# Toward a Graph-Theoretic Model of Belief: Confidence, Credibility, and Structural Coherence

arXiv: https://arxiv.org/abs/2508.03465 · HTML: https://mlsanity.com/paper/2508.03465/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 31 references that are in the map.
- First posted on arXiv 5 Aug 2025.

## Builds on (most cited first, 4 of 4)

- [Tractable Uncertainty for Structure Learning](https://mlsanity.com/paper/2204.14170/) (2022)
- [Epistemic Graphs for Representing and Reasoning with Positive and Negative Influences of Arguments](https://mlsanity.com/paper/1802.07489/) (2018)
- [Tracking Network Dynamics using Probabilistic State-Space Models](https://mlsanity.com/paper/2409.08238/) (2024)
- [Temporal Network Epistemology: on Reaching Consensus in Real World Setting](https://mlsanity.com/paper/2203.05368/) (2022)

## Built on by (most cited first, 1 of 1)

- [Belief Graphs with Reasoning Zones: Structure, Dynamics, and Epistemic Activation](https://mlsanity.com/paper/2510.10042/) (2025)

## Abstract (arXiv)

Belief systems are often treated as globally consistent sets of propositions or as scalar-valued probability distributions. Such representations tend to obscure the internal structure of belief, conflate external credibility with internal coherence, and preclude the modeling of fragmented or contradictory epistemic states. This paper introduces a minimal formalism for belief systems as directed, weighted graphs. In this framework, nodes represent individual beliefs, edges encode epistemic relationships (e.g., support or contradiction), and two distinct functions assign each belief a credibility (reflecting source trust) and a confidence (derived from internal structural support). Unlike classical probabilistic models, our approach does not assume prior coherence or require belief updating. Unlike logical and argumentation-based frameworks, it supports fine-grained structural representation without committing to binary justification status or deductive closure. The model is purely static and deliberately excludes inference or revision procedures. Its aim is to provide a foundational substrate for analyzing the internal organization of belief systems, including coherence conditions, epistemic tensions, and representational limits. By distinguishing belief structure from belief strength, this formalism enables a richer classification of epistemic states than existing probabilistic, logical, or argumentation-based approaches.