1 / 31

Rules and Ontologies in F-logic

Rules and Ontologies in F-logic. Michael Kifer State University of New York at Stony Brook. Outline. Introduction Overview of F-logic (with examples using the FLORA-2 system ) F-logic / FLORA-2 and ontologies. What is F-Logic?. An object-oriented first-order logic

addo
Download Presentation

Rules and Ontologies in F-logic

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Rules and Ontologies in F-logic Michael Kifer State University of New York at Stony Brook Reasoning Web Summer School, Msida, Malta

  2. Outline • Introduction • Overview of F-logic (with examples using the FLORA-2 system) • F-logic/ FLORA-2 and ontologies Reasoning Web Summer School, Msida, Malta

  3. What is F-Logic? • An object-oriented first-order logic • Extends predicate logic with • Objects with complex internal structure • Class hierarchies and inheritance • Typing • Encapsulation • A basis for object-oriented logic programming and knowledge representation • Background: • Basic theory: [Kifer & Lausen SIGMOD-89], [Kifer,Lausen,Wu JACM-95] • Path expression syntax: [Frohn, Lausen, Uphoff VLDB-84] • Semantics for non-monotonic inheritance: [Yang & Kifer, ODBASE 2002] • Meta-programming + other extensions: [Yang & Kifer, Journal on Data Semantics 2003] O-O programming Relational programming = F-logic Predicate calculus Reasoning Web Summer School, Msida, Malta

  4. F-logic and Logic Programming • The flavors of F-logic: • First-order flavor • Logic programming flavor F-logic programming Logic programming FO F-logic Predicate logic Reasoning Web Summer School, Msida, Malta

  5. Relationship to Description Logic FO F-logic Description F-Logic Description Logic OWL Predicate logic - A description logic subset exists within the first-order variant of F-logic [Balaban 1995, The F-logic Approach for Description Languages] - But most known uses of F-logic are in the rule-based (F-logic programming) domain Reasoning Web Summer School, Msida, Malta

  6. Relationship to Description Logic (cont’d) • F-logic (rule-based flavor) • Computationally complete • Object-oriented • Classes as object, reification of statements • Can query data and schema in the same language • Has useful tractable subsets (eg, function-free rules) • Based on non-monotonic (non-classical) logic • Description logic • Has its own decidable subsets (but practically questionable, since expressive versions are exponential) • Can reason by cases • Can represent existential information • Based on monotonic, classical logic Reasoning Web Summer School, Msida, Malta

  7. Applications of F-logic • Semantic Web: • Ontology management • Semantic Web Services • Information integration • Software engineering • Intelligent agents • Anything that requires manipulation of complex structured or (especially) semi-structured data Reasoning Web Summer School, Msida, Malta

  8. What is FLORA-2 ? • F-LOgic tRAnslator (to XSB) – a popular implementation of F-logic (and more) • Realizes the vision of logic-based KR with frames, meta-programming, and side-effects. Based on • F-logic • HiLog • Transaction Logic • Practical & usable KR and programming environment • Declarative • Object-oriented • Rule-based • Open source: http://flora.sourceforge.net/ Reasoning Web Summer School, Msida, Malta

  9. Other Major F-logic Based Languages • Ontobroker – commercial system from Ontoprise.de • WSMO (Web Service Modeling Ontology) – a large EU project that developed an F-logic based language for Semantic Web Services, WSML-Rule • SWSI (Semantic Web Services Initiative) – an international group that proposed an F-logic based language SWSL-Rules (also for Semantic Web Services) • FORUM – a user group whose aim is to standardize/web-ize the various flavors of F-logic (FLORA-2, Ontobroker, WSML-Rule, SWSL-Rules) Reasoning Web Summer School, Msida, Malta

  10. F-logic: Simple Examples Object Id Single-valued attribute Object description: john[name -> ‘John Doe’, phones ->> {6313214567, 6313214566}, children ->> {bob, mary}] mary[name->’Mary Doe’, phones ->> {2121234567, 2121237645}, children ->> {anne, alice}] Structure can be nested: sally[spouse->john[address-> ‘123 Main St.’] ] Set-valued attribute Reasoning Web Summer School, Msida, Malta

