Jesse Heyninck

NMR Workshop 2025 Conference Paper

A Unifying Framework for Semiring-Based Constraint Logic Programming With Negation

• Jeroen Paul Spaans
• Jesse Heyninck

Extended abstract of a paper published at IJCAI 20251 [2]—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 (AFT), 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.

IJCAI Conference 2025 Conference Paper

A Unifying Framework for Semiring-Based Constraint Logic Programming With Negation

• 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 generalisations. 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 to extend them with a more expressive language.

AAAI Conference 2025 Conference Paper

An Algebraic Notion of Conditional Independence, and Its Application to Knowledge Representation

• 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.

AAAI Conference 2025 Conference Paper

An Alternative Theory of Stable Revision for Nondeterministic Approximation Fixpoint Theory and the Relationships

• Spencer Killen
• Jia-Huai You
• Jesse Heyninck

Approximation fixpoint theory (AFT) is a robust and popular mathematical framework that characterizes many nonmonotonic semantics, where the construction of stable fixpoints, called stable revision, play a central role. Nondeterministic AFT is a recent development that redefines AFT for a nondeterministic setting to capture disjunctive semantics. This theory departs from traditional AFT by introducing distinct definitions, thus raising the question of whether deterministic AFT can be adopted directly to define nondeterministic stable revision. This work proposes such an alternate theory and creates a new way to study disjunctive semantics in terms of normal (non-disjunctive) knowledge bases. To demonstrate the viability of our framework, we show how to capture stable and partial stable models for disjunctive logic programs. We then study the relationships between this alternative theory and the state-of-the-art nondeterministic AFT.

KR Conference 2025 Conference Paper

An Analysis of the Role of Syntax in Inductive Inference

• Jesse Heyninck
• Richard Booth
• Thomas Meyer
• Lars-Phillip Spiegel

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.

IJCAI Conference 2025 Conference Paper

Approximation Fixpoint Theory as a Unifying Framework for Fuzzy Logic Programming Semantics

• Pascal Kettmann
• Jesse Heyninck
• Hannes Strass

Fuzzy logic programming is an established approach for reasoning under uncertainty. Several semantics from classical, two-valued logic programming have been generalized to the case of fuzzy logic programs. In this paper, we show that two of the most prominent classical semantics, namely the stable model and the well-founded semantics, can be reconstructed within the general framework of approximation fixpoint theory (AFT). This not only widens the scope of AFT from two- to many-valued logics, but allows a wide range of existing AFT results to be applied to fuzzy logic programming. As first examples of such applications, we clarify the formal relationship between existing semantics, generalize the notion of stratification from classical to fuzzy logic programs, and devise “more precise” variants of the semantics.

NMR Workshop 2025 Conference Paper

Autoformalisation Answer Set Programs for Scheduling Problems using Few-Shot Learning and Chain-of-Thought

• Jesse Heyninck
• Bart van Gool
• Stefano Bromuri
• Tjitze Rienstra

Large language models (LLMs) have caused a veritable revolution in the field of AI. However, LLMs do come with some considerable caveats including the lack of logical reasoning ability. This can make it challenging to use LLMs in environments where they need to give reliably correct answers. Recently, attempts have been made to alleviate this concern by generating a more transparent way of solving the problem using an LLM, instead of solving the problem directly with an LLM (so-called autoformalisation). Among others, answer set programs have been tried as a problem-solving intermediary in this context. However, current attempts at autoformalisation of answer set programs has been limited to toy examples or single, simple rules. In this work, we investigate the capabilities of LLMs in generating ASP that solve real-world scheduling problems, and identify techniques such as few-shot learning and chain-of-thought as particularly succesful.

