On Nested Justification Systems (full version)

Marynissen, Simon; Heyninck, Jesse; Bogaerts, Bart; Denecker, Marc

doi:10.48550/arxiv.2205.04541

Cited by 2 publications

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“…Additionally, defined symbols are only allowed to occur positively in rule bodies. The semantics of FO(FD), explained in full detail in Appendix E of the full version of this article (Marynissen et al 2022), is given in terms of (two-valued) interpretations, and is defined iteratively, by means of an immediate consequence operator Γ D (I). Consistent with the idea of capturing a definition, a unique model according to these semantics is guaranteed to exist.…”

Section: S Marynissen Et Almentioning

confidence: 99%

“…For brevity and for emphasizing the relation with logic programming, we have here only written down the rules for positive facts. The rules for negative facts can be obtained automatically by means of a technique called complementation; more details can be found in Appendix A of the full version of this article (Marynissen et al 2022). These systems differ only in their inner justification system, that is, in which justifications for the atom atLeastTwo they accept.…”

Section: Example 34mentioning

confidence: 99%

“…Even though the compression-based and merging-based characterisation of semantics are based on quite different mechanisms, they give rise to the same evaluations for nested justification systems, that is, they are equivalent. Showing this is rather involved, and due to spatial limitations, the details are given in Appendix D of the full version of this article (Marynissen et al 2022) and illustrated schematically in Figure 1. The crucial idea for the proof of equivalence is the definition of two operations, shrinking and expanding, that allow converting justifications in Compress(JS) to justifications in Merge(JS) and vice versa.…”

Section: Equivalence Of Compression-and Merging-based Characterisationsmentioning

confidence: 99%

“…, JS ∇n to ensure that first-order formulae are treated adequately. This translation, as well as the correspondence results, are detailed in Appendix E of the full version of this article (Marynissen et al 2022).…”

Section: Sv Tmentioning

confidence: 99%

See 3 more Smart Citations

On Nested Justification Systems

Marynissen¹,

Heyninck²,

Bogaerts³

et al. 2022

Theory and Practice of Logic Programming

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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., 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 characterization of semantics for nested justification systems leads to the loss of information relevant for explanations. In view of this problem, we provide an alternative characterization of their semantics and show that it is equivalent to the original one. Furthermore, we show how nested justification systems allow representing fixpoint definitions.

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Section: S Marynissen Et Almentioning

confidence: 99%

Section: Example 34mentioning

confidence: 99%

Section: Equivalence Of Compression-and Merging-based Characterisationsmentioning

confidence: 99%

Section: Sv Tmentioning

confidence: 99%

See 2 more Smart Citations

On Nested Justification Systems

Marynissen¹,

Heyninck²,

Bogaerts³

et al. 2022

Theory and Practice of Logic Programming

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Explanations for Answer Set Programming

Alviano,

Trieu,

Cao Son

et al. 2023

Electron. Proc. Theor. Comput. Sci.

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The paper presents an enhancement of xASP, a system that generates explanation graphs for Answer Set Programming (ASP). Different from xASP, the new system, xASP2 , supports different clingo constructs like the choice rules, the constraints, and the aggregates such as #sum, #min. This work formalizes and presents an explainable artificial intelligence system for a broad fragment of ASP, capable of shrinking as much as possible the set of assumptions and presenting explanations in terms of directed acyclic graphs.

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On Nested Justification Systems (full version)

Cited by 2 publications

References 0 publications

On Nested Justification Systems

On Nested Justification Systems

Explanations for Answer Set Programming

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