Axiom Patterns. COMP60421 Robert Stevens University of Manchester

Transcription

1 Axiom Patterns COMP60421 Robert Stevens University of Manchester 1

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 2

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 3

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 4

5 Label annotations for the class Head Class: <#Head> Annotations: rdfs:label rdfs:label rdfs:label rdfs:label 5

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 for an introduction 6

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 7

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 8

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? 9

10 The Margherita Pizza hastopping some TomatoTopping and hastopping some MozarellaTopping I 1 I 2 TomatoTopping TomatoTopping MargheritaPizza MargheritaPizza BeefTopping MozarellaTopping BeefTopping MozarellaTopping 10

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 BeefTopping MozarellaTopping BeefTopping MozarellaTopping 11

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 12

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 13

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) 14

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) 15

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) 16

17 Sex as an example Class: Sex Class: Male SubClassOf: Sex Class: Female SubClassOf: Sex Male DisjointWith: Female Sex SubClassOf: (Male or Female) All individuals of Male are also individuals of Sex All individuals of Female are also individuals of Sex An individual of Sex cannot be both an individual of Male and an individual of Female (the disjointness axiom) An individual of type Sex must be an individual of either Male or Female (the SubClassOf: (Male or Female) axiom 17

18 More information. Lots of short, accessible articles about ontology stuff 18

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 19

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). 20

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 IsA IsA has_size Small Medium Large 21

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 22

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 23

24 Composition, Parts and Wholes 24

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? 25

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 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. 26

27 Properties of Composition Winston et. al. describe properties of composition Configuration/Functionality Do the parts bear a functional or structural relationship to one another or the object they constitute? functional/non-functional Homeomerous Are the parts the same kind of thing as the whole? homeomerous/non-homeomerous Invariance Can the parts be separated from the whole? separable/inseparable We can then discuss combinations of these properties. We ll consider Odell s classification 27

28 Component-Integral Object functional non-homeomeric separable A configuration of parts within a whole Bristles - toothbrush Scene - film A particular arrangement (not just haphazard) If components cease to support the overall pattern then different associations may arise Handle ripped from a door of the car. No longer a part but a piece 28

29 Material-Object functional non-homeomeric non-separable Parts can t be removed Capuccino is partly milk Bread is partly flour Define what objects are made of. Component-Integral can be separated Car without a door handle still a Car Material-Object can t Bread without flour not bread 29

30 Portion-Object functional homeomeric separable Cf Material-Object, but parts are the same kinds of thing Slice of bread is a portion of bread meter is part of a kilometer A slice of bread is bread. So slices in a loaf are similar Portions divided by standard measures meter/kilometer hour/day Selective inheritance of properties Ingredients of bread are ingredients of slice of bread But with different quantities Slice, helping, segment, lump, drop etc. 30

31 Place-Area Unlike Portion-Object, pieces cannot be removed functional homeomeric non-seperable Manchester part of England Peak part of a mountain Often between places and locations. Pieces similar in nature. 31

32 Member-Bunch non-functional non-homeomeric separable No requirement for a particular structural or functional relationship Tree part of a Forest Employee part of the Union Ship part of a Fleet Member-Bunch is not subclass!!! 32

33 Member-Partnership An invariant form of Member-Bunch non-functional non-homeomeric non-seperable Stan Laurel is part of Laurel and Hardy Fred and Ginger are a dancing couple Removal of member destroys the partnership a different partnership may result 33

34 Summary of Odell s Compositional Relationships Functional Homeomeric Seperable Component-Integral Y N Y Material-Object Y N N Portion-Object Y Y Y Place-Area Y Y N Member-Bunch N N Y Member-Partnership N N N 34

35 Non Compositional Relationships Topological inclusion I am in the lecture theatre Classification inclusion Catch 22 is a Book It s an instance of Book, not a part of it, so not Member-Bunch Attribution Properties of an object can be confused with composition Height of a Lighthouse isn t part of it Attachment Earrings aren t part of Ears Toes are part of Feet Sometimes attachments are parts, but not always Ownership A bicycle has wheels I have a bicycle A lot of modelling is about making the right distinctions and thus helping 35

36 So what? 36

37 Transitivity X is part of Y, Y is part of Z, thus X is part of Z We might expect part-whole or composition relationships to behave transitively. But this is generally only true with the same kind of composition. Engine part of the Car Pistons part of the Engine Pistons part of the Car Sean s arm part of Sean Sean part of School of Computer Science Sean s arm part of School of Computer Science 37

38 Transitivity X is part of Y, Y is part of Z, thus X is part of Z We might expect part-whole or composition relationships to behave transitively. But this is generally only true with the same kind of composition. Engine part of the Car Pistons part of the Engine Pistons part of the Car ispartof isconstituentof isportionof ismemberof... Sean s arm part of Sean Sean part of School of Computer Science Sean s arm part of School of Computer Science 38

39 Transitivity In partonomies, we may want to identify direct parts Piston directpartof Engine; Engine directpartof Car Piston is not directpartof Car, but is a partof Car I want to query for all the direct parts of the Car, but not the direct parts of its direct parts. So directpartof shouldn t be transitive Solution: provide a transitive superproperty Queries can use the superproperty to query transitive closure Assertions use the direct part of relationship A standard ontology design pattern, sometimes referred to as transitive reduction. 39

