Contestable AI requires that AI-driven decisions align with given preferences. Various types of argumentation frameworks have been shown to support forms of contestability. In this paper we focus on the little-studied Edge-Weighted Quantitative Bipolar Argumentation Frameworks (EW-QBAFs), where arguments have a base score as in QBAFs but attacks and supports (edges) are weighted. After generalising gradual semantics and properties thereof from QBAFs to EW-QBAFs, we introduce the contestability problem for EW-QBAFs, which asks how to modify edge weights to achieve a desired strength for a specific topic argument. To address this problem, we propose gradient-based relation attribution explanations (G-RAEs), which quantify the sensitivity of the topic argument's strength to changes in individual edge weights, thus providing interpretable guidance for weight adjustments towards contestability. Building on G-RAEs, we develop a heuristic algorithm that progressively adjusts the edge weights to attain the desired strength. We evaluate our approach experimentally on synthetic EW-QBAFs that simulate the structural characteristics of personalised recommender systems and multi-layer perceptrons, demonstrating that it can support contestability effectively.
As schema languages for RDF data become more mature, we are seeing efforts to extend them with recursive semantics, applying diverse ideas from logic programming and description logics. While ShEx has an official recursive semantics based on greatest fixpoints (GFP), the discussion for SHACL is ongoing and seems to be converging towards least fixpoints (LFP). A practical study we perform shows that, indeed, ShEx validators implement GFP, whereas SHACL validators are more heterogeneous. This situation creates tension between ShEx and SHACL, as their semantic commitments appear to diverge, potentially undermining interoperability and predictability. We aim to clarify this design space by comparing the main semantic options in a principled yet accessible way, hoping to engage both theoreticians and practitioners, especially those involved in developing tools and standards. We present a unifying formal semantics that treats LFP, GFP, and supported model semantics (SMS), clarifying their relationships and highlighting a duality between LFP and GFP on stratified fragments. Next, we investigate to which extent the directions taken by SHACL and ShEx are compatible. We show that, although ShEx and SHACL seem to be going in different directions, they include large fragments with identical expressive power. Moreover, there is a strong correspondence between these fragments through the aforementioned principle of duality. Finally, we present a complete picture of the data and combined complexity of ShEx and SHACL validation under LFP, GFP, and SMS, showing that SMS comes at a higher computational cost under standard complexity-theoretic assumptions.
Probabilistic logic-based languages offer an expressive framework for encoding uncertain information in a human-interpretable way. Among existing formalisms, Probabilistic Answer Set Programming (PASP) stands out for its ease of modeling complex scenarios. The current definition of PASP is limited to programs consisting of disjunctive rules and probabilistic facts only. To enhance the expressivity of the framework, we introduce Optimal Probabilistic Answer Set Programming, which extends the language by allowing the inclusion of weak constraints within PASP specifications. We motivate this extension through some real-world application scenarios and present a detailed computational complexity analysis for both the inference and Most Probable Explanation (MPE) tasks.
We propose a framework for reasoning from inconsistent knowledge bases using minimal hitting sets, i. e., sets of interpretations such that each formula of the knowledge base is satisfied by at least one those interpretations. By additionally considering preference orders over minimal hitting sets, we can define a wide variety of non-monotonic inference relations. We consider concrete preference orders based on set inclusion, cardinality, the number of conflicting atoms within the hitting set, and using the Hamming distance between pairs of interpretations. We compare the resulting inference relations, characterize their logical properties, and position them relative to classical inference from maximal consistent subsets. Finally, we show that inference based on minimal conflicting atoms coincides with reasoning in Priest’s 3-valued logic.
Learning-based planning systems learn domain-specific knowledge that helps them to solve unseen tasks from the same planning domain. For this purpose they require a diverse set of training instances. A recent proposal for formal specifications of planning domains allows us to exactly characterize which instances are legal for a domain. We automatically generate planning tasks from such formal specifications by means of a translation to answer set programming. We experimentally examine the scalability of the approach and the suitability for learning-based planning, following the setup of the learning track of the International Planning Competition.
The dialogue game-based approach to argumentation semantics proposes to determine the acceptance status of arguments through two-party zero-sum dialogue games. Furthermore, by selecting different sets of rules to govern the moves of arguments in the game, it allows for the characterization of distinct argumentation semantics. This approach has proven significant for theoretical and practical reasons. Accordingly, the ability to identify the most suitable semantics for a given domain is a key element in promoting the adoption of dialogue game-based semantics in real-world systems. This paper introduces a set of principles for systematically analyzing dialogue game-based semantics. We aim to contribute to existing frameworks by enabling a deeper understanding of the theoretical foundations of such argumentation semantics. In doing so, our framework may also guide the development of new dialogue game-based semantics.
