On the Relation Between Approximation Fixpoint Theory and Justification Theory

Marynissen, Simon; Bogaerts, Bart; Denecker, Marc

doi:10.24963/ijcai.2021/272

Cited by 3 publications

(3 citation statements)

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“…The basic idea is to compress a nested justification system in a regular justification system, starting from the leaves of the nesting tree and iteratively moving up. In a compressible nested system, the branch evaluations of subsystems are parametric and hence we know (by Proposition 3 of Marynissen et al 2021) that, if the interpretation of the open facts is fixed, there is a unique model in which the value of a fact depends solely on the values of the opens. Therefore, the model can be represented by a set of rules for which the body contains only open facts.…”

Section: Compression-based Characterisation Of Semantics For Nested S...mentioning

confidence: 99%

Section: Compression-based Characterisation Of Semantics For Nested S...mentioning

confidence: 99%

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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: Compression-based Characterisation Of Semantics For Nested S...mentioning

confidence: 99%

Section: Compression-based Characterisation Of Semantics For Nested S...mentioning

confidence: 99%

On Nested Justification Systems

Marynissen¹,

Heyninck²,

Bogaerts³

et al. 2022

Theory and Practice of Logic Programming

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“…We present the core definitions of justification theory, based on the formalization of Marynissen et al [11,12].…”

Section: Preliminariesmentioning

confidence: 99%

Tree-Like Justification Systems are Consistent

Marynissen

Bogaerts

2022

Electron. Proc. Theor. Comput. Sci.

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Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are justifications for a fact and justifications for its negation suitably related. Two variants of justification theory exist: one in which justifications are trees and one in which they are graphs. In this work we resolve the consistency problem once and for all for the tree-like setting by showing that all reasonable tree-like justification systems are consistent. * This work was partially supported by Fonds Wetenschappelijk Onderzoek -Vlaanderen (project G0B2221N). 1 Nested justification systems were originally defined by Denecker et al. [3], but have remained largely unexplored since then. In a companion paper to this paper [13], we provide a systematic study of nested systems and their properties

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