Year: 2025
Type: dissertation
Abstract: This work deals with a popular logic programming paradigm called answer set programming, ASP for short, which is a rule-based formalism for modeling and solving optimization, decision or search problems. In ASP we write symbolic rules to declare what is to be solved, and then delegate the how to a solver, which implements the logical formalism required to deduce and consequently present solutions to us. The solving is done without any action on our part, we simply encode the given problem as a logic program whose so-called answer sets represent solutions to the problem. Due to its rich yet simple modeling language with great tooling support, ASP has found widespread applications across several areas of symbolic artificial intelligence, in particular in the field of knowledge representation and reasoning. Certainly, in practical applications the answer sets of a program ought to convey meaning and valuable information to ASP users. Accordingly, several different perspectives to reason with answer sets have been studied in the past. However, there is one rather basic yet very common issue that has not been tackled as much, namely, being confronted with way too many answer sets to handle. Indeed, this work is not motivated by lack of advanced technology, but, if anything, by the astonishing capabilities of solvers and the nature of search problems themselves, which due to the involved combinatorics typically admit a tremendous amount of answer sets. In fact, state-of-the-art ASP solvers can enumerate millions of answer sets within seconds, which begs the question: how do we make sense of a prompt full of answer sets? Staying on top of things is per se difficult if we have to relate an overwhelming amount of answer sets to each other. Parsing sequences of emerging answer sets on the fly is mostly close to impossible. Scrolling millions of answer sets up and down, once the solver has finished enumerating answer sets, is quite tedious and remains challenging. Perhaps, we could opt for canceling enumeration here and there, to get an impression of what is going on. For example, we could inspect answer sets in, say, chunks of 3. However, since enumeration is typically non-deterministic, how do we ensure to not always see the same or rather similar answer sets? Indeed, step-by-step changing the encoding manually is an option, however a rather tedious one. No matter how we slice it, prompts full of answer sets pose a challenge. In this thesis, we study the concept of answer set navigation to provide a comprehensive overview of several different systematic approaches for overcoming the challenges of dealing with too many answer sets. Alongside conducting experiments to evaluate prototypical implementations, we also present theoretical results relating to formal properties of practical methods or the computational complexity of relevant decision problems. The most ideas revolve around the notion of facets and how to reason with them. A facet is a piece of information that can be found in some, but not every answer set of a program. In more detail, we propose a systematic framework for filtering designated answer sets based on qualitative facet reasoning, and study different kinds of quantitative facet reasoning. Since quantitative facet reasoning involves answer set counting, which is a hard problem, we also suggest a novel counting technique tailored to answer set navigation. As a counterpart idea to filtering answer sets, we also discuss a notion of representative answer sets, and present methods to collect representative answer sets. Finally, we suggest methods to support interactive visualizations of answer sets.
Author: Rusovac, Dominik
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6989279924