Belief Graphs with Reasoning Zones: Structure, Dynamics, and Epistemic Activation

• URL: http://arxiv.org/abs/2510.10042v1
• Date: Sat, 11 Oct 2025 06:02:00 GMT
• Title: Belief Graphs with Reasoning Zones: Structure, Dynamics, and Epistemic Activation
• Abstract summary: Beliefs are nodes in a directed, signed, weighted graph whose edges encode support and contradiction.<n> Confidence is obtained by a contractive propagation process that mixes a stated prior with structure-aware influence.<n>We outline an empirical protocol on synthetic signed graphs with planted zones, reporting zone recovery, stability under shocks, and runtime.
• Score: 1.7244210453129227
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Belief systems are rarely globally consistent, yet effective reasoning often persists locally. We propose a novel graph-theoretic framework that cleanly separates credibility--external, a priori trust in sources--from confidence--an internal, emergent valuation induced by network structure. Beliefs are nodes in a directed, signed, weighted graph whose edges encode support and contradiction. Confidence is obtained by a contractive propagation process that mixes a stated prior with structure-aware influence and guarantees a unique, stable solution. Within this dynamics, we define reasoning zones: high-confidence, structurally balanced subgraphs on which classical inference is safe despite global contradictions. We provide a near-linear procedure that seeds zones by confidence, tests balance using a parity-based coloring, and applies a greedy, locality-preserving repair with Jaccard de-duplication to build a compact atlas. To model belief change, we introduce shock updates that locally downscale support and elevate targeted contradictions while preserving contractivity via a simple backtracking rule. Re-propagation yields localized reconfiguration-zones may shrink, split, or collapse--without destabilizing the entire graph. We outline an empirical protocol on synthetic signed graphs with planted zones, reporting zone recovery, stability under shocks, and runtime. The result is a principled foundation for contradiction-tolerant reasoning that activates classical logic precisely where structure supports it.

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