  11. Examples (cont’d) ISA hierarchy: john : person // class membership mary : person alice : student student:: person // subclass relationship student: entityType person : entityType Class & instance in different contexts Reasoning Web Summer School, Msida, Malta

  12. Examples (cont’d) • Methods: like attributes, but take arguments • P[ageAsOf(Year) -> Age] :- • P:person, P[born-> B] and Age is Year–B. • Attributes can be viewed as methods with no arguments Queries: ?–john[ageAsOf(Y) -> 30, children->> C] and C[born-> B] and B>Y. John’s children who were born when he was 30+ years old. Reasoning Web Summer School, Msida, Malta

  13. Examples (contd.) Browsing IsA hierarchy: ?-john : X. // all superclasses of the object john ?- student ::Y. // all superclasses of class student Virtual class: X : redcar :-X:car and X[color -> red]. Meta-query about schema: O[attributesOf(Class) ->>A] :- O[A->V orA->>V] and V:Class. Rule that defines a virtual class of red cars Rule that defines a method that returns attributes whose range is class Class Reasoning Web Summer School, Msida, Malta

  14. Type Signatures • Type info is specified using statements like this (called signatures): person[name *=> string, spouse *=> person, children *=>> person]. • *=> means inheritable instance attribute (like instance variable in Java) • Signatures are formulas in F-logic (just like the data-level statement john[name ->’John Doe’] is a formula) • The notion of well-typedness relates signatures to data Reasoning Web Summer School, Msida, Malta

  15. Semantics • The FO F-logic semantics & proof theory are general, as in classical logic; sound & complete, and are not limited to rules • But FLORA-2 is a programming language based on F-logic. Hence it uses nonmonotonic, non-classical semantics. So … :-…, notP, … means “true if cannot proveP”– so called “negation as failure.” The exact semantics for negation used in FLORA-2 is derived from the Well-Founded Semantics [Van Gelder et al., JACM 1991, http://citeseer.nj.nec.com/gelder91wellfounded.html] Reasoning Web Summer School, Msida, Malta

  16. Semantics (cont’d) • The Well-Founded semantics is 3-valued: p:-notq. r:- notr. pis true, qfalse, but r is undefined • And non-monotonic: P |= Q does not imply PP’ |= Q For instance: p:-notq implies ptrue. But q and p:-notq implies pfalse. • So, truth values don’t grow monotonically. In contrast, classical logic is both 2-valued and monotonic Reasoning Web Summer School, Msida, Malta

  17. Inheritance in F-logic • Inheritance of structure vs. inheritance of behavior • Structuralinheritance = inheritance of type signatures of a method (will not discuss here) • Behavioralinheritance = inheritance of the definition of a method • Subtle problems arise when inference by inheritance interacts with inference by rules (illustrated next) Reasoning Web Summer School, Msida, Malta

  18. Behavioral Inheritance: Non-monotonicity Elephant[color *->grey] Means default value royalElephant[color *->white] fred clyde Overriding Inherited: fred[color ->grey] clyde[color ->grey] white ? Reasoning Web Summer School, Msida, Malta

  19. inherited derived [ m*-> w ] defeated?? [ m-> v ] Behavioral Inheritance: Problem with Rules • Inheritance is hard to even define properly in the presence of rules. a [ m*-> v ] c[m*-> w]:- b[m-> v] c b Reasoning Web Summer School, Msida, Malta

  20. Behavioural Inheritance: Solutions • Hard to define semantics for multiple inheritance + overriding + rules • Several semantics might appear to look “reasonable” • The original semantics in [Kifer,Lausen,Wu: JACM-95] was one of the problematic “reasonable” semantics • A number of other problematic semantics of various degrees of “reasonableness” were proposed over time • Problem solved in [Yang&Kifer: ODBASE 2002, 2003] • Based on semantic postulates • An extension of Van Gelder’s Well-Founded Semantics for negation Reasoning Web Summer School, Msida, Malta

  21. HiLog • Allows certain forms of logically clean, yet tractable, meta-programming • Syntactically appears to be higher-order, but semantically is first-order and tractable • [Chen,Kifer,Warren, HiLog: A Foundation for Higher-Order Logic Programming, J. of Logic Programming, 1993] Reasoning Web Summer School, Msida, Malta

