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Explanatory relations in arbitrary logics based on satisfaction systems, cutting and retraction

Aiguier, Marc; Atif, Jamal; Bloch, Isabelle; Pino Pérez, Ramón (2018), Explanatory relations in arbitrary logics based on satisfaction systems, cutting and retraction, International Journal of Approximate Reasoning, 102, p. 1-20. 10.1016/j.ijar.2018.07.014

Type
Article accepté pour publication ou publié
Date
2018
Journal name
International Journal of Approximate Reasoning
Volume
102
Pages
1-20
Publication identifier
Metadata
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Author(s)
Aiguier, Marc
Mathématiques et Informatique pour la Complexité et les Systèmes [MICS]
Atif, Jamal
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Bloch, Isabelle cc
Laboratoire Traitement et Communication de l'Information [LTCI]
Pino Pérez, Ramón
Departamento de Matematicas
Abstract (EN)
The aim of this paper is to introduce a new framework for defining abductive reasoning operators based on a notion of retraction in arbitrary logics defined as satisfaction systems. We show how this framework leads to the design of explanatory relations satisfying properties of abductive reasoning, and discuss its application to several logics. This extends previous work on propositional logics where retraction was defined as a morphological erosion. Here weaker properties are required for retraction, leading to a larger set of suitable operators for abduction for different logics.
Subjects / Keywords
Explanatory relation; Retraction; Cutting; Satisfaction systems