Abstract
The aim in this paper is to define an Abductive Question-Answer System for the minimal logic of formal inconsistency mathsf {mbC}. As a proof-theoretical basis we employ the Socratic proofs method. The system produces abductive hypotheses; these are answers to abductive questions concerning derivability of formulas from sets of formulas. We integrated the generation of and the evaluation of hypotheses via constraints of consistency and significance being imposed on the system rules.
Highlights
In abductive reasoning we aim at filling a certain gap between a knowledge base Γ and a puzzling phenomenon A, unattainable from Γ
There are four primary ingredients of the algorithmic account of abduction [17, p. 2]: (i) a basic logic, (ii) a proof method, (iii) a hypotheses generation mechanism
The intuitions underlying those constraints are the following: in cases when we want to generate abductive hypothesis that is consistent with the knowledge base Γ, we look for those formulas, that are consistent with at least one Hintikka set
Summary
In abductive reasoning we aim at filling a certain gap between a knowledge base Γ and a puzzling phenomenon A, unattainable from Γ (cf. [15,23]). More expressive language allows for formulation of such abductive hypotheses that could not be obtained by means of classical logic. In light of this arguments we can say that the abductive procedure we describe in this paper does not contradict procedures based on classical logic but extends them. We start with introducing the minimal logic of formal inconsistency, mbC (Section 2) and its proof theory employing the Socratic proofs method (Section 3). On this basis we define our abductive procedure (Section 4), including an algorithm for generation of abductive hypotheses
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