Chapter 5 Logic and Inference: Rules Grigoris Antoniou Frank van Harmelen 1 Chapter 5 A Semantic Web Primer
1 Chapter 5 A Semantic Web Primer Chapter 5 Logic and Inference: Rules Grigoris Antoniou Frank van Harmelen
Lecture Outline Introduction 2. Monotonic Rules: EXample 3. Monotonic Rules: Syntax Semantics 4. Nonmonotonic Rules: Syntax 5. Nonmonotonic Rules: Example 6. A dTd For Monotonic rules 7. Adtd For nonmonotonic rules Chapter 5 A Semantic Web primer
2 Chapter 5 A Semantic Web Primer Lecture Outline 1. Introduction 2. Monotonic Rules: Example 3. Monotonic Rules: Syntax & Semantics 4. Nonmonotonic Rules: Syntax 5. Nonmonotonic Rules: Example 6. A DTD For Monotonic Rules 7. A DTD For Nonmonotonic Rules
Knowledge Representation o The subjects presented so far were related to the representation of knowledge o Knowledge Representation was studied long before the emergence of Ww in Al o Logic is still the foundation of KR, particularly in the form of predicate logic first-order logic) 3 Chapter 5 A Semantic Web primer
3 Chapter 5 A Semantic Web Primer Knowledge Representation ⚫ The subjects presented so far were related to the representation of knowledge ⚫ Knowledge Representation was studied long before the emergence of WWW in AI ⚫ Logic is still the foundation of KR, particularly in the form of predicate logic (first-order logic)
The Importance of Logic e High-level language for expressing knowledge High expressive power Well-understood formal semantics Precise notion of logical consequence statements syntactically from a set of erive Proof systems that can automatically de premises Chapter 5 A Semantic Web primer
4 Chapter 5 A Semantic Web Primer The Importance of Logic ⚫ High-level language for expressing knowledge ⚫ High expressive power ⚫ Well-understood formal semantics ⚫ Precise notion of logical consequence ⚫ Proof systems that can automatically derive statements syntactically from a set of premises
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 primer
5 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