1 / 18

DL Overview

Ming Fang 6/12/2009. DL Overview. Outlines. Classical logics Introduction to DL Syntax of DL Semantics of DL KR in DL Reasoning in DL Applications. Classical Logics. Logics are formal languages for representing information such that conclusions can be drawn. Important Questions.

laurie
Download Presentation

DL Overview

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. Ming Fang 6/12/2009 DL Overview

  2. Outlines • Classical logics • Introduction to DL • Syntax of DL • Semantics of DL • KR in DL • Reasoning in DL • Applications

  3. Classical Logics • Logics are formal languages for representing information such that conclusions can be drawn.

  4. Important Questions • Expressive Power of representation language  able to represent the problem • Soundness of entailment procedure no false conclusions are drawn • Completeness of entailment procedure all correct conclusions are drawn • Decidability of entailment problem  there exists a (terminating) algorithm to compute entailment • Complexity  resources needed for computing the solution

  5. Two Familiar Logics • Propositional Logic atomic formula + connectives  propositional formula • First-order Logic atomic formula + connectives + existential and universal quantifiers  well formed formulas

  6. An Example

  7. Introduction to DL • To form a middle ground solution, DL includes some more expressive operations than propositional logic and has decidable or more efficient decision problems than first-order predicate logic • A fragment of FOL • Inherits open-world assumption and non-unique name assumption

  8. Introduction to DL cont’ • Originated from frames and semantic networks • Provides formal logical extension • Structured logic

  9. Syntax of DL • Unary predicates: denote concepts e.g. student(Ming) • Binary predicates: denote roles e.g. major(Ming, CS) • FOL constructors: intersection, union, negation, universal quantifier, etc. • Other constructors: inverse, transitivity, etc. • Any (basic) Description Logic is a subset of L3, i.e. the function-free FOL using only at most three variable names

  10. Syntax of DL cont’

  11. Semantics of DL • An atomic concept is interpreted as a set of individuals that is a subset of the domain. • An atomic role is interpreted as a set of pairs of individuals from the domain, i.e., a binary relation over the domain. In this case, if an individual x is related to y via a role R, then y is called an R-successor of x. • The top concept is interpreted as the whole domain. • The bottom concept is interpreted as the empty set. • The interpretation of ¬C is the set of all individuals in the domain which does not belong to the interpretation of C. • Intersection of two concepts C and D is interpreted, as set-intersection i.e., the set of all individuals in the domain that belongs to both the interpretation of C and the interpretation of D. • The value restriction ∀R.C is interpreted as the set of all individuals in the domain whose R-successors (if any) all belong to the interpretation of C. • The limited existential restriction is interpreted as the set of all individuals in the domain that have at least one R-successor.

  12. KR in DL • A DL KB typically contains two components: TBox and ABox • TBox (terminological box): contains intensional knowledge in the form of a terminology, e.g. • Normally doesn’t change • Assumed to be acyclic

  13. KR in DL cont’ • ABox (assertional box): contains extensional knowledge that is specific to individuals, e.g. • Subject to occasional or even constant change • The TBox/ABox distinction is not significant

  14. Reasoning in DL • TBox

  15. Reasoning in DL cont’

  16. Reasoning in DL cont’ • ABox

  17. Applications • OWL cornerstone of the semantic web for its use in the design of ontologies OWL DL and Lite are basted on DL OWL DLP: intersection of DL and Horn Logic Programs. It’s the largest fragment on which the choice for CWA and UNA doesn’t matter

  18. Applications cont’ • Configuration • Conceptual Modeling • Query Optimization and View Maintenance • Natural Language Semantics • I3 (Intelligent Integration of Information) • Information Access and Intelligent Interfaces • Terminologies and Ontologies • Software Management • Planning

More Related