Description Logics (DLs) excel at representing structured knowledge in several application domains, but fall very short when it comes to reasoning about their numeric aspects. We consider the expressive DL ALCHOIQ with closed predicates and extend it with features ranging over user-specified finite numeric intervals, feature assertions, and local additive constraints on feature values. We illustrate the power of this language for describing problems that involve ontological and numeric reasoning and study reasoning problems that go beyond satisfiability, such as finding models that minimize some costs. We show that these additional numeric modeling and reasoning capabilities can be accommodated by extending a standard reasoning technique for ALCHOIQ using linear inequalities, and the extension does not necessarily increase the worst-case computational cost.
Model counting (also known as #SAT) is a fundamental problem in knowledge representation and reasoning, with applications ranging from probabilistic inference to formal verification. However, state-of-the-art model counters are limited by computational resources on a single machine. In this paper, we propose a novel distributed framework for model counting, exploiting the embarrassingly parallel nature of the problem. By decomposing the search space into independent subproblems and distributing them across different computation nodes, our approach achieves near-linear scalability on practical instances. Extensive experiments on standard benchmarks demonstrate both the effectiveness and efficiency of our framework.
Inductive inference is a well-studied form of nonmonotonic reasoning in which various inference is based on conditional belief bases rather than belief bases consisting of classical logic statements. Given its nonmonotonic nature, many important logical properties that are taken for granted in the classical case do not necessarily carry over to inference involving conditionals. In this paper we consider two such properties---equivalence and language-independence. More specifically, we provide different notions of equivalence in the conditional case, and show which of these are satisfied by which forms of conditional inference. Similarly, we consider different versions of language independence, and test various forms of conditional inference against these. As its main overall contribution, the paper provides deeper theoretical insights into the field of inductive inference.
Statistical statements are an expressive tool for representing statistical information of a domain of interest. Recently, these statements were given a meaning in the context of Probabilistic Answer Set Programming (PASP), allowing one to encode properties like "x% of elements of a domain have the feature y". Although the computational complexity of different tasks in PASP is well known, the complexity of restricted programs composed only of statistical statements and probabilistic facts has not been studied. As a first contribution, we address this problem, confirming that even in seemingly restricted cases the complexity is high. Indeed, even with this restriction we do not lose expressiveness, reaching higher levels of the polynomial hierarchy. To mitigate these high complexities, we focus on the structure of the programs. Thereby, we design novel structure-guided reductions, demonstrating how one can efficiently answer queries along treewidth decompositions. We obtain precise upper bounds and we show that under reasonable assumptions in complexity theory we cannot significantly improve, as we give matching lower bounds.
Assumption-Based Argumentation (ABA) is a prominent formalism for structured argumentation, widely applied in domains such as healthcare, law, and robotics. Despite its inherent computational complexity, ABA has seen the development of effective techniques that successfully address key tasks, including evaluating the acceptability of literals and computing framework extensions. These approaches typically involve translating the initial ABA framework into an intermediate formalism, such as an Answer Set Program or an Abstract Argumentation Framework, which is then encoded into a Boolean satisfiability (SAT) problem. However, this translation can lead to large and complex intermediate representations, posing challenges for state-of-the-art SAT solvers. In this work, we propose a Counterexample-Guided Abstraction Refinement (CEGAR) approach that bypasses the initial translation step, at the cost of incrementally discovering certain ABA constraints that are not explicitly captured in the initial SAT encoding. We analyze the performance of our method and demonstrate that it outperforms state-of-the-art approaches on specific problem classes, while remaining competitive with the best existing solvers more broadly.
Complex Event Recognition (CER) systems receive as input a stream of time-stamped events and identify situations of interest that satisfy a given pattern. Streaming environments are characterized by the high rate and volume of input data, and thus, scalability is of crucial importance. At the same time, noise and uncertainty are ubiquitous in temporal data, and not considering them, leads to erroneous detections. To confront these challenges, we present a tensor-based formalization of the Event Calculus (EC) for probabilistic inference, and demonstrate the scalability of our approach with the use of CER datasets from two real-world application domains. Moreover, we demonstrate the benefits of our approach, in terms of processing time, by comparing it against a probabilistic logic programming implementation of EC.
