Abductive reasoning

About: Abductive reasoning is a research topic. Over the lifetime, 1917 publications have been published within this topic receiving 44645 citations. The topic is also known as: abduction & abductive inference.

Abduction and Question Answering

Abstract: Abduction can be viewed as self-questioning, where the search for an explanation is analogous to answering a “why” question. The question is of the form Why P?, where P is an observation or fact that has come to an agent’s attention. An abductive hypothesis is a possible answer to the question Why P? When abduction is viewed as a type of question answering, abductive hypotheses can be seen as a subset of hypothetical (or conditional) answers. These answers are comprised of two components: a hypothesis that is consistent with an agent’s knowledge, but whose validity can not be determined, and an associated specific or generic answer, whose correctness hinges on the validity of the associated hypoth esis. Hypothetical answering and abductive reasoning are both ways of coping with incomplete information. The difference between the two lies in the way in which the hypothetical information is employed. In abduction, a reasoner chooses to believe an abductive hypothesis based on factors such as belonging to a set of abducibles and informativeness. In question answering (excepting the case of self-questioning), t he answering agent is reasoning in service of a distinct questioner, and has no reason to adopt or consider the hypothesis associated with a hypothetical answer as an update to its knowledge base. It is in the interest of an abductive reasoner to place higher value an abductive hypothesis that is more informative than other abductive hypotheses. This is true for the questioner also. The difference between abduction and question answering is that the answering agent does not customarily have access to the questioner’s knowledge base. This means that the informativeness of a hypothetical answer can not be determined by an answering agent, making it necessary to provide hypothetical answers at all possible levels of generality. It is generally not possible for the answering agent to measure the “informativeness” of an abductive hypothesis. This paper presents a discussion of the relationship between question answering and abduction. 2 Background

A science of reasoning: extended abstract

Abstract: How can we understand reasoning in general and mathematical proofs in particular? It is argued that a high-level understanding of proofs is needed to complement the low-level understanding provided by Logic. A role for computation is proposed to provide this high-level understanding, namely by the association of proof plans with proofs. Criteria are given for assessing the association of a proof plan with a proof.

Abduction and Truthlikeness

Abstract: Earlier chapters deal with abductive inferences to explanations which are deductive or inductive-probabilistic. This more or less standard account has so far ignored the fact that explanatory and predictive success in science is often approximate. Therefore, the analysis of abduction should cover also approximate explanations, which is illustrated by Newton’s explanation of Kepler’s harmonic law (Sect. 8.1). The notions of approximate truth (closeness to being true), verisimilitude (closeness to complete qualitative or quantitative truth) and legisimilitude (closeness to the true law) are defined in Sect. 8.2. This leads us to generalize Peirce’s model of abduction to cases where the conclusion states that the best theory is truthlike or approximately true, with illustrations from idealized theories and models (Sect. 8.3). In a comparative formulation, if theory Y is a better explanation of the available evidence E than theory X, then conclude for the time being that Y is more truthlike than X. To justify such abduction, we need a method of estimating degrees of truthlikeness by their expected values. Another tool is the notion of probable approximate truth. Then, in order to answer to Laudan’s challenge, the probabilistic link between empirical success and truth has to be replaced with a fallible bridge from the approximate empirical success of a theory to its truthlikeness (Sect. 8.4). Section 8.5 gives some remarks on abductive belief revision, which is related to cases where the evidence is conflict with the theory. This theme extends Aliseda’s way of linking belief revision models with abductive reasoning.

Abduction and the Emergence of Necessary Mathematical Knowledge

Abstract: The prevailing epistemological perspective on school mathematical knowledge values the central role of induction and deduction in the development of necessary mathematical knowledge with a rather taken-for-granted view of abduction This chapter will present empirical evidence that illustrates the relationship between abductive action and the emergence of necessary mathematical knowledge