We present a solution to real-world train scheduling problems, involving routing, scheduling, and optimization, based on Answer Set Programming (ASP). To this end, we pursue a hybrid approach that extends ASP with difference constraints to account for a fine-grained timing. More precisely, we exemplarily show how the hybrid ASP system clingo[DL] can be used to tackle demanding planning-and-scheduling problems. In particular, we investigate how to boost performance by combining distinct ASP solving techniques, such as approximations and heuristics, with preprocessing and encoding techniques for tackling large-scale, real-world train scheduling instances.

We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed probability distribution. PAC semantics, introduced by Valiant, is one rigorous, general proposal for learning to reason in formal languages: although weaker than classical entailment, it allows for a powerful model theoretic framework for answering queries while requiring minimal assumptions about the form of the distribution in question. To date, however, the most significant limitation of that approach, and more generally most machine learning approaches with robustness guarantees, is that the logical language is ultimately essentially propositional, with finitely many atoms. Indeed, the theoretical findings on the learning of relational theories in such generality have been resoundingly negative. This is despite the fact that first-order logic is widely argued to be most appropriate for representing human knowledge.

Axiom pinpointing refers to the task of finding the specific axioms in an ontology which are responsible for a consequence to follow. This task has been studied, under different names, in many research areas, leading to a reformulation and reinvention of techniques. In this work, we present a general overview to axiom pinpointing, providing the basic notions, different approaches for solving it, and some variations and applications which have been considered in the literature. This should serve as a starting point for researchers interested in related problems, with an ample bibliography for delving deeper into the details.

Computation Tree Logic (CTL) is one of the central formalisms in formal verification. As a specification language, it is used to express a property that the system at hand is expected to satisfy. From both the verification and the system design points of view, some information content of such property might become irrelevant for the system due to various reasons e.g., it might become obsolete by time, or perhaps infeasible due to practical difficulties. Then, the problem arises on how to subtract such piece of information without altering the relevant system behaviour or violating the existing specifications. Moreover, in such a scenario, two crucial notions are informative: the strongest necessary condition (SNC) and the weakest sufficient condition (WSC) of a given property. To address such a scenario in a principled way, we introduce a forgetting-based approach in CTL and show that it can be used to compute SNC and WSC of a property under a given model. We study its theoretical properties and also show that our notion of forgetting satisfies existing essential postulates. Furthermore, we analyse the computational complexity of basic tasks, including various results for the relevant fragment CTLAF.

Characterizing hybrid ASP solving in a generic way is difficult since one needs to abstract from specific theories. Inspired by lazy SMT solving, this is usually addressed by treating theory atoms as opaque. Unlike this, we propose a slightly more transparent approach that includes an abstract notion of a term. Rather than imposing a syntax on terms, we keep them abstract by stipulating only some basic properties. With this, we further develop a semantic framework for hybrid ASP solving and provide aggregate functions for theory variables that adhere to different semantic principles, show that they generalize existing aggregate semantics in ASP and how we can rely on off-the-shelf hybrid solvers for implementation.

In this paper, we explore the issue of inconsistency handling over prioritized knowledge bases (KBs), which consist of an ontology, a set of facts, and a priority relation between conflicting facts. In the database setting, a closely related scenario has been studied and led to the definition of three different notions of optimal repairs (global, Pareto, and completion) of a prioritized inconsistent database. After transferring the notions of globally-, Pareto- and completion-optimal repairs to our setting, we study the data complexity of the core reasoning tasks: query entailment under inconsistency-tolerant semantics based upon optimal repairs, existence of a unique optimal repair, and enumeration of all optimal repairs. Our results provide a nearly complete picture of the data complexity of these tasks for ontologies formulated in common DL-Lite dialects. The second contribution of our work is to clarify the relationship between optimal repairs and different notions of extensions for (set-based) argumentation frameworks. Among our results, we show that Pareto-optimal repairs correspond precisely to stable extensions (and often also to preferred extensions), and we propose a novel semantics for prioritized KBs which is inspired by grounded extensions and enjoys favourable computational properties. Our study also yields some results of independent interest concerning preference-based argumentation frameworks.

Reasoning over knowledge graphs is traditionally built upon a hierarchy of languages in the Semantic Web Stack. Starting from the Resource Description Framework (RDF) for knowledge graphs, more advanced constructs have been introduced through various syntax extensions to add reasoning capabilities to knowledge graphs. In this paper, we show how standardized semantic web technologies (RDF and its query language SPARQL) can be reproduced in a unified manner with dependent type theory. In addition to providing the basic functionalities of knowledge graphs, dependent types add expressiveness in encoding both entities and queries, explainability in answers to queries through witnesses, and compositionality and automation in the construction of witnesses. Using the Coq proof assistant, we demonstrate how to build and query dependently typed knowledge graphs as a proof of concept for future works in this direction.

We describe nearly fifteen years of General Game Playing experimental research history in the context of reproducibility and fairness of comparisons between various GGP agents and systems designed to play games described by different formalisms. We think our survey may provide an interesting perspective of how chaotic methods were allowed when nothing better was possible. Finally, from our experience-based view, we would like to propose a few recommendations of how such specific heterogeneous branch of research should be handled appropriately in the future. The goal of this note is to point out common difficulties and problems in the experimental research in the area. We hope that our recommendations will help in avoiding them in future works and allow more fair and reproducible comparisons.

Question answering (QA) in natural language (NL) has been an important aspect of AI from its early days. Winograd's ``councilmen'' example in his 1972 paper and McCarthy's Mr. Hug example of 1976 highlights the role of external knowledge in NL understanding. While Machine Learning has been the go-to approach in NL processing as well as NL question answering (NLQA) for the last 30 years, recently there has been an increasingly emphasized thread on NLQA where external knowledge plays an important role. The challenges inspired by Winograd's councilmen example, and recent developments such as the Rebooting AI book, various NLQA datasets, research on knowledge acquisition in the NLQA context, and their use in various NLQA models have brought the issue of NLQA using ``reasoning'' with external knowledge to the forefront. In this paper, we present a survey of the recent work on them. We believe our survey will help establish a bridge between multiple fields of AI, especially between (a) the traditional fields of knowledge representation and reasoning and (b) the field of NL understanding and NLQA.

Defining sound and complete specifications for robots using formal languages is challenging, while learning formal specifications directly from demonstrations can lead to over-constrained task policies. In this paper, we propose a Bayesian interactive robot training framework that allows the robot to learn from both demonstrations provided by a teacher, and that teacher's assessments of the robot's task executions. We also present an active learning approach -- inspired by uncertainty sampling -- to identify the task execution with the most uncertain degree of acceptability. We demonstrate that active learning within our framework identifies a teacher's intended task specification to a greater degree of similarity when compared with an approach that learns purely from demonstrations. Finally, we also conduct a user-study that demonstrates the efficacy of our active learning framework in learning a table-setting task from a human teacher.