Explanation Selection in Abductive Learning

Abductive learning (ABL) offers a promising framework that connects machine learning and logical reasoning in a mutually beneficial loop. However, this bidirectional feedback can also reinforce incorrect concept semantics, since different interpretations of intermediate concepts may explain the same observed reasoning outcomes. Static analyses characterize this ambiguity but leave open which explanation training selects and whether its labels can still be corrected. We develop a dynamical analysis of a fixed-feature binary ABL model that links the local stability of competing explanations to differences in their concept labels. We prove that Gram matrices with identical spectra can select different explanations even under the same supervision, objective, and initialization. We further identify conditions under which a selected explanation is guaranteed to persist despite subsequent changes in optimization geometry. Changing its labels would require crossing a region with lower probability of satisfying all constraints, creating an evidence barrier. Even when the correct explanation is the only realizable one, the updates can converge to a finite, strictly suboptimal state with incorrect concept labels. Experiments on visual ABL tasks support this distinction between selecting among compatible explanations and recovering a uniquely realizable correct explanation.