The Importance of Logic (2) There exist proof systems for which semantic logical consequence coincides with syntactic derivation within the proof system Soundness completeness Predicate logic is unique in the sense that sound and complete proof systems do exist Not for more expressive logics(higher-order logics) trace the proof that leads to a logical consequence Logic can provide explanations for answers By tracing a proof 5 Chapter 5 A Semantic Web primer5 Chapter 5 A Semantic Web Primer The Importance of Logic (2) ⚫ There exist proof systems for which semantic logical consequence coincides with syntactic derivation within the proof system – Soundness & completeness ⚫ Predicate logic is unique in the sense that sound and complete proof systems do exist. – Not for more expressive logics (higher-order logics) ⚫ trace the proof that leads to a logical consequence. ⚫ Logic can provide explanations for answers – By tracing a proof