  22. Examples of HiLog Variables over predicates and function symbols: p(X,Y):-X(a,Z), Y(Z(b)). Variables over atomic formulas (reification): p(q(a)). r(X) :- p(X) and X. A use of HiLoginFLORA-2 (e.g.,querying of schema): O[unaryMethods(Class)->>M] :- O[M(Arg) -> V or M(Arg) ->> V] and V:Class. Meta-variable: ranges over method names Reasoning Web Summer School, Msida, Malta

  23. Reification (AnotherApplication of HiLog to F-logic) • Reification: making an object out of a formula: • john[believes->> ${mary[likes ->> bob]} ] • Introduced in [Yang & Kifer, ODBASE 2002] • Rules can be reified, too! Object made out of the formula mary[likes->> bob] Reasoning Web Summer School, Msida, Malta

  24. HiLog in FLORA-2 • Allows high degree of meta-programming purely in logic • Variables can be bound to predicate and function symbols and thus queried • Formulas can be represented as terms and manipulated in flexible ways • Can mix frame syntax (F-logic) and predicate syntax (HiLog) in the same query/program: a[b -> c, g(X,e) ->> d] and p(f(X),a). Reasoning Web Summer School, Msida, Malta

  25. Ontologies • A typical ontology has three components: • A taxonomy (class hierarchy) No-brainer in F-logic: Use : and :: • Concept definitions Use type signatures. For instance person[name *=> string, children *=> person]. • Definitions of instances This is just specification of data that populates ontologies. Specified using rules and facts. For instance: john:student. john[name -> ’John Doe’, address -> ’1 Main St.’]. X:grandfather :- X:person[children -> C[children -> GC]]. Reasoning Web Summer School, Msida, Malta

  26. Example of Ontology Domain: Semantic Web Services Scenario: Finding travel services according to various criteria (the Web service discovery problem) Reasoning Web Summer School, Msida, Malta

  27. Taxonomy • germany, europe, etc. – classes of cities • newyork, vienna, etc. – cities germany :: europe. austria :: europe. usa : region. europe : region. newyork : usa. vienna : austria. bonn : germany. frankfurt : germany. R:region :- R1:region and R::R1. // every subclass of a region is a region L:location :- L:R and R:region. // every member of a region is also a location Reasoning Web Summer School, Msida, Malta

  28. User Goals and Related Concepts • Concepts: goal[requestId *=> request, request *=> travelSearchQuery, result *=>> service]. search(From,To,Date) : travelSearchQuery :- From : (region or location) and To : (region or location). • Instance: g123[ requestId -> 12345, request -> search (bonn,vienna,’7/7/2005’), result ->> serv123 ]. Reasoning Web Summer School, Msida, Malta

  29. Service Concept & Instance • Concept: service[name *=> string, effect(travelSearchQuery) *=> formula, mediators *=>> mediator ]. • Instance: serv123[ name -> ’Fly High Travel’, effects(Input) -> ${ (itinerary(Req)[from ->From, to ->To, date ->Date] :- Input = search(From:germany, To:austria, Date)) }, usedMediators -> med1 ]. Reasoning Web Summer School, Msida, Malta

  30. Having Fun with F-logic • Working with F-logic is fun! FLORA-2 is a full-fledged knowledge representation/logic programming system. Has a range of other interesting features: • Module system with encapsulation • Control flow constructs • Aggregates • Non-logical constructs for procedural diehards • Debugging support • Integration with databases, Web, Java, etc. Reasoning Web Summer School, Msida, Malta

  31. Conclusion • F-logic is an object-oriented extension of predicate logic, which is particularly suitable for representing ontologies on the Semantic Web • Based on the proven paradigm of rule-based logic languages • Has a number of popular implementations, including commercial ones • A basis for two W3C proposals in the semantic Web services domain • Also proposed to W3C as the basis rule-based languages for the Semantic Web • WRL • SWSL-Rules • In fact, the N3 language is also nothing but a slightly altered syntax of F-logic, but with no semantics Reasoning Web Summer School, Msida, Malta

More Related