Inferences and Modal Vocabulary
This work tackles foundational issues in logic and inference theory, with potential implications for improving machine learning methods, though it appears incremental in its approach.
The paper addresses the problem of assessing the quality of non-monotonic inferences, such as abduction, by proposing a modal interpretation of implications to express conceptual relations, which also reveals limitations in machine learning labeling applications.
Deduction is the one of the major forms of inferences and commonly used in formal logic. This kind of inference has the feature of monotonicity, which can be problematic. There are different types of inferences that are not monotonic, e.g. abductive inferences. The debate between advocates and critics of abduction as a useful instrument can be reconstructed along the issue, how an abductive inference warrants to pick out one hypothesis as the best one. But how can the goodness of an inference be assessed? Material inferences express good inferences based on the principle of material incompatibility. Material inferences are based on modal vocabulary, which enriches the logical expressivity of the inferential relations. This leads also to certain limits in the application of labeling in machine learning. I propose a modal interpretation of implications to express conceptual relations.