In this paper, I will discuss the work I am currently doing as a Ph.D. student at the University of Potsdam, under the tutoring of T. Schaub. I'm currently looking into action description in ASP. More precisely, my goal is to explore how to represent actions with durations in ASP, in different contexts. Right now, I'm focused on Multi-Agent Path Finding (MAPF), looking at how to represent speeds for different agents and contexts. Before tackling duration, I wanted to explore and compare different representations of action taking in ASP. For this, I started comparing different simple encodings tackling the MAPF problem. Even in simple code, choices and assumptions have been made in their creations. The objective of my work is to present the consequences of those design decisions in terms of performance and knowledge representation. As far as I know, there is no current research on this topic. Besides that, I'm also exploring different ways to represent duration and to solve related problems. I planed to compare them the same way I described before. I also want this to help me find innovative and effective ways to solve problems with duration.

Artificial Intelligence (AI) applications are being used widely among people with different background and interests. For these applications to be successful, two of the important features (and challenges) needed by AI methods are flexibility and explainability. A flexible AI method developed to solve a problem can accommodate variations of the problem, and thus can be used to investigate different options for a better understanding. An explainable AI method can provide answers to queries about the (in)feasibility and the optimality of solutions. One of the well-studied problems in AI that necessitates solutions for these two challenges is the multi-agent path finding (MAPF) problem.

We consider the problem of finding relevant consistent concepts in a conversational AI system, particularly, for realizing a conversational socialbot. Commonsense knowledge about various topics can be represented as an answer set program. However, to advance the conversation, we need to solve the problem of finding relevant consistent concepts, i.e., find consistent knowledge in the "neighborhood" of the current topic being discussed that can be used to advance the conversation. Traditional ASP solvers will generate the whole answer set which is stripped of all the associations between the various atoms (concepts) and thus cannot be used to find relevant consistent concepts. Similarly, goal-directed implementations of ASP will only find concepts directly relevant to a query. We present the DiscASP system that will find the partial consistent model that is relevant to a given topic in a manner similar to how a human will find it. DiscASP is based on a novel graph-based algorithm for finding stable models of an answer set program. We present the DiscASP algorithm, its implementation, and its application to developing a conversational socialbot.

Answer Set Programming (ASP) [4, 5] is a popular paradigm for decision making and problem solving in Knowledge Representation and Reasoning. It has been successfully applied in a variety of applications such as robotics, planning, diagnosis, etc. ASP is an attractive programming paradigm as it is a declarative language, where programmers focus on the representation of a specific problem as a set of rules in a logical format, and then leave computational solutions of that problem to an answer set solver. However, this mechanism typically gives little insight into why something is a solution and why some proposed set of literals is not a solution. This type of reasoning falls within the scope of explainable Artificial Intelligence and is useful to enhance the understanding of the resulting solutions as well as for debugging programs. So far, only a limited number of approaches have been proposed [1, 6, 7].

We introduce Natlog, a lightweight Logic Programming language, sharing Prolog's unification-driven execution model, but with a simplified syntax and semantics. Our proof-of-concept Natlog implementation is tightly embedded in the Python-based deep-learning ecosystem with focus on content-driven indexing of ground term datasets. As an overriding of our symbolic indexing algorithm, the same function can be delegated to a neural network, serving ground facts to Natlog's resolution engine. Our open-source implementation is available as a Python package at https://pypi.org/project/natlog/ .

Interpretability in machine learning is the ability to explain or to present in understandable terms to a human [8]. Interpretability is particularly important when, for example the goal of the user is to gain knowledge from some form of explanations about the data or process through machine learning models, or when making high-stakes decisions based on the outputs from the machine learning models where the user has to be able to trust the models. In this work we address the problem of explaining and understanding tree-ensemble learners by extracting meaningful rules from them. This problem is of practical relevance in business domains where the understanding of the behavior of high-performing machine learning models and extraction of knowledge in human readable form can aid users in the decision making process. We use Answer Set Programming (ASP) [14, 22] to generate rule sets from tree-ensembles.

Answer set programming (ASP) is an efficient problem-solving approach, which has been strongly supported both scientifically and technologically by several solvers, ongoing active research, and implementations in many different fields. However, although researchers acknowledged long ago the necessity of epistemic operators in the language of ASP for better introspective reasoning, this research venue did not attract much attention until recently. Moreover, the existing epistemic extensions of ASP in the literature are not widely approved either, due to the fact that some propose unintended results even for some simple acyclic epistemic programs, new unexpected results may possibly be found, and more importantly, researchers have different reasonings for some critical programs. To that end, Cabalar et al. have recently identified some structural properties of epistemic programs to formally support a possible semantics proposal of such programs and standardise their results. Nonetheless, the soundness of these properties is still under debate, and they are not widely accepted either by the ASP community. Thus, it seems that there is still time to really understand the paradigm, have a mature formalism, and determine the principles providing formal justification of their understandable models. In this paper, we mainly focus on the existing semantics approaches, the criteria that a satisfactory semantics is supposed to satisfy, and the ways to improve them. We also extend some well-known propositions of here-and-there logic (HT) into epistemic HT so as to reveal the real behaviour of programs. Finally, we propose a slightly novel semantics for epistemic ASP, which can be considered as a reflexive extension of Cabalar et al.'s recent formalism called autoepistemic ASP.

Weighted knowledge bases for description logics with typicality have been recently considered under a "concept-wise" multipreference semantics (in both the two-valued and fuzzy case), as the basis of a logical semantics of Multilayer Perceptrons. In this paper we consider weighted conditional EL^bot knowledge bases in the two-valued case, and exploit ASP and asprin for encoding concept-wise multipreference entailment for weighted KBs with integer weights.

SHACL is a W3C-proposed language for expressing structural constraints on RDF graphs. The recommendation only specifies semantics for non-recursive SHACL; recently, some efforts have been made to allow recursive SHACL schemas. In this paper, we argue that for defining and studying semantics of recursive SHACL, lessons can be learned from years of research in non-monotonic reasoning. We show that from a SHACL schema, a three-valued semantic operator can directly be obtained. Building on Approximation Fixpoint Theory (AFT), this operator immediately induces a wide variety of semantics, including a supported, stable, and well-founded semantics, related in the expected ways. By building on AFT, a rich body of theoretical results becomes directly available for SHACL. As such, the main contribution of this short paper is providing theoretical foundations for the study of recursive SHACL, which can later enable an informed decision for an extension of the W3C recommendation.

Answer Set Programming (ASP) is a successful method for solving a range of real-world applications. Despite the availability of fast ASP solvers, computing answer sets demands a very large computational power, since the problem tackled is in the second level of the polynomial hierarchy. A speed-up in answer set computation may be attained, if the program can be split into two disjoint parts, bottom and top. Thus, the bottom part is evaluated independently of the top part, and the results of the bottom part evaluation are used to simplify the top part. Lifschitz and Turner have introduced the concept of a splitting set, i.e., a set of atoms that defines the splitting. In this paper, We show that the problem of computing a splitting set with some desirable properties can be reduced to a classic Search Problem and solved in polynomial time. This allows us to conduct experiments on the size of the splitting set in various programs and lead to an interesting discovery of a source of complication in stable model computation. We also show that for Head-Cycle-Free programs, the definition of splitting sets can be adjusted to allow splitting of a broader class of programs.