Axiom Patterns COMP60421 Robert Stevens University of Manchester - PowerPoint PPT Presentation

Axiom Patterns COMP60421 Robert Stevens University of Manchester robert.Stevens@manchester.ac.uk 1

Previously on COMP60421 We’ve looked at operational knowledge of OWL We’ve looked at acquiring knowledge to put in an ontology We’ve looked at formalising knowledge We’ve looked at the semantics of OWL Now we look at putting OWL axioms together in patterns to say certain things in certain ways 2

Patterns of axioms • An axiom pattern is a recurring regularity in how axioms are used or appear within an ontology • The most common may be a tree of classes made with SubClassOf • … but they get much more complex than that • Usually, we’re referring to syntactic patterns; how axioms are written, but remember “axioms” are inferred as well as written 3

Patterns and design patterns • Software Design Patterns are well accepted solutions for common issues met in software construction • Ontology Design Patterns are the same; but ontology engineers have barely agreed on well accepted problems, let alone their solutions • ODP often depend on one’s philosophical stance and more of those kinds of pattern later • Meanwhile, we’ll mostly talk about patterns as recurring regularities of asserted axioms 4

Coding style • Is a sort of pattern … • What we want is: – Classes: Singular nouns with initial capital letter, spaces indicated by CamelCase • Individuals: All lower case, spaces indicated by _ • Properties: Initial lower case letter, camel case – usually start with “is” or “has” • All classes and individuals have a label, creator, description annotation properties 5

Label annotations for the class Head Class: <#Head> Annotations: rdfs:label "Kopf"@de, rdfs:label "Testa"@it, rdfs:label "Tête"@fr, rdfs:label "Head"@en 6

Naming conventions • Adopt one • For both labels and URI fragments • Both for the URI fragment and for the label • Having a label is a “good practice” • Naming conventions determine what words, in what order and what one does about symbols and acronyms • See http://ontogenesis.knowledgeblog.org/948 for an introduction 7

Names can help modelling • Thigh, shin, foot and toe are not “leg”, but “leg part” • Slice of tomato, tomato sauce, and tomato puree are not “Tomato” but “Tomato based product” • Professor (Robert) and professor (the academic role) are different things; name them differently and consistently • Card sorting and the three card trick can help you here • More on this later when we talk about upper level ontologies 8

Types of axiom patterns • Domain modelling patterns: How to organise the axioms describing a domain • Works both in the large – the whole ontology – and in the small – how to describe a type of sushi • Language patterns: Used to take advantage of language features or work around something missing in a language • The latter are used in the former 9

The Margherita Pizza Class: `Margherita pizza’ SubClassOf Pizza, hasTopping some MozzarellaCheese, hasTopping some tomatoSauce • Does this pizza have a cheese topping? • Does this Pizza have a tomato sauce topping? • Does this Pizza have an beef topping? 10

The Margherita Pizza hasTopping some TomatoTopping and hasTopping some MozarellaTopping I 1 I 2 TomatoTopping TomatoTopping MargheritaPizza MargheritaPizza MozarellaTopping MozarellaTopping BeefTopping BeefTopping 11

The Margherita Pizza (with closure) hasTopping some TomatoTopping and hasTopping some MozarellaTopping hasTopping only (MozzarellaTopping or TomatoTopping) I 1 I 2 TomatoTopping TomatoTopping MargheritaPizza MargheritaPizza MozarellaTopping MozarellaTopping BeefTopping BeefTopping 12

OWL’s open world assumption • Unless we know something to be false it may be true • OWL has an “open world assumption” • Unless we add suitable constraints, interpretations may be possible • A lot of answers to queries may be “I don’t know” • We often need to add “closure” axioms 13

The Closure Axioms • The existential quantifier “some” tells us that each margherita pizza has at least one hasTopping property to a mozzarella individual • Due to OWL’s open world assumption, it may have other toppings – we just don’t know • We need to say “it has these toppings and no others” 14

