Belief Graphs with Reasoning Zones: Structure, Dynamics, and Epistemic Activation
Saleh Nikooroo, Thomas Engel
TL;DR
Belief systems are typically fragmented and contradictory, yet effective reasoning requires stable local inferences. The authors introduce a graph-theoretic framework that separates external credibility from internal confidence, and compute the latter via a contractive propagation yielding a unique fixed point. They define reasoning zones as locally balanced, confidence-supported subgraphs that permit safe classical inference within globally inconsistent graphs, and construct a near-linear atlas with deduplication and governance. A local contradiction-shock mechanism preserves contraction while enabling targeted reconfiguration, producing stable, localized updates rather than global collapse. The evaluation plan on synthetic signed graphs demonstrates zone recovery, atlas stability, and resilience to shocks, establishing a practical pathway toward contradiction-tolerant, zone-aware reasoning for complex belief substrates.
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.