Argumentation is a central subarea of Artificial Intelligence (AI) for modeling and reasoning about arguments. The semantics of abstract argumentation frameworks (AFs) is given by sets of arguments (extensions) and conditions on the relationship between arguments, such as stable or admissible. Today's solvers implement tasks such as finding extensions, deciding credulously or skeptically acceptance, counting, or enumerating extensions. While these tasks are well charted, the area between decision and counting/enumeration and fine-grained reasoning requires expensive reasoning so far. We introduce a novel concept (facets) for reasoning between decision and enumeration. Facets are arguments that belong to some extensions (credulous) but not to all extensions (skeptical). They are most natural when a user aims to navigate, filter, or comprehend specific arguments, according to their needs. We study the complexity and show that tasks involving facets are much easier than counting extensions. Finally, we provide an implementation, and conduct experiments to demonstrate feasibility.
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We address the context of Single-Audience Value-Based Abstract Argumentation Framework (AVAF), where the arguments are labeled with the social values that they promote and the activation/deactivation of the attacks depends on the audience profile (expressed as a set of preferences between the social values). Herein, we introduce a new notion of robustness for measuring the sensitivity of the outcome of the reasoning to the extent of changes in the audience profile. In particular, for a set of arguments S or a single argument a, we define the robustness degree of the status of S or a as the maximum number k* of deletions/insertions of preferences from/into the audience profile that are tolerable, in the sense that S remains an extension (or a non-extension) or a accepted (or unaccepted) after performing at most k* deletions/insertions. We introduce the decision problems related to the computation of the robustness degree and focus on thoroughly investigating their computational complexity.
Temporal Equilibrium Logic (TEL) extends Answer Set Programming (ASP) with linear-time temporal operators (LTL), enabling reasoning about dynamic systems. However, TEL enforces strong minimization criteria that may preclude intuitive models. Liveness formulas, for instance, tend to fail to have infinite equilibrium models, as TEL minimization postpones satisfaction forever. We address this limitation by introducing eager temporal operators (eager Until, eager Release, etc.), and present non-disjunctive temporal programs (NDTP) as a framework for modeling dependencies, inertia, and non-determinism. The fragment of tight temporal programs (TTP), which can be recognized efficiently based on automata techniques for loop detections, guarantees polynomial encodability into LTL. Practical examples, such as request-grant protocols and user permissions in distributed systems, illustrate the applicability of our approach.
Answer Set Programming (ASP) is a popular nonmonotonic formalism used for common-sense reasoning and problem-solving based on stable model semantics. Equilibrium logic is a generalisation of ASP for arbitrary propositional theories and thus provides a logical characterisation of the nonmonotonic stable model semantics. In difference to classical logic, which can be defined via proof or model theory, nonmonotonic reasoning formalisms are defined via their models exclusively. Equilibrium logic is no exception here, as it has no proper proof-theoretic axiomatisation. Besides this being a theoretical imbalance, it also has consequences regarding notions of justification and explainability. In this work, we fill this gap by providing a sequent calculus for answer set entailment. Our calculus builds upon ideas from existing calculi for other nonmonotonic formalisms and utilises calculi for the logic of here and there, which is the underlying base logic of equilibrium logic. We show that the calculus is sound and complete and discuss pitfalls as well as alternative axiomatisations. Finally, we address how our approach can be of use for explainability in ASP.
Boolean circuits in d-DNNF (determinstic Decomposable Negation Normal Form) enable tractable probabilistic inference, motivating research into compilers that transform arbitrary Boolean circuit into this form. However, d-DNNF compilers commonly require the input to be in conjunctive normal form (CNF), which means that a user must first convert their Boolean circuit into CNF. In this work, we argue that d-DNNF compilation would substantially benefit from reasoning over the original input circuit's structure, rather than solely relying on its CNF representation. To this end, we adapt an existing compiler and implement an optimisation that becomes more readily available once we reason over the input circuit: the identification and elimination of don't care variables. We empirically demonstrate the effectiveness of this approach, achieving a significant improvement in both the number of solved instances and the size of the resulting circuits.
A Logic-based Framework for Decoding Enthymemes in Argument Maps Involving Implicitness in Premises and Claims
PDF ↗Argument mining is a natural language processing technology aimed at identifying the explicit premises and claims of arguments in text, and the support and attack relationships between them. To better understand, and automatically analyse, the argument maps that are output from argument mining, it would be desirable to instantiate the arguments in the argument map with logical arguments. However, most real-world arguments are enthymemes (i.e. some of the premises and/or claim are implicit), which need to be decoded (i.e. the implicit aspects need to be identified). A key challenge is to decode enthymemes so as to respect the support and attack relationships in the argument map. addressing the problem of identifying the missing premises and/or claim, and discerning the relationships between them. To address this, we present a novel framework, based on default logic, for representing arguments including enthymemes. We show how decoding an enthymeme means identifying the default rules that are implicit in the premises and claims. We then show how choosing a decoding of the enthymemes in an argument map can be formalized as an optimization problem, and that a solution can be obtained using MaxSAT solvers.
