ABSTRACT. Answer set programming (ASP) and reasoning from conditional belief bases are two most prominent approaches to nonmonotonic reasoning. Both frameworks are rule-based in principle, yet substantially different with respect to syntax and semantics. Recently, approaches to combine ASP programs with conditional belief bases to prioritize answer sets have been proposed. A crucial question for applying such approaches is to decide which knowledge and beliefs should be modeled in which part of the combined knowledge base, ASP or conditionals. In this paper, we investigate the differences between encoding information in ASP vs. as conditionals in more detail. We point out general differences between the reasoning processes of ASP vs. conditionals and provide guidelines for knowledge engineering with ASP and conditionals. Moreover, we illustrate how choosing either of the two frameworks has significant effects on the resulting solutions. In particular, we focus on how factual information can be taken into account in the combined framework of ASP and conditionals in various ways. Furthermore, we build bridges between ASP and conditional reasoning by showing how conditionals with a suitable syntax can be encoded as weak constraints in ASP. Conversely, this may also help to find suitable weights for weak constraints in ASP programs.

ABSTRACT. Human reasoning often operates through qualitative concepts expressed by linguistic labels such as high, low, expensive, or cheap, whose interpretation depends on context and is usually vague, despite being rooted in numerical data. This paper explores a novel fuzzy-logic-based qualitative extension of Answer Set Programming (ASP) to bridge numerical information and qualitative reasoning. The underlying language, formally introduced in a separate work, provides a principled framework that avoids rigid thresholds and supports robust reasoning under vagueness. Focusing on a representative use case, we illustrate how the framework integrates numerically grounded inputs (such as outputs of machine learning models) with symbolic reasoning over qualitative labels. Key features, including learning-based membership functions and semantically enriched predicates, enable the combination of expert knowledge, contextual factors, and subjective interpretations within a unified declarative setting.

ABSTRACT. We consider a *definitional fragment* of Temporal Equilibrium Logic (TEL), which allows to capture temporal rules containing complex (implication-free) temporal formulas in rule bodies. We show that the basic reasoning tasks in this fragment are PSPACE-complete, under the assumption that formulas are interpreted over finite traces. This shows a significant drop from the EXPSPACE-completeness of unrestricted TEL. Our method is based on characterizing stable models in terms of different kinds of *type sequences*, which allow to reason both about existence and non-existence of stable models. In addition to handling tasks like stable model existence, we also show how the set of all stable models of a program can be represented as a non-deterministic finite state automaton (NFA). Our method is self-contained in the sense that, in contrast to previous approaches, it does not rely on technical automata-theoretic results as black boxes. Our method can be implemented using SAT solving techniques and a prototype system is available.

ABSTRACT. In this paper, we introduce ranking-based semantics for incomplete argumentation frameworks (IAFs). These frameworks are extensions of Dung's abstract argumentation framework with qualitative uncertainty about the existence of arguments and attacks. Up to this point reasoning on incomplete argumentation framework have only followed Dung's extension-based approaches, where a set of arguments is either jointly accepted or not. We discuss several approaches how to rank the individual arguments. The first two approaches rely on the acceptance status of the arguments with respect to an extension-based semantics. Another family of approaches utilises ranking-based semantics on the individual completions of an IAF (i.e. AFs where the uncertainty is ``resolved'') and then aggregate the resulting rankings with voting rules. In addition, we propose a number of principles the ranking-based semantics for IAFs should follow, some adapted from existing principles out of the formal argumentation literature, others novel principles tailored to IAFs. We determine which of these properties are satisfied by our approaches.

ABSTRACT. We show that deciding whether an argument a is stronger than an argument b with respect to the discussion-based semantics of Amgoud and Ben-Naim is decidable in polynomial time. At its core, this problem is about deciding whether, for two vertices in a graph, the number of walks of each length ending in those vertices is the same. We employ results from automata theory and reduce this problem to the equivalence problem for semiring automata. This offers a new perspective on the computational complexity of ranking semantics, an area in which the complexity of many semantics remains open.

ABSTRACT. Skeptical acceptance under the preferred semantics is one of the most intricate reasoning problems in abstract argumentation. That is why efficient solving approaches are of utmost importance for this problem. In this work, we investigate algorithmic shortcuts that can be used to solve this reasoning problem with considerably less resources than sound and complete approaches. Besides an overview of the state-of-the-art, we also propose several novel shortcuts to improve the applicability of such techniques. Finally, we perform an extensive evaluation of all shortcuts regarding their potential to improve the runtime efficiency of argumentation solvers. As our results show, we can significantly improve the runtime of state-of-the-art argumentation solvers by utilizing a variety of shortcuts.

ABSTRACT. Intelligent agents interacting with their environment need to reason about the effects their actions will have on their surroundings. For actions with deterministic outcome this problem is well investigated in the context of planning problems. But many real-world actions may not always result in their typical outcome, and exceptional outcomes of an action have to be taken into account. In this work we present a framework for reasoning about actions with uncertain outcomes. Inspired by conditionals, we introduce defeasible action rules that capture the typical outcome of action, without committing to what happens in exceptional circumstances. As semantics of these rules we introduce uncertain transition schemas: graph-based representations of transitions between possible worlds in which edges between states are assigned a rank indicating their typicality. We define an inference operator for defeasible action rules inspired by rational closure, adapting its intuitive semantics to the dynamic setting. Furthermore, we explore a generalization of this framework that uses partial or total orderings over transitions instead of ranks. This generalization strictly increases expressive power and enables more refined reasoning operators. Finally, we extend the language of defeasible action rules with a notation to express that certain properties are not affected by the execution of an action, thus allowing to explicitly formulate frame axioms in this defeasible setting.

ABSTRACT. Action reversibility deals with the problem of whether and under what circumstances we can undo effects of a given action. Recent works established the notions of action reversibility in the propositional settings. Action reversibility represents whether, for each state of concern, effects of an action can be undone by some action sequence. The present paper studies the concept of action reversibility in lifted STRIPS settings that represent the environment by first-order predicates and define action schemas defined over those predicates. In particular, we define the notions of lifted reversibility and lifted uniform reversibility. Although undecidable in its most general form, due to the undecidability of first-order logic, we show that several results from the propositional settings can be generalized to the lifted settings.