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 o They define reasonable subsets of logic o Trade-off between the expressive power and the computational complexity The more expressive the language, the less efficient the corresponding proof systems 6 Chapter 5 A Semantic Web primer
6 Chapter 5 A Semantic Web Primer 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
Specializations of Predicate Logic Horn Logic ● a rule has the form:A1,,,,An→>B Ai and b are atomic formulas o 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 Al. An are true, then carry out the action B 7 Chapter 5 A Semantic Web primer
7 Chapter 5 A Semantic Web Primer 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
Description Logics VS Horn Logic e Neither of them is a subset of the other e It is impossible to assert that persons who study and live in the same city are home students"in OWL This can be done easily using rules studies(X, Y), lives(X, 2), loc(Y,U), loc(z,U)) home Student(X 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 8 Chapter 5 A Semantic Web primer
8 Chapter 5 A Semantic Web Primer Description Logics vs. Horn Logic ⚫ Neither of them is a subset of the other ⚫ It is impossible to assert that persons who study and live in the same city are “home students” in OWL – This can be done easily using rules: studies(X,Y), lives(X,Z), loc(Y,U), loc(Z,U) → homeStudent(X) ⚫ 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
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 But what happens if a customer refuses t R2: If not birthday, then not special discot provide his birthday due to privacy concerns? 9 Chapter 5 A Semantic Web primer
9 Chapter 5 A Semantic Web Primer 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?
Monotonic vs, non -monotonic Rules (2) Solution 2 R1: If birthday then special discount R2: If birthday is not known, then not special discount Solves the problem but The premise of rule R2 is not within the expressive power of predicate logic We need a new kind of rule system 10 Chapter 5 A Semantic Web primer
10 Chapter 5 A Semantic Web Primer Monotonic vs. Non-monotonic Rules (2) Solution 2 R1: If birthday, then special discount R2’: If birthday is not known, then not special discount ⚫ Solves the problem but: – The premise of rule R2' is not within the expressive power of predicate logic – We need a new kind of rule system