We propose a general framework for assessing the exposure of sensitive knowledge in policy-protected knowledge bases (KBs), where knowledge is represented as logical theories and data protection policies are defined declaratively using epistemic dependencies. The framework models scenarios in which confidential parts of the KB may be publicly known due to security breaches. We study two fundamental decision problems: determining whether the exposed knowledge violates the data protection policy (leakage), and whether there exists a secure view of the KB that complies with the policy. We analyze the computational complexity (specifically, data complexity) of these problems, focusing on the DL-Lite_R and EL_\bot Description Logics. Our findings show that, for DL-Lite_R with restricted forms of policy, both the problems can be efficiently solved through query rewriting methods. For EL_\bot, we establish conditions for tractable computational bounds. Our results highlight the potential of this framework for practical applications in confidentiality-preserving knowledge management.
The standard ``serial'' (aka ``singleton'') model of belief contraction models the manner in which an agent's corpus of beliefs responds to the removal of a single item of information. One salient extension of this model introduces the idea of ``parallel'' (aka ``package'' or ``multiple'') change, in which an entire set of items of information are simultaneously removed. Existing research on the latter has largely focussed on single-step parallel contraction: understanding the behaviour of beliefs after a single parallel contraction. It has also focussed on generalisations to the parallel case of serial contraction operations whose characteristic properties are extremely weak. Here we consider how to extend serial contraction operations that obey stronger properties. Potentially more importantly, we also consider the iterated case: the behaviour of beliefs after a sequence of parallel contractions. We propose a general method for extending serial iterated belief change operators to handle parallel change based on an n-ary generalisation of Booth & Chandler's TeamQueue binary order aggregators.
Despite efforts to better understand the constraints that operate on single-step parallel (aka ``package'', ``multiple'') revision, very little work has been carried out on how to extend the model to the iterated case. A recent paper by Delgrande & Jin outlines a range of relevant rationality postulates. While many of these are plausible, they lack an underlying unifying explanation. We draw on recent work on iterated parallel contraction to offer a general method for extending serial iterated belief revision operators to handle parallel change. This method, based on a family of order aggregators known as TeamQueue aggregators, provides a principled way to recover the independently plausible properties that can be found in the literature, without yielding the more dubious ones.
We introduce First-Order Coalition Logic (FOCL), which combines key intuitions behind Coalition Logic (CL) and Strategy Logic (SL). Specifically, FOCL allows for arbitrary quantification over actions of agents. FOCL is interesting for several reasons. First, we show that FOCL is strictly more expressive than existing coalition logics. Second, we provide a sound and complete axiomatisation of FOCL, which, to the best of our knowledge, is the first axiomatisation of any variant of SL in the literature. Finally, while discussing the satisfiability problem for FOCL, we reopen the question of the recursive axiomatisability of SL.
A General Framework for Representing Controlled Natural Language Sentences and Translation to KR Formalisms
PDF ↗Languages for Knowledge Representation and Reasoning, such as ASP, CP, and SMT, excel at solving some complex problems, but encoding them into a higher-level language may be more profitable, leaving these formalisms as targets for solving. Recent studies aim to convert controlled natural languages into formal representations, yet these solutions are often tailored to specific languages and require significant effort. This paper introduces a general framework that generates grammars for target representation languages, enabling the translation of problems stated in CNL into formal representations. The related system, CNLWizard, offers a flexible, high-level approach to defining desired grammars, significantly reducing the time and effort needed to create custom grammars. Finally, we demonstrate the system's effectiveness through an experimental analysis.
We perform a refined complexity-theoretic analysis of three classical problems in the context of Hierarchical Task Network Planning: the verification of a provided plan, whether an executable plan exists, and whether a given state can be reached. Our focus lies on identifying structural properties which yield tractability. We obtain new polynomial algorithms for all three problems on a natural class of primitive networks, along with corresponding lower bounds. We also obtain an algorithmic meta-theorem for lifting polynomial-time solvability from primitive to general task networks, and prove that its preconditions are tight. Finally, we analyze the parameterized complexity of the three problems.
We introduce a notion of conditional independence in (flat) assumption-based argumentation (ABA), where independence between (sets of) assumptions amounts to the presence of information about one set of assumptions not impacting the acceptability of another. We study general properties, computational complexity, and the relation to independence in abstract argumentation. In light of the high computational complexity of deciding independence, we introduce sound methods for checking independence in polynomial time via two different routes: the first utilizes the strongly connected components (SCCs) of the instantiated abstract argumentation framework; the second exploits the structure of the ABA framework directly. Along the way, we introduce the notion of SCC-recursiveness for ABA.
