Jesse Heyninck

Simon Marynissen, Jesse Heyninck, Bart Bogaerts et al.

Justification theory is a general framework for the definition of semantics of rule-based languages that has a high explanatory potential. Nested justification systems, first introduced by Denecker et al. (2015), allow for the composition of justification systems. This notion of nesting thus enables the modular definition of semantics of rule-based languages, and increases the representational capacities of justification theory. As we show in this paper, the original semantics for nested justification systems lead to the loss of information relevant for explanations. In view of this problem, we provide an alternative characterization of semantics of nested justification systems and show that this characterization is equivalent to the original semantics. Furthermore, we show how nested justification systems allow representing fixpoint definitions (Hou and Denecker 2009).

Jesse Heyninck, Ofer Arieli, Bart Bogaerts

Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as logic programming, default logic and autoepistemic logic. In this paper, we extend AFT to dealing with non-deterministic constructs that allow to handle indefinite information, represented e.g. by disjunctive formulas. This is done by generalizing the main constructions and corresponding results of AFT to non-deterministic operators, whose ranges are sets of elements rather than single elements. The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming.

Jesse Heyninck, Badran Raddaoui, Christian Straßer

In formal argumentation, a distinction can be made between extension-based semantics, where sets of arguments are either (jointly) accepted or not, and ranking-based semantics, where grades of acceptability are assigned to arguments. Another important distinction is that between abstract approaches, that abstract away from the content of arguments, and structured approaches, that specify a method of constructing argument graphs on the basis of a knowledge base. While ranking-based semantics have been extensively applied to abstract argumentation, few work has been done on ranking-based semantics for structured argumentation. In this paper, we make a systematic investigation into the behaviour of ranking-based semantics applied to existing formalisms for structured argumentation. We show that a wide class of ranking-based semantics gives rise to so-called culpability measures, and are relatively robust to specific choices in argument construction methods.

Lars-Phillip Spiegel, Jonas Haldimann, Jesse Heyninck et al.

In nonmonotonic reasoning from conditional belief bases, an inference operator satisfying syntax splitting postulates allows for taking only the relevant parts of a belief base into account, provided that the belief base splits into subbases based on disjoint signatures. Because such disjointness is rare in practice, safe conditional syntax splitting has been proposed as a generalization of syntax splitting, allowing the conditionals in the subbases to share some atoms. Recently this overlap of conditionals has been shown to be limited to trivial, self-fulfilling conditionals. In this article, we propose a generalization of safe conditional syntax splittings that broadens the applicability of splitting postulates. In contrast to safe conditional syntax splitting, our generalized notion supports syntax splittings of a belief base Δ where the subbases of Δ may share atoms and nontrivial conditionals. We illustrate how this new notion overcomes limitations of previous splitting concepts, and we identify genuine splittings, separating them from simple splittings that do not provide benefits for inductive inference from Δ. We introduce adjusted inference postulates based on our generalization of conditional syntax splitting, and we evaluate several popular inductive inference operators with respect to these postulates. Furthermore, we show that, while every inductive inference operator satisfying generalized conditional syntax splitting also satisfies conditional syntax splitting, the reverse does not hold.

Jesse Heyninck, Matthias Knorr, João Leite

Dialectical frameworks are a unifying model of formal argumentation, where argumentative relations between arguments are represented by assigning acceptance conditions to atomic arguments. Their generality allow them to cover a number of different approaches with varying forms of representing the argumentation structure. Boolean regulatory networks are used to model the dynamics of complex biological processes, taking into account the interactions of biological compounds, such as proteins or genes. These models have proven highly useful for comprehending such biological processes, allowing to reproduce known behaviour and testing new hypotheses and predictions in silico, for example in the context of new medical treatments. While both these approaches stem from entirely different communities, it turns out that there are striking similarities in their appearence. In this paper, we study the relation between these two formalisms revealing their communalities as well as their differences, and introducing a correspondence that allows to establish novel results for the individual formalisms.

Jesse Heyninck, Ofer Arieli

This paper continues an established line of research about the relations between argumentation theory, particularly assumption-based argumentation, and different kinds of logic programs. In particular, we extend known result of Caminada, Schultz and Toni by showing that assumption-based argumentation can represent not only normal logic programs, but also disjunctive logic programs and their extensions. For this, we consider some inference rules for disjunction that the core logic of the argumentation frameworks should respect, and show the correspondence to the handling of disjunctions in the heads of the logic programs' rules. Under consideration in Theory and Practice of Logic Programming (TPLP).

Pascal Kettmann, Hannes Strass, Jesse Heyninck et al.

In logic programming, negation can be interpreted in various ways. Probably best known is the concept of "negation as failure", where "$\mathit{not}\, p$" is true if we have no evidence for $p$. On the other hand, strong negation requires that we have evidence for $p$ being false. Defining semantics for logic programs containing both kinds of negation is a challenging task, and this becomes even more challenging when combining this with other extensions of logic programming, e.g. fuzziness. In this work, we use the framework of approximating fixpoint theory to formulate well-behaved semantics for fuzzy logic programs containing both "by-failure" and strong negation. We show that this framework generalizes several existing semantics as well as giving rise to a host of new semantics.

Jesse Heyninck

Choice constructs are an important part of the language of logic programming, yet the study of their semantics has been a challenging task. So far, only two-valued semantics have been studied, and the different proposals for such semantics have not been compared in a principled way. In this paper, an operator-based framework allow for the definition and comparison of different semantics in a principled way is proposed.

