Inferences and Modal Vocabulary

TL;DR

This paper explores how modal vocabulary enhances logical inference expressivity, particularly in non-monotonic reasoning like abduction, and proposes a modal interpretation of implications for conceptual relations.

Contribution

It introduces a modal interpretation of implications to better express and assess non-monotonic inferences such as abduction.

Findings

Modal vocabulary enriches logical expressivity.

Material inferences based on modal logic can improve inference assessment.

Limits in machine learning labeling are addressed through modal interpretation.

Abstract

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.