IJCAI Conference 2025 Conference Paper

Generalized Safe Conditional Syntax Splitting of Belief Bases

• Lars-Phillip Spiegel
• Jonas Haldimann
• Jesse Heyninck
• Gabriele Kern-Isberner
• Christoph Beierle

Splitting techniques in knowledge representation help focus on relevant parts of a belief base and reduce the complexity of reasoning generally. In this paper, we propose a generalization of safe conditional syntax splittings that broadens the applicability of splitting postulates for inductive inference from belief bases. In contrast to safe conditional syntax splitting, our generalized notion supports syntax splittings of a belief base ∆ where the subbases of ∆ 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 ∆. We introduce adjusted inference postulates based on our generalization of conditional syntax splitting. We evaluate several inductive inference operators with respect to these postulates, and show that generalized safe conditional syntax splitting is a strictly stronger requirement for inductive inference operators, covering more syntax splitting applications.

NMR Workshop 2025 Conference Paper

The KLM Representation Theorem for System C, Formally

• Jonathan Walther
• Kai Sauerwald
• Jesse Heyninck

We present a formalization of the proof of the correspondence between cumulative non-monotonic reasoning and System C in a proof assistant. Reasoning based on System C is the cornerstone of non-monotonic reasoning and was given a semantics via cumulative models by Kraus, Lehmann and Magidor. Our proof is inspired by the original proof and written in the proof system Rocq and focuses on propositional logic. Due to the features of Rocq, the proof implicitly yields a verified implementation of System C reasoning.

FLAP Journal 2025 Journal Article

The Semantical Structure of Conditionals, and its Relation to Formal Argumentation

• Jesse Heyninck
• Gabriele Kern-Isberner
• Tjitze Rienstra
• Kenneth Skiba
• Matthias Thimm

Conditionals, i. e. expressions of the logical form “if A, then B”, have been a central topic of study ever since logic was on the academic menu. In contem- porary logic, there is a consensus that the semantics of conditionals are best obtained by stipulating a subset of possible worlds in which the antecedent is true, and verifying whether the consequent is true in those worlds. Such a subset of possible worlds can represent, for example, the most typical worlds in which the antecedent is true. This idea has proven a fruitful basis, allowing for many systematic characterisation results as well as for making connections to other topics, such as belief revision and modal logic. In formal argumentation, the potential of these semantical ideas has not gone unnoticed in the last years, and

NMR Workshop 2025 Conference Paper

Toward Defeasible Reasoning Using Knowledge Compilation Techniques

• Luke Slater
• Thomas Andreas Meyer
• Jesse Heyninck

We explore the use of ordered binary decision diagrams (OBDDs) and multi-terminal binary decision diagrams (MTBDDs) for compiling and executing defeasible reasoning, focusing on System Z, also known as rational closure. We introduce an OBDD-based algorithm for System Z inference that parallels traditional SAT-based approaches. Additionally, we investigate the use of MTBDDs for encoding ordinal conditional functions (OCFs), providing a more general and unified knowledge compilation framework for defeasible reasoning tasks involving ranking functions. While our primary focus is on System Z, the proposed techniques are applicable to other forms of defeasible reasoning and conditional logic more broadly. Experimental results demonstrate that OBDDs can significantly accelerate inference. However, our evaluation is limited to synthetically generated belief bases, and further research is needed to validate benefits in real-world scenarios. Overall, our findings suggest that binary decision diagrams offer a promising alternative to SAT-based methods for defeasible reasoning, and warrant further investigation.

NMR Workshop 2024 Conference Paper

Abstract Dialectical Frameworks are Boolean Networks

• Jesse Heyninck
• Matthias Knorr 0001
• João Leite 0001

Abstract 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 allows 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.

