Rules and Ontologies in Flogic

1
Rules and Ontologies in F-logic

• Michael Kifer
• State University of New York
• at Stony Brook

2
Outline

• Introduction
• Overview of F-logic (with examples using the
  FLORA-2 system)
• F-logic/ FLORA-2 and ontologies

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
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
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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
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Relationship to Description Logic (contd)

• 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

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

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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/

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)

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F-logic Simple Examples
Single-valued attribute
Object Id
Object description johnname -gt John
Doe, phones -gtgt 6313214567, 6313214566,
children -gtgt bob, mary
maryname-gtMary Doe, phones -gtgt 2121234567,
2121237645, children -gtgt anne,
alice Structure can be nested
sallyspouse -gt johnaddress -gt 123 Main St.
Set-valued attribute
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Examples (contd)

• ISA hierarchy
• john person // class
  membership
• mary person
• alice student
• student person // subclass
  relationship
• student entityType
• person entityType

Class instance in different contexts
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Examples (contd)

• Methods like attributes, but take arguments
• PageAsOf(Year) -gt Age -
• Pperson, Pborn -gt B and
  Age is YearB.
• Attributes can be viewed as methods with no
  arguments

Queries ? johnageAsOf(Y) -gt 30,
children -gtgt C and Cborn -gt B and
BgtY. Johns children who were born when he was
30 years old.
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Examples (contd.)
Browsing IsA hierarchy ?- john X.
// all superclasses of the object john ?-
student Y. // all superclasses of class
student Virtual class X redcar -
Xcar and Xcolor -gt red. Meta-query about
schema OattributesOf(Class) -gtgtA -
OA -gtV or A -gtgtV and VClass.
Rule that defines a virtual class of red cars
Rule that defines a method that returns
attributes whose range is class Class
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Type Signatures

• Type info is specified using statements like this
  (called signatures)
• personname gt string,
• spouse gt person,
• children gtgt person.
• gt means inheritable instance attribute (like
  instance variable in Java)
• Signatures are formulas in F-logic (just like the
  data-level statement johnname -gt John Doe
  is a formula)
• The notion of well-typedness relates signatures
  to data

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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
• - , not P,
• means true if cannot prove P 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.htm
  l

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Semantics (contd)

• The Well-Founded semantics is 3-valued
• p - not q.
• r - not r.
• p is true, q false, but r is undefined
• And non-monotonic
• P Q does not imply P?P Q
• For instance
• p - not q implies p true.
• But
• q and p - not q implies p false.
  
• So, truth values dont grow monotonically. In
  contrast, classical logic is both 2-valued and
  monotonic

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Inheritance in F-logic

• Inheritance of structure vs. inheritance of
  behavior
• Structural inheritance inheritance of type
  signatures of a method (will not discuss here)
• Behavioral inheritance inheritance of the
  definition of a method
• Subtle problems arise when inference by
  inheritance interacts with inference by rules
  (illustrated next)

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Behavioral Inheritance Non-monotonicity
Elephantcolor -gt grey
Means default value
royalElephantcolor -gt white
fred
clyde
Overriding
Inherited fredcolor -gt grey
clydecolor -gt grey
white
?
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Behavioral Inheritance Problem with Rules

• Inheritance is hard to even define properly in
  the presence of rules.

a
m -gt v
cm -gt w - bm -gt v
c
b
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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 YangKifer ODBASE 2002,
  2003
• Based on semantic postulates
• An extension of Van Gelders Well-Founded
  Semantics for negation

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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

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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 HiLog in FLORA-2
(e.g., querying of schema)
OunaryMethods(Class) -gtgt M -
OM(Arg) -gt V or M(Arg) -gtgt V and VClass.
Meta-variable ranges over method names
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Reification (Another Application of HiLog to
F-logic)

• Reification making an object out of a formula
• johnbelieves -gtgt marylikes -gtgt bob
  
• Introduced in Yang Kifer, ODBASE 2002
• Rules can be reified, too!

Object made out of the formula marylikes -gtgt bob
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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
• ab -gt c, g(X,e) -gtgt d and p(f(X),a).

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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
• personname gt string, children gt person.
• Definitions of instances
• This is just specification of data that populates
  ontologies.
• Specified using rules and facts. For instance
• johnstudent.
• johnname -gt John Doe, address -gt 1 Main
  St..
• Xgrandfather - Xpersonchildren -gt
  Cchildren -gt GC.

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Example of Ontology
Domain Semantic Web Services Scenario
Finding travel services according to various
criteria (the Web service discovery
problem)
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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.
• Rregion - R1region and RR1. // every
  subclass of a region is a region
• Llocation - LR and Rregion. // every
  member of a region is also a location

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User Goals and Related Concepts

• Concepts
• goalrequestId gt request,
• request gt
  travelSearchQuery,
• result gtgt service.
• search(From,To,Date)
  travelSearchQuery -
• From
  (region or location) and To (region or
  location).
• Instance
• g123
• requestId -gt 12345,
• request -gt search
  (bonn,vienna,7/7/2005),
• result -gtgt serv123
• .

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Service Concept Instance

• Concept
• servicename
  gt string,
• effect(travelSearchQuery) gt
  formula,
• mediators
  gtgt mediator
• .
• Instance
• serv123 name -gt Fly High
  Travel,
• effects(Input) -gt
• (itinerary(Req)from -gtFrom, to
  -gtTo, date -gtDate -
• 
  Input search(Fromgermany, Toaustria,
  Date))
• ,
• usedMediators -gt med1
• .

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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.

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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