Chapter 5 A Semantic Web Primer 1 Chapter 5 Logic and Inference: Rules Grigoris Antoniou Frank van Harmelen
Chapter 5 A Semantic Web Primer 2 Lecture Outline 1. Introduction 2. Monotonic Rules: Example 3. Monotonic Rules: Syntax & Semantics 4. Description Logic Programs (DLP) 5. Semantic Web Rules Language (SWRL) 6. Nonmonotonic Rules: Syntax 7. Nonmonotonic Rules: Example 8. Rule Markup Language (RuleML)
Chapter 5 A Semantic Web Primer 3 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)
Chapter 5 A Semantic Web Primer 4 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
Chapter 5 A Semantic Web Primer 5 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
Chapter 5 A Semantic Web Primer 6 Specializations of Predicate Logic: RDF and OWL RDF/S and OWL (Lite and DL) are specializations of predicate logic – correspond roughly to a description logic They define reasonable subsets of logic Trade-off between the expressive power and the computational complexity: – The more expressive the language, the less efficient the corresponding proof systems
Chapter 5 A Semantic Web Primer 7 Specializations of Predicate Logic: Horn Logic A rule has the form: A1, . . ., An B – Ai and B are atomic formulas There are 2 ways of reading such a rule: – Deductive rules : If A1,..., An are known to be true, then B is also true – Reactive rules : If the conditions A1,..., An are true, then carry out the action B
Chapter 5 A Semantic Web Primer 8 Description Logics vs. Horn Logic Neither of them is a subset of the other It is impossible to assert that a person X who is brother of Y is uncle of Z (where Z is child of Y) in OWL – This can be done easily using rules: brother(X,Y), childOf(Z,Y) uncle(X,Z) Rules cannot assert the information that a person is either a man or a woman – This information is easily expressed in OWL using disjoint union
Chapter 5 A Semantic Web Primer 9 Monotonic vs. Non-monotonic Rules Example : An online vendor wants to give a special discount if it is a customer’s birthday Solution 1 R1: If birthday, then special discount R2: If not birthday, then not special discount But what happens if a customer refuses to provide his birthday due to privacy concerns?
Chapter 5 A Semantic Web Primer 10
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- Fall '16
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- Semantics, Logic Programming, Semantic Web Primer