The universal quantifier as closure • The universal quantifier “only” says that if this property exists between two individuals, then the RHS can only be of the type of the RHS • … , but the relationship need not exist • hasTopping some MozzarellaCheese (there exists a hasTopping property to a MozzarellaCheese individual) • hasTopping only MozzarellaCheese (if there is a hasTopping property to an individual, then that individual will be a MozzarellaCheese individual) 15

The closure pattern Class: `Margherita pizza’ SubClassOf Pizza, hasTopping some MozzarellaCheese, hasTopping some tomatoSauce hasTopping only (MozzarellaCheese or TomatoSauce) • The first two axioms say “there are these two toppings” • The last axiom says “the things at the end of hasTopping for MargheritaPizza will be of the union (MozzarellaCheese or TomatoSauce) 16

The Covering Axiom • Class X has subclasses Y and Z • There may be other kinds of X, we don’t know … • We want to say “any individual of class X has to be an individual of either class Y or class Z” • That is, class X is covered by classes Y and Z The pattern: Class: X SubClassOf: (Y or Z) 17

Sex as an example Class: Sex • All individuals of Male are also individuals of Sex • All individuals of Female are Class: Male also individuals of Sex SubClassOf: Sex • An individual of Sex cannot be both an individual of Male and Class: Female an individual of Female (the SubClassOf: Sex disjointness axiom) • An individual of type Sex must Male DisjointWith: Female be an individual of either Male or Female (the SubClassOf: (Male or Female) axiom Sex SubClassOf: (Male or Female) 18

More information … . • http://ontogenesis.knowledgeblog.org/1001 • Lots of short, accessible articles about ontology stuff 19

Value Partitions • OWL not much good at representing continuous things • Colour, size and so on • So we need a pattern to “partition” such values • We want to say “Size” must be one of the subclasses of Size and only one of those sizes – and that an individual size cannot be two kinds of size at the same time 20

Value Partitions • Used to model descriptive features of things. • The features are constrained to have certain values (e.g. Size: small, medium, large). • OWL elements: – Feature (Size): functional property (has_size) or class (Size). – Values: classes or individuals. – The values it can have are constrained by the range of the property. • Using classes allows to make subpartitions (e.g. very large, moderately large). • http://www.w3.org/TR/swbp-specified-values/ 21

Value Partitions • The feature to be partitioned is covered: defined by the union of its subclasses, the subclasses being disjoint: Size ≡ Small ∪ Medium ∪ Large Size Human IsA has_size IsA IsA Small Medium Large 22

Entity Property Quality (EPQ) pattern • A self-standing entity has a quality and should have only one of that quality • Colour, height, weight, size, speed, etc • Two coloured things have one colour per site and may have many sites • Class: Colour • Property: hasColour – functional, range – Colour – domain, anything that has a colour • The class colour is a value partition • Can use just hasQuality but have to muck around with cardinality constraints and it’s hard work 23

Using cardinality in EQ • hasQuality max 1 Size • hasQuality exactly 1 Large • Allows use of only one property (which can be good) • But is hard work keeping on top of the cardinalities and can be hard work for reasoners • EPQ means lots of different properties • One pays the money and makes the choice 24

Composition, Parts and Wholes 25

Composition or Aggregation • Forming an object whole using other objects as parts • Treating complex things as a single object • What are the primary composition relationships? • What inferences can we make? • What might we have in our representation languages to support this? http://www.flickr.com/photos/hartini/2429653007/ 26

Parts & wholes: Some examples • Bristles are part of a toothbrush • Wheels are part of a shopping trolley • A car is partly iron • A cappuccino is partly milk • A meter is part of a kilometer • Manchester is part of England • A tree is part of a forest • A slice of pie is part of the pie http://www.flickr.com/photos/aramisfirefly/4585596077 • A book chapter is part of a book • Stan Laurel is part of Laurel and Hardy • These are different kinds of composition, with different characteristics and properties. • Confusing them may result in incorrect (or undesirable) inferences. 27