Weighted Abstract Dialectical Frameworks through the Lens of Approximation Fixpoint Theory

Bogaerts, Bart

doi:10.1609/aaai.v33i01.33012686

Cited by 15 publications

(9 citation statements)

References 18 publications

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“…The independent criteria are fitting for many real-life decision-makings, since it is common that assessments as to why a proposal (a suspect) should/must be accepted (guilty) and as to why it (the suspect) should/must be rejected (acquitted) are separately made before, based on them, a final decision is delivered. The may-mustconditions based on the cardinality of accepted or rejected attacking arguments are, as far as we are aware, not considered in ADF including [12,10]. Some more technical comparisons are found in the conclusion of this paper.…”

Section: Related Workmentioning

confidence: 99%

“…Fuzziness as a varying attack strength [30] and as a varying degree of acceptability of an argument [16,12,10] have been discussed in the literature, both of which are closely related to ranking-based argumentation. The kind of fuzziness that we deal with in this paper, however, is not, again borrowing the expression in [23], about 'exogeneously given information about the relative strength of arguments' or the relative degree of acceptability, but about an endogenous property of an argumentation graph, the cardinality of attackers.…”

Section: Related Workmentioning

confidence: 99%

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Broadening Label-Based Argumentation Semantics with May-Must Scales

Arisaka

Ito

2020

Lecture Notes in Computer Science

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The semantics as to which set of arguments in a given argumentation graph may be acceptable (acceptability semantics) can be characterised in a few different ways. Among them, the labelling-based approach allows for a concise and flexible determination of acceptability statuses of arguments through assignment of a label indicating acceptance, rejection, or undecided to each argument. In this work, we contemplate a way of broadening it by accommodating mayand must-conditions for an argument to be accepted and rejected, as determined by the number(s) of rejected and accepted attacking arguments. We show that the broadened label-based semantics can be used to express more mild indeterminacy than inconsistency for acceptability judgement when, for example, it may be the case that an argument is accepted and when it may also be the case that it is rejected. We identify that finding which conditions a labelling satisfies for every argument can be an undecidable problem, which has an unfavourable implication to semantics. We propose to address this problem by enforcing a labelling to maximally respect the conditions, while keeping the rest that would necessarily cause non-termination labelled undecided.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Broadening Label-Based Argumentation Semantics with May-Must Scales

Arisaka

Ito

2020

Lecture Notes in Computer Science

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“…Even in case semantics are already defined, applying AFT can be a sanity check. A striking example of this is the fact that applications of AFT uncovered some issues in the semantics of (weighted and non-weighted) Abstract Dialectic Frameworks [24,10,4]. • It provides access to a large body of theoretical results, including theorems on stratification [27,6],…”

Section: Introductionmentioning

confidence: 99%

Fixpoint Semantics for Recursive SHACL

Bogaerts¹,

Jakubowski²

2021

Electron. Proc. Theor. Comput. Sci.

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SHACL is a W3C-proposed language for expressing structural constraints on RDF graphs. The recommendation only specifies semantics for non-recursive SHACL; recently, some efforts have been made to allow recursive SHACL schemas. In this paper, we argue that for defining and studying semantics of recursive SHACL, lessons can be learned from years of research in non-monotonic reasoning. We show that from a SHACL schema, a three-valued semantic operator can directly be obtained. Building on Approximation Fixpoint Theory (AFT), this operator immediately induces a wide variety of semantics, including a supported, stable, and well-founded semantics, related in the expected ways. By building on AFT, a rich body of theoretical results becomes directly available for SHACL. As such, the main contribution of this short paper is providing theoretical foundations for the study of recursive SHACL, which can later enable an informed decision for an extension of the W3C recommendation.

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“…This approach underlies many non-monotonic formalisms, including all the major semantics for autoepistemic and default logic (Denecker, Marek, and Truszczyński 2000;Denecker, Marek, and Truszczyński 2003), a variety of logic programs including first order logic programs, and formal argumenta-tion (Strass 2013). AFT also allows to define attractive semantics for non-monotonic formalisms, such as extensions of logic programs (Pelov, Denecker, and Bruynooghe 2007;Antić, Eiter, and Fink 2013;Charalambidis, Rondogiannis, and Symeonidou 2018) and weighted abstract dialectical frameworks (ADFs, (Bogaerts 2019)).…”

Section: Introductionmentioning

confidence: 99%

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

Heyninck

Arieli

2021

Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning

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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.

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Weighted Abstract Dialectical Frameworks through the Lens of Approximation Fixpoint Theory

Cited by 15 publications

References 18 publications

Broadening Label-Based Argumentation Semantics with May-Must Scales

Broadening Label-Based Argumentation Semantics with May-Must Scales

Fixpoint Semantics for Recursive SHACL

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

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