In this paper, we explore the issue of inconsistency handling in DatalogMTL, an extension of Datalog with metric temporal operators. Since facts are associated with time intervals, there are different manners to restore consistency when they contradict the rules, such as removing facts or modifying their time intervals. Our first contribution is the definition of relevant notions of conflicts (minimal explanations for inconsistency) and repairs (possible ways of restoring consistency) for this setting and the study of the properties of these notions and the associated inconsistency-tolerant semantics. Our second contribution is a data complexity analysis of the tasks of generating a single conflict / repair and query entailment under repair-based semantics.
We introduce initial models for abstract dialectical frameworks (ADFs) as a notion of minimal justifiable valuations and based on that, generalise the concept of serialisability of argumentation semantics to ADFs. In particular, we show that the characteristic operator-based semantics for ADFs can be characterised through serialisation sequences, which are, essentially, decompositions of a model into a series of initial models, representing a more fine-grained view into why a model is acceptable wrt. the semantics. We also analyse the computational complexity of tasks related to initial models.
Existential rules, a.k.a. tuple-generating dependencies (TGDs), form a well-established formalism for specifying ontologies. In particular, the warded language is a well-behaved fragment of TGD-based ontologies, striking a good balance between expressive power and computational complexity of answering Ontology-Mediated Queries (OMQs). The theoretical foundations of answering OMQs over warded ontologies are by now well-understood, but to the best of our knowledge, very few efforts exist that exploit such a rich theory for building practical query answering algorithms. Our goal is to fill the above gap by designing a novel Datalog rewriting algorithm for OMQs over warded ontologies which is amenable to practical implementations, as well as providing an implementation and an experimental evaluation, with the aim of understanding how key input parameters affect the performance of this approach, and what are its limits when combined with off-the-shelf Datalog-based engines.
In this work, we present the first general logic of attention. Attention is a powerful cognitive ability that allows agents to focus on potentially complex information, such as logically structured propositions, higher-order beliefs, or what other agents pay attention to. This ability is a strength, as it helps to ignore what is irrelevant, but it can also introduce biases when some types of information or agents are systematically ignored. Existing dynamic epistemic logics for attention cannot model such complex attention scenarios, as they only model attention to atomic formulas. Additionally, such logics quickly become cumbersome, as their size grows exponentially in the number of agents and announced literals. Here, we introduce a logic that overcomes both limitations. First, we generalize edge-conditioned event models, which we show to be as expressive as standard event models yet exponentially more succinct (generalizing both standard event models and generalized arrow updates). Second, we extend attention to arbitrary formulas, allowing agents to also attend to other agents' beliefs or attention. Our work treats attention as a modality, like belief or awareness. We introduce attention principles that impose closure properties on that modality and that can be used in its axiomatization. Throughout, we illustrate our framework with examples of AI agents reasoning about human attention, demonstrating how such agents can discover attentional biases.
Case-based prediction (CBP) methods do not learn a model of the target decision function but instead perform an inference process that depends on two similarity measures and a reference case base. This paper proposes a strategy, called EnergyCompress, to learn an effective case base by selecting relevant cases from an initial set. Use of EnergyCompress decreases CBP inference time, through case base compression, and also increases prediction performance, for a wide variety of CBP algorithms. EnergyCompress relies on the proposition of a general formulation of the CBP task in the framework of energy-based models, which leads to a new and valuable characterization of the notion of competence in case-based reasoning, in particular at the source case level. Extensive experimental results on 18 benchmark datasets comparing EnergyCompress to 5 reference algorithms for case base maintenance support the benefit of the proposed strategy.
Integrating Answer Set Programming and Large Language Models for Enhanced Structured Representation of Complex Knowledge in Natural Language
PDF ↗Answer Set Programming (ASP) and Large Language Models (LLMs) have emerged as powerful tools in Artificial Intelligence, each offering unique capabilities in knowledge representation and natural language processing, respectively. In this paper, we combine the strengths of the two paradigms with the aim of improving the structured representation of complex knowledge encoded in natural language. In a nutshell, the structured representation is obtained by combining syntactic structures extracted by LLMs and semantic aspects encoded in the knowledge base. The interaction between ASP and LLMs is driven by a YAML file specifying prompt templates and domain-specific background knowledge. The proposed approach is evaluated using a set of benchmarks based on a dataset obtained from problems of ASP Competitions. The results of our experiment show that ASP can sensibly improve the F1-score, especially when relatively small models are used.
Counterfactual Explanations Under Model Multiplicity and Their Use in Computational Argumentation
PDF ↗Counterfactual explanations (CXs) are widely recognised as an essential technique for providing recourse recommendations for AI models. However, it is not obvious how to determine CXs in model multiplicity scenarios, where equally performing but different models can be obtained for the same task. In this paper, we propose novel qualitative and quantitative definitions of CXs based on explicit, nested quantification over (groups) of model decisions. We also study properties of these notions and identify decision problems of interest therefor. While our CXs are broadly applicable, in this paper we instantiate them within computational argumentation where model multiplicity naturally emerges, e.g. with incomplete and case-based argumentation frameworks. We then illustrate the suitability of our CXs for model multiplicity in legal and healthcare contexts, before analysing the complexity of the associated decision problems.