40 Transitivity In partonomies, we may want to identify direct parts Piston directpartof Engine; Engine directpartof Car Piston is not directpartof Car, but is a partof Car I want to query for all the direct parts of the Car, but not the direct parts of its direct parts. So directpartof shouldn t be transitive Solution: provide a transitive superproperty Property: ispartof Characteristics: Transitive Property: isdirectpartof SubPropertyOf: ispartof Queries can use the superproperty to query transitive closure Assertions use the direct part of relationship A standard ontology design pattern, sometimes referred to as transitive reduction. 40

41 Aside: Transitivity and Subproperties Transitive property R is one s.t. for any x,y,z, if x R y and y R z, then z R z Transitivity is not inherited by subproperties. Nor is a superproperty of a transitive property necessarily transitive Property: knows Property: hasfriend SubPropertyOf: knows Characteristics: Transitive Property: hasbestfriend SubPropertyOf: hasfriend 41

42 A note on Inverses OWL allows us to define inverse relationships haspet / ispetof hasparent / ischildof (x R y) iff (y inv-r x) Be careful about what you can infer about inverse relationships X SubClassOf (haspart some Y) All X s have a part which is a Y Are all Y s a part of some X? 42

43 Composition Composition provides a mechanism for forming an object whole using its parts By considering basis properties if this part-whole relationship, we can identify different kinds of relationship The different relationships then help us in identifying when, for example, we can (or can t) apply transitivity. Explicitly separating these in our representation can avoid incorrect/invalid inferences. 43

44 Ontology Normalisation 44

45 Ontology Normalisation Poly-hierarchies are the norm Harry Potter and the Philosopher s stone is a book, a children s book, a work of fiction, a big book, written in English, and a fantasy book Poly-hierarchies allow knowledge to be captured and appropriately queried They are difficult to build by hand Essentially impossible to get right and maintain We can use OWL and automated reasoners to do the work for us but how does one manage this and get it right? 45

46 A tangled ontology of amino acids 46

47 There are several dimensions of classification here The amino acids themselves a chemical dimension The size of the amino acids side chain The charge on the side chain The polarity of the side chain The hydrophobicity of the side chain We can normalise these into separate hierarchies then put them back together again Our goal is to put entities into separate trees all formed on the same basis Size only talks about size; amino acid only talks about chemical composition (based on an alpha-carbon with an amino and carboxylic acid group);and so onof classification 47

48 The dimensions separated Charge Negative Neutral Positive Size Tiny Small Medium Large Polarity Polar Nonpolar Hydrophobicity Hydrophobic Hydrophilic Amino Acids Alanine Arginine Asparagine Cysteine Glutamate Glutamine Glycine Histidine Isoleucine Leucine Lysine Methionine Phenylalanine Proline Serine Threonine Tryptophan Tyrosine Valine 48

49 The process Hand-crafted ontologies with multiple inheritance are tangled Usually axiomatically lean We classify along one axis and use restrictions to other modules to capture other axes Then re-build the multiple inheritance using the axiomatically rich ontology 49

50 Pulling out dimensions Each separate tree must be the same kind of thing We don t mix self-standing things, processes, modifiers (qualities) We don t mix our classificaiton by, for instance, structure and then charge We do that compositionally via defined classes and the automated reasoners 50

51 The amino acid pattern Class: AminoAcid SubClassOf: hassize some Size, haspolarity some Polar, hascharge some Charge, hashydrophobicity some hydrophobicity 51

52 An amino acid Class: Lysine SubClassOf: AminoAcid, hassize some Large, hascharge some Positive, haspolarity some Polar, hashydrophobicity some Hydrophilic 52

53 Rebuilding the hierarchy Class: LargeAminoAcid EquivalentTo: AminoAcid and hassize some Large Class: PositiveAminoAcid EquivalentTo: AminoAcid and hascharge some Positive Class: LargePositiveAminoAcid EquivalentTo: LargeAminoAcid and PositiveAminoAcid 53

54 Patterns used The Amino acids ontology uses these five patterns: Normalisation EPQ Closure (via it s functional properties A covering axiom for all the amino acids It s own pattern for amino acids There is more information via

55 A tangled ontology of amino acids 55

56 Upper Level Ontologies 56

57 Upper Level Ontologies Domain neutral description of all entities Should be able to be used to describe any domain: biology, art, politics, business, medicine, The basic divisions: processes and the things that participate in processes are the two major divisions that many upper ontologies make Much philosophical discussion (been trying since 437 BCE and still not sorted it out) So, we ll do something simple. 57

58 The PIMPS ontology in context 58

59 PIMPS: A Simple Domain Neutral Ontology Thing Process Immaterial Material Properties Quality Function Role Disposition Sites 59

60 Material entities Self-standing things I can hold in my hand A ball, a car, a person, a leg, a pizza, a piece of seaweed, etc etc All of it exists at any one point in time All of Robert exists at any point in time, even though Robert himself actually changes It retains its identity 60

61 Processes An entity that unfolds over time such that its identity changes Not all of a process is present at a given time-point in that process My life unfolds over time and is different at each point in time Living, dying, eating, drinking, breathing, Lots of -ation and ing words 61

62 Why use an upper level ontology? Consistent modelling style both within and between ontologies Primarily a guide to using properties consistently Continuants have parts that are continuants Processes have parts that are processes Independent continuants hasquality some Quality and playrole some Role Independent continuant hasfunction some Function Independent continuants participate in processes Sites occupy some material entity Use property hierarchies 62

63 What have we done Lots of stuff about modelling Patterns to take advantage of language features and to work around some infelicities of a language Modelling the same kind of entities in the same way Choosing the right place for entities Getting the choice of properties right Designing your patterns for sushi 63