A Formal Logic for Abductive Reasoning

Abstract

This paper presents and illustrates a formal logic for the abduction of singular hypotheses. The logic has a semantics and a dynamic proof theory that is sound and complete with respect to the semantics. The logic presupposes that, with respect to a specific application, the set of explananda and the set of possible explanantia are disjoint (but not necessarily exhaustive). Where an explanandum can be explained by different explanantia, the logic allows only for the abduction of their disjunction.

A deontic logic framework allowing for factual detachment

“…Furthermore, proper detachment should be blocked in strong CTD cases. While in the case of specificity the more general primary obligation is blocked, the situation is now inverse: Furthermore, we instrumentally prioritize more specific obligations over incompatible general norms 22 : However, L + does not yet give a satisfactory account of detachment. In order to show this we take a look at two paradigmatic proofs: one for example (A) (to the left) and one for example (G) (to the right, we presuppose g k): This is where ALs come in, since these logics allow for conditional applications of certain rules which enable them to interpret a premise set "as normally as possible" with respect to some given criterion for normality.…”

USE: A Concept-Based Recommendation System to Support Creative Search

“…We have already applied the concept of reasoning-driven abduction in a model of a real industrial process, and a trace of the abduction inferences can be found at [11] 2 . The formal logic used in our proposal is LA r , presented in [13]. LA r is a logic based on Classical Logic with a non-monotonic dynamical process in which deductive steps are combined with abductive steps.…”

Identifying Efficient Abductive Hypotheses Using Multicriteria Dominance Relation

“…Various procedures for generation of abducibles have been proposed so far; some are designed for Classical Propositional Calculus (CPC for short) [1], others for more sophisticated propositional logics [29,26] or for first-order logic [16,25,28]. Those procedures, which are defined in a strictly logical setting, use, for example, the proof methods of analytic tableaux [1,26,25], of sequent calculi [26,25], or the dynamic proof method of adaptive logics [29,28].…”

“…Those procedures, which are defined in a strictly logical setting, use, for example, the proof methods of analytic tableaux [1,26,25], of sequent calculi [26,25], or the dynamic proof method of adaptive logics [29,28]. In this paper we will consider an implementation of a procedure generating abductive hypotheses for CPC.…”