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A. Liliana Reyes-Cabello, Atocha Aliseda-Llera, Ángel Nepomuceno-Fernández, Towards Abductive Reasoning in First-order Logic, Logic Journal of the IGPL, Volume 14, Issue 2, March 2006, Pages 287–304, https://doi.org/10.1093/jigpal/jzk019
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Abstract
Abductive problems have been widely studied in propositional logic. First order abduction, however, has been viewed as intractable, for the undecidability of logical consequence. In this paper, we propose a notion of abductive problem, N-abductive problem, which is relative to the cardinality of the minimal model satisfying the given theory. We use a notion of restricted satisfaction, also relative to a domain cardinality. Finally, we propose an effective procedure for the searching of abductive solutions, by means of a modification of Beth's tableaux.