that \(X\) is colored by the same color of \(Y\) (named \(Z\) in the rule):  
\[\gets edge(X,Y),\ colored(X,Z),\ colored(Y,Z).\]  
These two rules allow us to encode the result in a sound and complete the 3-coloring problem, also offering, thanks to the symbolic approach, an almost immediate understanding for a human being of the meaning encoded in the rules. As highlighted in the brief history of AI, logic programming in recent years has interacted with the statistical approaches of AI, providing its symbolic language, understandable by humans, aiming to offer explanations to the answers produced by the black box of machine learning algorithms or to clarify the background knowledge on which neural networks are trained. Some recent application examples can be found in the context of question answering, data classification, autonomous driving, and dialogue systems. In summary, we can, therefore, state that Logics have provided a formal basis for the study and development of systems and applications in Artificial Intelligence (AI). In particular, logic became relevant to AI research thanks to the fast satisfiability solvers used for solving combinatorial search problems. Logic-based AI approaches have contributed to knowledge representation, natural language understanding, automated planning and commonsense reasoning. Currently, they are fundamental in the increasing need for explainability, comprehensibility and reliability to improve statistical-based AI systems. Hence, logic-based approaches are of paramount importance to identify promising research perspectives. The present Special Issue collected three articles of state-of-the-art research on the topic of logic-based AI approaches and technologies and their main application areas. In particular, the articles range from answer set programming to equilibrium logic, description logic and probabilistic reasoning. The first paper, \"Fact-Checking Reasoning System for Fake Review Detection Using Answer Set Programming\", is by [PERSON], [PERSON], and [PERSON] [1]. The authors proposed a framework based on answer set programming (ASP) and natural language processing to identify fake reviews. Indeed, the fake review detection problem has been transformed into an optimization problem solved via ASP by showing the high capability of this logic programming paradigm to solve these kinds of problems. The second paper, \"A Brief Roadmap into Uncertain Knowledge Representation via Probabilistic Description Logics\", is by [PERSON] [2]. The author focuses on uncertain knowledge representation, a key topic for realistic applications, by showing many different languages in the context of description logic. Finally, the third paper, \"Comparing the Reasoning Capabilities of Equilibrium Theories and Answer Set Programs\", is by [PERSON], [PERSON], [PERSON], and [PERSON] [3]. The authors provide a theoretical comparison between equilibrium theories and answer set programs based on their inference capability.