KR Conference 2024 Conference Paper

Conditional Splittings of Belief Bases and Nonmonotonic Inference with c-Representations

• Christoph Beierle
• Lars-Phillip Spiegel
• Jonas Haldimann
• Marco Wilhelm
• Jesse Heyninck
• Gabriele Kern-Isberner

The concept of conditional syntax splitting for inductive inference from conditional belief bases has been proposed as a generalization of syntax splitting which also covers cases where the conditionals in the subbases share some atoms. p-Entailment and system Z fail to satisfy conditional syntax splitting, and up to now, only two inductive inference operators, lexicographic inference and system W, have been shown to satisfy this property. In this paper, we introduce the concept of conditional semantic splitting. We show that c-representations satisfy a core postulate relating conditional splittings on the syntax and the semantic level. Based on these findings, we investigate conditional syntax splitting for nonmonotonic inference with c-representations. Regarding single c-representations, we utilize the concept of selection strategies, and show that a straightforward property of the selection strategy leads to inference operators satisfying conditional syntax splittings. Furthermore, we show that c-inference taking all c-representations of a belief base into account also fully complies with conditional syntax splitting.

AIJ Journal 2024 Journal Article

Non-deterministic approximation fixpoint theory and its application in disjunctive logic programming

• 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.

KR Conference 2024 Conference Paper

Operator-Based Semantics for Choice Programs: Is Choosing Losing?

• 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.

IJCAI Conference 2024 Conference Paper

Semantics for Non-Flat Assumption-Based Argumentation, Revisited

• Jesse Heyninck
• Ofer Arieli

Assumption-based argumentation (ABA) is an argumentative formalism that allows for reasoning on the basis of defeasible assumptions and strict rules. Standard semantics for this formalism sometimes give rise to problematic behaviour in the presence of rules with assumptions in their heads. In this paper, we introduce a six-valued labelling semantics that overcomes these shortcomings while preserving all the usual properties of the standard Dung-style three-valued semantics for ABA frameworks, including existence of the complete semantics, uniqueness of the grounded semantics and preservation of the computational complexity of all main reasoning processes.

NMR Workshop 2024 Conference Paper

The Role of Syntax in Inductive Inference: A Property-based Study

• Jesse Heyninck
• Richard Booth 0001
• Thomas Andreas Meyer

The study of inference operators frequently involves the introduction of properties to which such operators should conform. Amongst other advantages, the property-based approach helps to restrict the range of operators, and to classify and categorise the type of inference being studied. This paper continues this tradition by proposing a number of properties for the class of inductive inference operators. We study the interaction of these properties, both with one another, and with other well-known properties for inductive inference. We also test a number of well-known inductive inference operators against the newly proposed, and some existing properties.

NMR Workshop 2023 Conference Paper

An Algebraic Notion of Conditional Independence, and its Application to Knowledge Representation (Preliminary Report)

• 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 languageindependent 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. Furthermore, relations to existing notions of conditional independence are discussed and the framework is applied to normal logic programming.

AAAI Conference 2023 Conference Paper

Conditional Syntax Splitting for Non-monotonic Inference Operators

• Jesse Heyninck
• Gabriele Kern-Isberner
• Thomas Meyer
• Jonas Philipp Haldimann
• Christoph Beierle

Syntax splitting is a property of inductive inference operators that ensures we can restrict our attention to parts of the conditional belief base that share atoms with a given query. To apply syntax splitting, a conditional belief base needs to consist of syntactically disjoint conditionals. This requirement is often too strong in practice, as conditionals might share atoms. In this paper we introduce the concept of conditional syntax splitting, inspired by the notion of conditional independence as known from probability theory. We show that lexicographic inference and system W satisfy conditional syntax splitting, and connect conditional syntax splitting to several known properties from the literature on non-monotonic reasoning, including the drowning effect.

IJCAI Conference 2023 Conference Paper

Ranking-based Argumentation Semantics Applied to Logical Argumentation

• 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 accept- ability 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 be- haviour 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.

