Towards automated first-order abduction: the cut-based approach

M. Finger
2010 Logic Journal of the IGPL  
Traditional abduction imposes as a precondition the restriction that the background information may not derive the goal data. In first-order logic such precondition is, in general, undecidable. To avoid such problem, we present a first-order cutbased abduction method, which has KE-tableaux as its underlying inference system. This inference system allows for the automation of non-analytic proofs in a tableau setting, which permits a generalization of traditional abduction that avoids the
more » ... ble precondition problem. After demonstrating the correctness of the method, we show how this method can be dynamically iterated in a process that leads to the construction of non-analytic first-order proofs and, in some terminating cases, to refutations as well. We use letters p, q, r, s for atomic propositional or predicate symbols; an enumerable set of variables V ={x 1 ,x 2 ,...}; logical constants ⊥ and ; connectives ∧ (conjunction), ∨ (disjunction), ¬ (negation) and → (implication); and quantifiers ∃ and ∀.
doi:10.1093/jigpal/jzq052 fatcat:4hpw27rrlvb6noqonwqcg7y4pq