# The Differential Meaning of Models: A Framework for Analyzing the Structural Consequences of Semantic Modeling Decisions

## TL;DR

This paper introduces a semiotic framework based on Peirce's theory to analyze the meaning and consequences of semantic modeling decisions across various types of models, emphasizing their interpretive and relational aspects.

## Contribution

It provides a novel theoretical framework for comparing and understanding semantic models using semiotic principles, addressing a gap in cross-model analysis.

## Key findings

- Models measure latent symbol geometries.
- Models can be understood relationally through contrast.
- Framework enables analysis of modeling decisions' interpretive effects.

## Abstract

The proliferation of methods for modeling of human meaning-making constitutes a powerful class of instruments for the analysis of complex semiotic systems. However, the field lacks a general theoretical framework for describing these modeling practices across various model types in an apples-to-apples way. In this paper, we propose such a framework grounded in the semiotic theory of C. S. Peirce. We argue that such models measure latent symbol geometries, which can be understood as hypotheses about the complex of semiotic agencies underlying a symbolic dataset. Further, we argue that in contexts where a model's value cannot be straightforwardly captured by proxy measures of performance, models can instead be understood relationally, so that the particular interpretive lens of a model becomes visible through its contrast with other models. This forms the basis of a theory of model semantics in which models, and the modeling decisions that constitute them, are themselves treated as signs. In addition to proposing the framework, we illustrate its empirical use with a few brief examples and consider foundational questions and future directions enabled by the framework.