KR Conference 2023 Conference Paper

Revising Typical Beliefs: One Revision to Rule Them All

• Jesse Heyninck
• Giovanni Casini
• Thomas Meyer
• Umberto Straccia

Propositional Typicality Logic (PTL) extends propositional logic with a connective • expressing the most typical (alias normal or conventional) situations in which a given sentence holds. As such, it generalises e. g. ~preferential logics that formalise reasoning with conditionals such as ``birds typically fly''. In this paper, we study revision of sets of PTL-sentences. We first show why it is necessary to extend the PTL-language with a possibility operator, and then define the revision of PTL-sentences syntactically and characterise it semantically. We show that this allows us to represent a wide variety of existing revision methods, such as propositional revision and revision of epistemic states. Furthermore, we provide several examples showing why our approach is innovative. In more detail, we study revision of a set of conditionals under preferential closure, and the addition and contraction of possible worlds from an epistemic state.

AIJ Journal 2023 Journal Article

Revision, defeasible conditionals and non-monotonic inference for abstract dialectical frameworks

• Jesse Heyninck
• Gabriele Kern-Isberner
• Tjitze Rienstra
• Kenneth Skiba
• Matthias Thimm

For propositional beliefs, there are well-established connections between belief revision, defeasible conditionals, and nonmonotonic inference. In argumentative contexts, such connections have not yet been investigated. On the one hand, the exact relationship between formal argumentation and nonmonotonic inference relations is a research topic that keeps on eluding researchers despite recently intensified efforts, whereas argumentative revision has been studied in numerous works during recent years. In this paper, we show that relationships between belief revision, defeasible conditionals, and nonmonotonic inference similar to those in propositional logic hold in argumentative contexts as well. We first define revision operators for abstract dialectical frameworks, and use such revision operators to define dynamic conditionals by means of the Ramsey test. We show that such conditionals can be equivalently defined using a total preorder over three-valued interpretations, and study the inferential behaviour of the resulting conditional inference relations.

NMR Workshop 2023 Conference Paper

Semantics for Logic Programs with Choice Constructs on the Basis of Approximation Fixpoint Theory (Preliminary Report)

• Jesse Heyninck

Choice constructs are an important addition to the language of logic programming that greatly increase its modeling capabilities. Their semantics are non-deterministic, in the sense that their might be several interpretations that satisfy a choice construct. In this paper, the semantics of logic programs with choice operators are studied using the recently proposed non-deterministic approximation fixpoint theory. We show that this allows to represent the semantics of Liu, Pontenelli, Son and Trusczczyński and generalize these semantics to the three-valued case. Furthermore, the framework allows us to give a principled account of the difference and similarities between stable model semantics of choice programs and disjunctive logic programs.

KR Conference 2023 Conference Paper

Simple Contrapositive Assumption-Based Argumentation with Partially-Ordered Preferences

• Ofer Arieli
• Jesse Heyninck

We show that assumption-based argumentation frameworks, based on contrapositive logics and partially-ordered preference functions, provide a solid platform for argumentation-based reasoning. Two useful properties of the preference functions are identified (selectivity and max-lower-boundedness), and extended forms of attacks relations are supported (exists-attacks and forall-attacks), which assure several desirable properties and a variety of reasoning modes.

JELIA Conference 2023 Conference Paper

Splitting Techniques for Conditional Belief Bases in the Context of c-Representations

• Marco Wilhelm
• Meliha Sezgin
• Gabriele Kern-Isberner
• Jonas Haldimann
• Christoph Beierle
• Jesse Heyninck

Abstract Splitting belief bases is fundamental for efficient reasoning and for better understanding interrelationships among the knowledge entities. In this paper, we survey the most important splitting techniques for conditional belief bases in the context of c-representations which constitute a specific class of ranking models with outstanding behavior not only with respect to belief base splitting, as shown in recent papers. We provide a splitting hierarchy, in particular by proving that safe conditional syntax splittings and case splittings are so-called CSP-constraint splittings. We advance the level of knowledge about CSP-constraint splittings and present an algorithm for computing CSP-constraint splittings.

