Towards Abductive Reasoning in First-order Logic

Abduction viaC-tableaux and δ-resolution

“…It has been used for abduction in (Nepomuceno, 2002;Reyes-Cabello et al, 2006), as an extension of the abductive approach originally presented in (Cialdea Mayer et al, 1993;Aliseda, 1997). In this paper, we define C-tableaux with respect to the set C of constants which defines a class of C-structures, rather than the cardinality of the searched models.…”

“…The added novelty is that we combine two calculi used previously, but separately, to solve abductive problems. These calculi are based on semantic tableaux and resolution (Reyes-Cabello et al, 2006;Soler-Toscano et al, 2006b). Our approach is specially useful and hopefully interesting for abductive applications in contexts with finite domains.…”

“…This calculus is based on a proposed modification of our N -tableaux (introduced by us in (Reyes-Cabello et al, 2006)), which in turn are a modification of the well-known classical semantic tableaux, this time restricted to a set of constants, what characterizes a class of C-structures. A set of lemmas and a corollary give place to our Fundamental Theorem of C-tableaux, which states that a δ-clausal form of a C-tableau T (Θ) C , denoted by Cδ(T (Θ) C ), and Θ are C-equivalent.…”

An epistemic and dynamic approach to abductive reasoning: selecting the best explanation

“…Of particular interest to us are approaches based on logical criteria. But, though there are several proposals (most of them based on the idea of minimality [1,32,42]), it is typically argued that purely logical approaches are limited because they are unable to reason under uncertainty or to estimate the likelihood of alternative explanations. There are also approaches based on preferential orders over formulas or theories, but they have been also criticized because such orders are treated as external devices working on top of the logical or deductive part of the explanatory mechanism, and therefore seem to fall outside a logical framework.…”

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

“…Note that semantic tableau methods have been extended to modal logic[6,15], first-order logic[33,38], DL[28], etc., and in the same way we would be able to generate a cutting from them.…”