Evaluating multi-turn dialogue systems remains challenging because response quality depends not only on the current prompt, but also on previously established entities, claims, and conversational commitments. Existing automatic evaluators, including LLM-as-a-judge frameworks and embedding-based metrics, largely rely on flat or turn-isolated representations, making them less effective at detecting long-range issues such as contradiction, topic drift, and entity inconsistency. To address this, we propose SKG-Eval, a quasi-deterministic and interpretable framework that models dialogue as an evolving Semantic Knowledge Graph (SKG) of entities, relations, and commitments across turns. The framework incrementally updates the graph through structured triple extraction and computes three complementary signals: (i) local relevance, measuring alignment with the current prompt and optional reference; (ii) historical consistency, evaluating how newly introduced information connects to prior conversational context using graph-based and embedding-driven signals; and (iii) logical coherence, assessed by a geometric contradiction engine that detects cross-turn conflicts without relying on NLI models or LLM judges. These signals are adaptively fused and aggregated into a length-invariant session score via recency-weighted trend analysis. Across multiple benchmarks, SKG-Eval achieves higher correlation with human judgments and substantially improves detection of long-range inconsistencies in extended conversations. In addition, the framework produces explicit contradiction certificates and deterministic scores for fixed inputs, enabling reproducible and auditable evaluation. Overall, our results suggest that structured externalized state tracking through semantic knowledge graphs provides a scalable alternative to implicit reasoning in LLM-based dialogue evaluators.