AAAI Conference 2022 Conference Paper

Conditional Abstract Dialectical Frameworks

• Jesse Heyninck
• Matthias Thimm
• Gabriele Kern-Isberner
• Tjitze Rienstra
• Kenneth Skiba

Abstract dialectical frameworks (in short, ADFs) are a unifying model of formal argumentation, where argumentative relations between arguments are represented by assigning acceptance conditions to atomic arguments. This idea is generalized by letting acceptance conditions being assigned to complex formulas, resulting in conditional abstract dialectical frameworks (in short, cADFs). We define the semantics of cADFs in terms of a non-truth-functional four-valued logic, and study the semantics in-depth, by showing existence results and proving that all semantics are generalizations of the corresponding semantics for ADFs.

IJCAI Conference 2022 Conference Paper

Conditional Independence for Iterated Belief Revision

• Gabriele Kern-Isberner
• Jesse Heyninck
• Christoph Beierle

Conditional independence is a crucial concept for efficient probabilistic reasoning. For symbolic and qualitative reasoning, however, it has played only a minor role. Recently, Lynn, Delgrande, and Peppas have considered conditional independence in terms of syntactic multivalued dependencies. In this paper, we define conditional independence as a semantic property of epistemic states and present axioms for iterated belief revision operators to obey conditional independence in general. We show that c-revisions for ranking functions satisfy these axioms, and exploit the relevance of these results for iterated belief revision in general.

NMR Workshop 2022 Conference Paper

Conditional Syntax Splitting, Lexicographic Entailment and the Drowning Effect

• Jesse Heyninck
• Gabriele Kern-Isberner
• Thomas Andreas Meyer

Lexicographic inference [1] is a well-behaved and popular approach to reasoning with non-monotonic conditionals. In recent work we have shown that lexicographic inference satisfies syntax splitting, which means we can restrict our attention to parts of the belief base that share atoms with a given query. In this paper, we introduce the concept of conditional syntax splitting, inspired by the notion of conditional independence as known from probability theory. We show that lexicographic inference satisfies conditional syntax splitting, and connect conditional syntax splitting to several known properties from the literature on non-monotonic reasoning, including the drowning effect.

IJCAI Conference 2022 Conference Paper

Lexicographic Entailment, Syntax Splitting and the Drowning Problem

• Jesse Heyninck
• Gabriele Kern-Isberner
• Thomas Meyer

Lexicographic inference is a well-known and popular approach to reasoning with non-monotonic conditionals. It is a logic of very high-quality, as it extends rational closure and avoids the so-called drowning problem. It seems, however, this high quality comes at a cost, as reasoning on the basis of lexicographic inference is of high computational complexity. In this paper, we show that lexicographic inference satisfies syntax splitting, which means that we can restrict our attention to parts of the belief base that share atoms with a given query, thus seriously restricting the computational costs for many concrete queries. Furthermore, we make some observations on the relationship between c-representations and lexicographic inference, and reflect on the relation between syntax splitting and the drowning problem.

IJCAI Conference 2022 Conference Paper

Possibilistic Logic Underlies Abstract Dialectical Frameworks

• Jesse Heyninck
• Gabriele Kern-Isberner
• Tjitze Rienstra
• Kenneth Skiba
• Matthias Thimm

Abstract dialectical frameworks (in short, ADFs) are one of the most general and unifying approaches to formal argumentation. As the semantics of ADFs are based on three-valued interpretations, we ask which monotonic three-valued logic allows to capture the main semantic concepts underlying ADFs. We show that possibilistic logic is the unique logic that can faithfully encode all other semantical concepts for ADFs. Based on this result, we also characterise strong equivalence and introduce possibilistic ADFs.

FLAP Journal 2021 Journal Article

A Comparative Study of Assumption-based Argumentative Approaches to Reasoning with Priorities.

