1 / 46

e ce 627 intelligent web: ontology and beyond

e ce 627 intelligent web: ontology and beyond. lecture 16: description logic - basic formalisms, TBox, ABox. description logic basic formalism. DL provides facilities to set up knowledge bases, to reason about their content, and to manipulate them. description logic basic formalism.

jenn
Download Presentation

e ce 627 intelligent web: ontology and beyond

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. ece 627intelligent web: ontology and beyond lecture 16: description logic - basic formalisms, TBox, ABox

  2. description logicbasic formalism DL provides facilities to set up knowledge bases, to reason about their content, and to manipulate them

  3. description logicbasic formalism TBox Description Language Reasoning ABox application program rules

  4. description logicbasic formalism vocabulary consists of concepts, that denote sets of individuals, and roles, that denote binary relationships between individuals in addition, DL systems allow their users to build complex descriptions of concepts and roles (Tbox can be used to assign names to them)

  5. description logicbasic formalism statements in the TBox and ABox can be identified with formulae in first-order logic or, in some cases, a slight extension of it

  6. description logicbasic formalism typical reasoning tasks (the previous lecture): determining if a description is satisfiable or whether one description is more general than the other – subsumption

  7. description logicbasic formalism important problems for ABox (the previous lecture): to find out if its set of assertions is consistent (has a model, and if individuals are instances of concept descriptions)

  8. description logicbasic formalism satisfiability checks descriptions and consistency checks assertions – all to determine whether a knowledge base is meaningful at all

  9. description logicbasic formalism rules – an extension of the logical core formalism – allow for adding assertions to a knowledge base

  10. description logicdescription language atomic concepts – A, B atomic roles – R concept descriptions – C, D description languages are distinguished by the constructors they provide – we look at the family of AL-languages (=attributive language)

  11. description logicdescription language – AL (atomic concept) (universal concept) (bottom concept) (atomic negation) (intersection) (value restriction) (limited exist. quant.)

  12. description logicdescription language – AL examples: atomic concepts – Person and Female Person Female Person Female Person hasChild. Person hasChild.Female

  13. description logicsemantics of AL–language to define semantics of AL-concepts – we consider interpretations I that consist of a non-empty set and an interpretation function for every atomic concept A: and a binary relation:

  14. description logicsemantics of AL–language

  15. description logicsemantics of AL–language examples:

  16. description logicfamily of AL–languages to obtain more expressive languages – we add further constructor to AL: union (U): full existential quantifier (E):

  17. description logicfamily of AL–languages number restrictions (N) negation (C) AL{U}{E}{N}{C} and others …

  18. description logicAL–language and predicate logic the semantics of concepts identifiers are fragments of first-order predicate logic – atomic concepts and roles are unary and binary predicates any concept C and be translated into a predicate logic formula FC(x), with one free variable x such that elements of satisfying FC(x) is exactly CI

  19. description logicAL–language and predicate logic examples: variable free syntax of DLs is much more concise

  20. description logicterminology forming complex descriptions of concepts: terminological axioms – make statements about how concepts or roles are related to each other definitions – specific axioms

  21. description logicterminology - axioms in the most general case inclusion: C D (R S) equality: C D (R S) C, D are concepts, R, S are roles

  22. description logicterminology - axioms an interpretation I satisfies an inclusion C D if , and it satisfies an equality C D if

  23. description logicterminology - axioms if T is a set of axioms then I satisfies T iffI satisfies each element of T, if I satisfies a set of axiom then we say that it is a model of this set of axioms

  24. description logicdefinitions an equality whose left-hand side is an atomic concept is a definition definitions are use to introduce symbolic names for complex descriptions Mother Woman hasChild.Person

  25. description logicTBox … a finite set of definitions T is called a terminology or TBox

  26. description logicTBox …

  27. description logicTBox … name symbols – symbols that appear on the left-hand side of axioms (also called defined concepts) base symbols – symbols that appear only on the right-hand side of axioms (also called primitive concepts)

  28. description logicTBox … if we know what the base symbols stand for – then the meaning of of the name symbols is completely determined* *additionally terminology has to be definitorial

  29. description logicTBox … an important (and related to the issue of being definitorial) question – are definitions of a terminology cyclic or not? Human’ Animal hasParent.Human’ (… is cyclic iff there exists an atomic concept that uses itself)

  30. description logicTBox …

  31. description logicTBox … there are terminologies with cycles that are definitorial …

  32. description logicTBox …with inclusion axioms for some concepts we will not be able to define them completely – we will state necessary conditions for concept membership using an inclusion Woman Person

  33. description logicTBox …with inclusion axioms if we do this – the terminology loses its definitorial impact, even if it is acyclic, then …

  34. description logicABox … the second component of a knowledge base a world description or ABox

  35. description logicABox … in ABox we describe a specific state of affairs of a given application domain we introduce individuals, by giving them names, and we asserts properties of these individuals

  36. description logicABox … we denote names as a, b, c using concepts C and roles R, we can make assertions of the following two kinds in the ABox C(a) R(b,c)

  37. description logicABox … C(a) – this concept assertion used to stat that a belongs to (the interpretation of C) R(b,c) – this role assertion states that c is a filler of the role R for b

  38. description logicABox … Father(PETER) – means that PETER is a father hasChild(MARY,PAUL) – means that Paul is a child of Mary

  39. description logicABox … examples: MotherWithoutDaughter(MARY) hasChild(MARY, PETER) hasChild(MARY, PAUL) Father(PETER) hasChild(PETER, HARRY)

  40. description logicABox … the semantic of ABox is “open-world semantics” – we cannot assume that the knowledge in the knowledge base is complete (on the contrary to “closed-world” semantics of classical databases)

  41. description logicABox … the semantic is given to ABoxs by extending interpretations to individual names

  42. description logicABox … now, an interpretation I not only maps atomic concepts and roles to sets and relations, but in addition it maps each individual name a to and element we assume that distinct individual names denote distinct objects

  43. description logicABox … the interpretation I satisfies the concept assertion C(a) if , and it satisfies the role assertion R(a, b) if

  44. description logicABox … an interpretation satisfies the ABox A if it satisfies each assertion in A in this case we say that I is a model of the assertion or the ABox the concept assertion

  45. description logicABox … I satisfies an ABox A with respect to a TBox T if in addition to being a model of A, it is a model of T

  46. description logicinference … and more …. … to be continued (sometime)

More Related