Jesse Heyninck

Conditional independence is a crucial concept supporting adequate modelling and efficient reasoning in probabilistics. In knowledge representation, the idea of conditional independence has also been introduced for specific formalisms, such as propositional logic and belief revision. In this paper, the notion of conditional independence is studied in the algebraic framework of approximation fixpoint theory. This gives a language-independent account of conditional independence that can be straightforwardly applied to any logic with fixpoint semantics. It is shown how this notion allows to reduce global reasoning to parallel instances of local reasoning, leading to fixed-parameter tractability results. Furthermore, relations to existing notions of conditional independence are discussed and the framework is applied to normal logic programming.

Racquel Dennison, Jesse Heyninck, Thomas Meyer

Defeasible entailment is concerned with drawing plausible conclusions from incomplete information. A foundational framework for modelling defeasible entailment is the KLM framework. Introduced by Kraus, Lehmann, and Magidor, the KLM framework outlines several key properties for defeasible entailment. One of the most prominent algorithms within this framework is Rational Closure (RC). This paper presents a declarative definition for computing RC using Answer Set Programming (ASP). Our approach enables the automatic construction of the minimal ranked model from a given knowledge base and supports entailment checking for specified queries. We formally prove the correctness of our ASP encoding and conduct empirical evaluations to compare the performance of our implementation with that of existing imperative implementations, specifically the InfOCF solver. The results demonstrate that our ASP-based approach adheres to RC's theoretical foundations and offers improved computational efficiency.

Jeroen Spaans, Jesse Heyninck

Constraint Logic Programming (CLP) is a logic programming formalism used to solve problems requiring the consideration of constraints, like resource allocation and automated planning and scheduling. It has previously been extended in various directions, for example to support fuzzy constraint satisfaction, uncertainty, or negation, with different notions of semiring being used as a unifying abstraction for these generalizations. None of these extensions have studied clauses with negation allowed in the body. We investigate an extension of CLP which unifies many of these extensions and allows negation in the body. We provide semantics for such programs, using the framework of approximation fixpoint theory, and give a detailed overview of the impacts of properties of the semirings on the resulting semantics. As such, we provide a unifying framework that captures existing approaches and allows extending them with a more expressive language.

Sanne Wielinga, Jesse Heyninck

Machine learning (ML) techniques play a pivotal role in high-stakes domains such as healthcare, where accurate predictions can greatly enhance decision-making. However, most high-performing methods such as neural networks and ensemble methods are often opaque, limiting trust and broader adoption. In parallel, symbolic methods like Answer Set Programming (ASP) offer the possibility of interpretable logical rules but do not always match the predictive power of ML models. This paper proposes a hybrid approach that integrates ASP-derived rules from the FOLD-R++ algorithm with black-box ML classifiers to selectively correct uncertain predictions and provide human-readable explanations. Experiments on five medical datasets reveal statistically significant performance gains in accuracy and F1 score. This study underscores the potential of combining symbolic reasoning with conventional ML to achieve high interpretability without sacrificing accuracy.

Kenneth Skiba, Tjitze Rienstra, Matthias Thimm et al.

In this paper, we present a general framework for ranking sets of arguments in abstract argumentation based on their plausibility of acceptance. We present a generalisation of Dung's extension semantics as extension-ranking semantics, which induce a preorder over the power set of all arguments, allowing us to state that one set is "closer" to being acceptable than another. To evaluate the extension-ranking semantics, we introduce a number of principles that a well-behaved extension-ranking semantics should satisfy. We consider several simple base relations, each of which models a single central aspect of argumentative reasoning. The combination of these base relations provides us with a family of extension-ranking semantics. We also adapt a number of approaches from the literature for ranking extensions to be usable in the context of extension-ranking semantics, and evaluate their behaviour.

Jesse Heyninck, Bart Bogaerts

Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of non-monotonic logics. In recent work, AFT was generalized to non-deterministic operators, i.e.\ operators whose range are sets of elements rather than single elements. In this paper, we make three further contributions to non-deterministic AFT: (1) we define and study ultimate approximations of non-deterministic operators, (2) we give an algebraic formulation of the semi-equilibrium semantics by Amendola, et al., and (3) we generalize the characterisations of disjunctive logic programs to disjunctive logic programs with aggregates.

Jesse Heyninck, Christian Straßer, Pere Pardo

This paper maps out the relation between different approaches for handling preferences in argumentation with strict rules and defeasible assumptions by offering translations between them. The systems we compare are: non-prioritized defeats i.e. attacks, preference-based defeats, and preference-based defeats extended with reverse defeat.

Mathieu Beirlaen, Jesse Heyninck, Christian Straßer

We extend the $ASPIC^+$ framework for structured argumentation so as to allow applications of the reasoning by cases inference scheme for defeasible arguments. Given an argument with conclusion `$A$ or $B$', an argument based on $A$ with conclusion $C$, and an argument based on $B$ with conclusion $C$, we allow the construction of an argument with conclusion $C$. We show how our framework leads to different results than other approaches in non-monotonic logic for dealing with disjunctive information, such as disjunctive default theory or approaches based on the OR-rule (which allows to derive a defeasible rule `If ($A$ or $B$) then $C$', given two defeasible rules `If $A$ then $C$' and `If $B$ then $C$'). We raise new questions regarding the subtleties of reasoning defeasibly with disjunctive information, and show that its formalization is more intricate than one would presume.

Jesse Heyninck, Christian Straßer

In this paper we make a contribution to the unification of formal models of defeasible reasoning. We present several translations between formal argumentation frameworks and nonmonotonic logics for reasoning with plausible assumptions. More specifically, we translate adaptive logics into assumption-based argumentation and ASPIC+, ASPIC+ into assumption-based argumentation and a fragment of assumption-based argumentation into adaptive logics. Adaptive logics are closely related to Makinson's default assumptions and to a significant class of systems within the tradition of preferential semantics in the vein of KLM and Shoham. Thus, our results also provide close links between formal argumentation and the latter approaches.