• Jesse Heyninck
• Christian Straßer

In this paper we study formal properties of approaches to the reasoning with prioritized defeasible assumptions. We focus on methods proposed in formal argumentation, more specifically in the context of assumption-based argumentation. We systematically compare two approaches for handling conflicts: preference-based defeats and preference-based defeats extended with reverse defeat. We investigate under which conditions these approaches give rise to the same output. We study several meta-theoretical properties including argumentation theoretical properties (such as Dung’s Fundamental Lemma and the consistency of extensions) and properties for nonmonotonic reasoning (such as Cautious Monotony and Cut) in a parametrized way, i.e., relative to specific constraints on the underlying deducability relation. Finally, we study the relationship between these approaches and preferred subtheories, a nonmonotonic reasoning formalism that is based on maximal consistent subsets of a totally ordered knowledge base. In the parametrized setting we study different sub-classes of assumptionbased argumentation frameworks. For instance, we identify a particularly wellbehaved sub-class of argumentation-based frameworks for which the different conflict-handling mechanisms coincide, which give the same outcomes as preferred subtheories and for which core properties of nonmonotonic logic are valid.

KR Conference 2021 Conference Paper

Approximation Fixpoint Theory for Non-Deterministic Operators and Its Application in Disjunctive Logic Programming

• Jesse Heyninck
• Ofer Arieli

Approximation fixpoint theory (AFT) constitutes 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 non-deterministic constructs such as disjunctive information. This is done by generalizing the main constructions and corresponding results 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.

FLAP Journal 2021 Journal Article

Logic-Based Approaches to Formal Argumentation.

• Ofer Arieli
• Annemarie Borg
• Jesse Heyninck
• Christian Straßer

We study the logical foundations of Dung-style argumentation frameworks. Logicbased methods in the context of argumentation theory are described from two perspectives: (a) a survey of logic-based instantiations of argumentation frameworks, their properties and relations, and (b) a review of logical methods for the study of argumentation dynamics. In this chapter we restrict ourselves to Tarskian logics, based on (propositional) languages and corresponding (constructive) semantics or syntactic rule-based systems.

IJCAI Conference 2021 Conference Paper

Ranking Extensions in Abstract Argumentation

• Kenneth Skiba
• Tjitze Rienstra
• Matthias Thimm
• Jesse Heyninck
• Gabriele Kern-Isberner

Extension-based semantics in abstract argumentation provide a criterion to determine whether a set of arguments is acceptable or not. In this paper, we present the notion of extension-ranking semantics, which determines a preordering over sets of arguments, where one set is deemed more plausible than another if it is somehow more acceptable. We obtain extension-based semantics as a special case of this new approach, but it also allows us to make more fine-grained distinctions, such as one set being "more complete'' or "more admissible'' than another. We define a number of general principles to classify extension-ranking semantics and develop concrete approaches. We also study the relation between extension-ranking semantics and argument-ranking based semantics, which rank individual arguments instead of sets of arguments.

KR Conference 2021 Conference Paper

Revision and Conditional Inference for Abstract Dialectical Frameworks

• Jesse Heyninck
• Gabriele Kern-Isberner
• Tjitze Rienstra
• Kenneth Skiba
• Matthias Thimm

For propositional beliefs, there are well-established connections between belief revision, defeasible conditionals and nonmonotonic inference. In argumentative contexts, such connections have not yet been investigated. On the one hand, the exact relationship between formal argumentation and nonmonotonic inference relations is a research topic that keeps on eluding researchers despite recently intensified efforts, whereas argumentative revision has been studied in numerous works during recent years. In this paper, we show that similar relationships between belief revision, defeasible conditionals and nonmonotonic inference hold in argumentative contexts as well. We first define revision operators for abstract dialectical frameworks, and use such revision operators to define dynamic conditionals by means of the Ramsey test. We show that such conditionals can be equivalently defined using a total preorder over three-valued interpretations, and study the inferential behaviour of the resulting conditional inference relations.

