owl - dl. dl system a knowledge base (kb) comprises two components, the tbox and the abox the tbox...

OWL - DL

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OWL - DL

DL System

• A knowledge base (KB) comprises two components,

• the TBox and the ABox• The TBox introduces the terminology, i.e.,

the vocabulary of an application domain,• The ABox contains assertions about

named individuals in terms of this vocabulary.

vocabulary

• The vocabulary consists of • concepts, which denote sets of individuals, • and roles, which denote binary relationships

between individuals.• DL systems allow their users to build complex

descriptions of concepts and roles by using atomic concepts and roles

• The TBox can be used to assign names to complex descriptions.

Page 4: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

A DL System

Page 5: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Another representation..

Page 6: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Description Language

• Elementary descriptions are atomic concepts and atomic roles

• Complex descriptions can be built from them inductively with concept constructors

• we use the letters A and B for atomic concepts• the letter R for atomic roles, • and the letters C and D for concept descriptions

Page 7: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Page 8: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Examples

Page 9: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Disjoint

• Animal ∏ plant = • Or

• Plant ⊑ animal

Page 10: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

subsumtion

• Tree ⊑ plant

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All values from

• Branch ⊑ Is_part_of.tree

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All values from

• leaf ⊑ Is_part_of.branch

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All values from, role union

• Herbivors=animals ∏ eats.(plant U is_part_of.plant )

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Some values from

• Carnivore = animal ∏ eats.animal

Page 15: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

• giraffe = herbivores ∏ eats.leaf

Page 16: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

• Lion=carnivore ∏ eats.herbivore

Page 17: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Tasty_plant = plant ∏ eaten_by.herbivore ∏ eaten_by.carnivore)

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Back to DL

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• Suppose that Person and Female are atomic concepts

• those persons that are female

• Those that are not female

• suppose that hasChild is an atomic role,• those persons that have a child

• those persons all of whose children are female

• those persons without a child

Page 20: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Page 21: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

• there is a set of objects that are Trees and a binary relation has-branch between objects that leads from a tree to its subtrees. Then the binary trees are the trees with at most two subtrees that are themselves binary trees:

Page 22: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

• A world description (ABox).

Page 23: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

One sort of reasoning• The simplest form of reasoning involves

computing the subsumption relation between two concept expressions,

• i.e., verifying whether one expression always denotes a subset of the objects denoted by another expression.

• Parent is a specialization of Person, i.e., Person subsumes Parent

Page 24: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Another sort of reasoning

• A more complex reasoning task consists in checking whether a certain assertion is logically implied by a knowledge base.

• For example, Bill is an instance of Parent.

Page 25: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Page 26: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Expansion of the family T-Box

ABox

Owl-DL Constructs

Page 30: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Owl-DL Axioms

Page 31: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Reasoning

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Inference

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Page 34: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

DL Inferences

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Structural Subsumption

• Normalize descriptions• Compare syntactical structure of normal

forms

Page 36: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Structural Subsumption

Page 37: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Structural Subsumption

Page 38: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Example: Structural Subsumption

Page 39: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

More expressive DLs

Page 40: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Page 41: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Negation Normal Form (NNF)

Example

Page 42: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Tableau inferencing

Page 43: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Tableau

Page 44: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Transformation rules

• Example

Page 45: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Example - Tableau Proof

Page 46: OWL - DL. DL System A knowledge base (KB) comprises two components, the TBox and the ABox The TBox introduces the terminology, i.e., the vocabulary of

Mad Cow Example

TWinSoft 11.06 SP3- Release notes€¦ · TWinSoft 11.06 SP3- Release notes September 12, 2016 TWinSoft build number: 1468 WebformStudio 2.0 11.06 TBox MS32 OS version: 1.37.410 TBox

dl. dl

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ABOX synopsis

Programming the Semantic Web - polito.it · –the basic unity –TBox axioms describe relations between classes and class expressions (equivalence, subsumption, disjointness) –ABox

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VERIFICATION OF DISTRIBUTED FIREWALLS ...nargeskh/AAI2.pdfFormal Veriﬁcation of Distributed Firewalls 761 ABox Assertions ABox assertions have the forms of C(a) or R(b,c).By the

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ABOX-E7L - ssdiskinfo.com · ABOX-E7L High performance industrial box computer Intel 6/7th Core i7/i5/i3 Desktop multi-core processors, with PCIe and MXM expansion Specification V2.0

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User Guide - ABOX

(Chapter 1)tbox

A HYBRID ABOX CALCULUS USING ALGEBRAIC REASONING FOR …haarslev/students/Laleh_Roosta_Po… · a hybrid abox calculus using algebraic reasoning for the description logic shiq laleh

Updating Wikipedia via DBpedia Mappings and SPARQLpolleres/publications/ahme-etal-ESWC2017.pdfing it into RDF triples (the DBpedia ABox), and Tis a TBox. The rules in Mare given by

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La Oficina Cero Papel con abox

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ABox Abduction in the Description Logic ALC

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owl - dl. dl system a knowledge base (kb) comprises two components, the tbox and the abox the tbox...

Documents

reasoning slide

abox slide

tableau slide

carnivore slide

tree slide

branch slide

b slide

leaf slide