Logic, Language, and Calculus

TL;DR

This paper explores the distinction between object-language and metalanguage in logic and its implications for natural language understanding, emphasizing the importance of normative assessment of inferences beyond formal logic.

Contribution

It introduces a logical analysis framework that evaluates the normative quality of inferences, extending beyond traditional formal metalanguage approaches.

Findings

Inferential relations in metalanguages cannot fully capture natural language conceptual relations.

A new logical analysis assesses the normative dimension of inferences.

Implications for improving natural language understanding and inference evaluation.

Abstract

The difference between object-language and metalanguage is crucial for logical analysis, but has yet not been examined for the field of computer science. In this paper the difference is examined with regard to inferential relations. It is argued that inferential relations in a metalanguage (like a calculus for propositional logic) cannot represent conceptual relations of natural language. Inferential relations govern our concept use and understanding. Several approaches in the field of Natural Language Understanding (NLU) and Natural Language Inference (NLI) take this insight in account, but do not consider, how an inference can be assessed as a good inference. I present a logical analysis that can assesss the normative dimension of inferences, which is a crucial part of logical understanding and goes beyond formal understanding of metalanguages.