JELIA Conference 2021 Conference Paper

Tractable Reasoning Using Logic Programs with Intensional Concepts

• Jesse Heyninck
• Ricardo Gonçalves 0001
• Matthias Knorr 0001
• João Leite 0001

Abstract Recent developments triggered by initiatives such as the Semantic Web, Linked Open Data, the Web of Things, and geographic information systems resulted in the wide and increasing availability of machine-processable data and knowledge in the form of data streams and knowledge bases. Applications building on such knowledge require reasoning with modal and intensional concepts, such as time, space, and obligations, that are defeasible. E. g. , in the presence of data streams, conclusions may have to be revised due to newly arriving information. The current literature features a variety of domain-specific formalisms that allow for defeasible reasoning using specific intensional concepts. However, many of these formalisms are computationally intractable and limited to one of the mentioned application domains. In this paper, we define a general method for obtaining defeasible inferences over intensional concepts, and we study conditions under which these inferences are computable in polynomial time.

ECAI Conference 2020 Conference Paper

Prioritized Simple Contrapositive Assumption-Based Frameworks

• Ofer Arieli
• Jesse Heyninck

Simple contrapositive assumption-based frameworks are a general setting for structured argumentation, providing a robust approach to reasoning with arguments and counter-arguments. In this paper we extend these frameworks with priorities and introduce some new results concerning the semantics of the resulting formalisms.

AAMAS Conference 2019 Conference Paper

A Fully Rational Argumentation System for Preordered Defeasible Rules

• Jesse Heyninck
• Christian Straßer

Structured argumentation is a family of formal approaches for the handling of defeasible, potentially inconsistent information. Many models for structured argumentation distinguish between strict and defeasible inference rules. Defeasible rules often come with varying degrees of strength which is formally represented by a preorder over the defeasible rules. Various lifting principles have been presented in the literature to determine the relative strength of an argument by considering the strength of the defeasible rules used in its construction. The strength of arguments then comes into play when determining whether an attack (a purely syntactic relationship between arguments) results in a defeat (i. e. a successful attack). In [5, 22], several rationality postulates were proposed that serve as a measure to assess the normative rationality of structured argumentation formalisms. In [14], the first formalism satisfying all rationality postulates for structured argumentation when taking into account totally ordered defeasible rules was proposed. In many settings, assuming a total order greatly limits the realistic modelling capabilities of a formal system, e. g. when agents do not know the actual preferences of each rule or since different agents have different preferences over defeasible rules. Our paper shows that in the more general setting of preorders, violations of several rationality postulates can occur. We show how for a wide class of lifting principles, these violations can be avoided, resulting in the first Dung-based system that satisfies all four rationality postulates for preordered defeasible rule bases.

FLAP Journal 2019 Journal Article

Relations Between Assumption-based Approaches in Nonmonotonic Logics and Formal Argumentation.

• Jesse Heyninck

AAMAS Conference 2019 Conference Paper

Simple Contrapositive Assumption-Based Frameworks

• Jesse Heyninck
• Ofer Arieli

We study the Dung semantics for extended forms of assumptionbased argumentation frameworks (ABFs), based on any contrapositive propositional logic, and whose defeasible rules are expressed by arbitrary formulas in that logic. New results on the well-founded semantics for such ABFs are reported, the redundancy of the closure condition is shown, and the use of disjunctive attacks is investigated. Useful properties of the generalized frameworks are also considered.

FLAP Journal 2018 Journal Article

Argument Strength in Formal Argumentation.

• Mathieu Beirlaen
• Jesse Heyninck
• Pere Pardo
• Christian Straßer

IJCAI Conference 2017 Conference Paper

Revisiting Unrestricted Rebut and Preferences in Structured Argumentation.

• Jesse Heyninck
• Christian Straßer

In structured argumentation frameworks such as ASPIC+, rebuts are only allowed in conclusions produced by defeasible rules. This has been criticized as counter-intuitive especially in dialectical contexts. In this paper we show that ASPIC-, a system allowing for unrestricted rebuts, suffers from contamination problems. We remedy this shortcoming by generalizing the attack rule of unrestricted rebut. Our resulting system satisfies the usual rationality postulates for prioritized rule bases.