Ontology A representation of the shared background knowledge for a community • Providing the intended meaning of a formal vocabulary used to describe a • certain conceptualisation of objects in a domain of interest In CS, ontology taken to mean an engineering artefact • A vocabulary of terms plus explicit characterisations of the assumptions • made in interpreting those terms Nearly always includes some notion of hierarchical classification (is-a) • OWL Semantics Richer languages allow the definition of classes through description of their • characteristics – Introduce the possibility of using inference to help in management and COMP60421 deployment of the knowledge. Sean Bechhofer University of Manchester sean.bechhofer@manchester.ac.uk 1 2 Toward Formalization What is a Taxonomy? • Acquisition Process • An organisation of entities – Elicit tacit knowledge – Typically hierarchical – A Set of terms/concepts – Subclass relationships • Organisationally Rigid • More explicit information – Things must be put in their Animal proper place. – Hierarchy and other relations – Multiple places for things? – Categorizing (modifiers) Mammal Domestic – Constraints and definitions Cat Cow Dog Person Pet Farmed • Hierarchical Relations – Nodes/Arcs representing a relationship (default IS-A) • Impoverished descriptions – What IS-A Is and Isn’t: An Analysis of Taxonomic Links in Semantic Cat Dog Cow Networks (Brachman) – Cats are carnivores • Why? • What is it to be a Carnivore? • What if we say something is a Carnivore and a Herbivore? 3 4
More Expressivity Structure of an Ontology • Not just term-term relationships • Ontologies typically have two distinct components: • Names for important concepts in the domain • Definitions – Paper is a concept whose members are papers. – A carnivore is an animal that eats only meat – Person is a concept whose members are persons • Background knowledge/constraints on the domain • Constraints – A Paper is a kind of ArgumentativeDocument – Carnivores are not herbivores (and vice versa) – All participants in a Workshop must be Persons. – No individual can be both an InProceedings and a Journal • What Entailments can we make? – Carnivores eat only Meat • Syntax required to allow us to state/express/write down this information – Cats eat only Mice – Operators that allow us to describe complex expressions – Mice are Meat – Thus Cats are Carnivores! 5 6 OWL Ontologies Operators • Individuals • A primitive or atomic class gives us no indication as to the individuals that are members of it. – Elements in the domain – We don’t know what it is to be a Cat • Things, objects, members of Robert’s family • Operators allow us to form class descriptions • Properties – Describing the characteristics of properties of the individuals that are – (Binary) Relations between objects members of the class • hasFather, hasSibling • Animals that live in the Forest – Attributes • Animals that eat other Animals • hasBirthDate • By expressing these definitions in a structured, explicit way, we can begin to • Classes derive benefit (inference) – Collections of things – Primitive, named classes • Person – Class descriptions built up from other classes using class forming operators. • Man • Axioms represent background knowledge/constraints 7 8
OWL Class Expressions (Informal) (Informal) Inference • Booleans Animal that eats some Animal – Human and Male – Doctor or Lawyer – not Male Remember: All these expressions describe • Restrictions Classes ! Animal that eats some Gazelle – hasChild some Man – hasChild only Woman – hasDescendant min 2 Doctor – hasAncestor max 2 Animal that eats some Gazelle – hasSibling exactly 1 Woman and eats some Grass (Assuming Gazelle is a kind of Animal) 9 10 Axioms OWL Axioms (Informal) • We can now describe classes through a description of their characteristics. • Class Axioms – Lions are Animals that eat other animals – Person SubClassOf Animal – Anything that eats only animals is a carnivore – (Person and Male) EquivalentTo Man – Robert is a Person • Axioms allow us to state these additional relationships that we expect to • Property Axioms hold between classes and individuals – transitivity – They encapsulate the assumptions that facilitate shared interpretations – reflexivity of our vocabulary. – functional • Individual Axioms – Robert type Person – Robert hasParent Margaret 11 12
Necessary and Sufficient Conditions Syntax atomicClass ::= [A-Z][a-zA-Z]* (in camel case) • Classes can be described in terms of necessary and sufficient conditions. atomicProperty ::= [a-z][a-zA-Z]* (in camel case) description ::= conjunction 'or' conjunction { 'or' conjunction } – This differs from some frame-based languages where we only have | conjunction necessary conditions. conjunction ::= classIRI 'that' [ 'not' ] restriction Constraints • Necessary conditions { 'and' [ 'not' ] restriction } – Must hold if an object is to be an instance of the | primary 'and' primary { 'and' primary } class | primary primary ::= [ 'not' ] ( restriction | atomic ) – SubClassOf axioms Definitions restriction ::= property 'some' primary • Sufficient conditions | property 'only' primary – Those properties an object must have in order to be recognised as a member • A simple grammar for expressions (aka, descriptions) of the class. • Examples – EquivalentTo axioms If it looks like a – Animal that eats only Animal duck and walks – eats some (not Animal) like a duck, then – not (eats only Animal and some Animal) it’s a duck! 13 Grammar is a slightly modified subset of the one given in: http://www.w3.org/TR/owl2-manchester-syntax/ 14 Formal Languages More Syntax The degree of formality of ontology languages varies widely classFrame ::= 'Class:' atomicClass • { 'Annotations:' annotation { ',' annotation } Increased formality makes languages more amenable to machine • | 'SubClassOf:' description { ',' annotation } processing (e.g. automated reasoning). | 'EquivalentTo:' description { ',' annotation } The formal semantics provides an unambiguous interpretation of the • descriptions. • A simple grammar for axioms (aka propositions) • Examples – Class: CarnivorousAnimal EquivalentTo: Animal that eats only Animal – Class: Cow SubClassOf: eats some (not Animal) – Class: ConfusedCow SubClassOf: not (eats only Animal and some Animal) 15 16
Why Semantics? OWL: The Web Ontology Language The W3C OWL 2 Web Ontology Language (OWL) is a What does an expression in an ontology language mean ? • Semantic Web language designed to represent rich and The semantics of a language can tell us precisely how to interpret a • complex knowledge about things, groups of things, and complex expression. relations between things. OWL is a computational logic- Well defined semantics are vital if we are to support machine interpretability • – They remove ambiguities in the interpretation of the descriptions. based language such that knowledge expressed in OWL can be reasoned with by computer programs either to verify the consistency of that knowledge or to make implicit knowledge explicit. OWL documents, known as ontologies, Telephone Black can be published in the World Wide Web and may refer to or be referred from other OWL ontologies. OWL is part of ? the W3C's Semantic Web technology stack, which includes RDF [RDF Concepts] and SPARQL [SPARQL]. http://www.w3.org/TR/owl-primer/ 17 18 Diversion: Semantics and Model Theories Set Based Model Theory Ontology/KR languages aim to model (part of) world Many logics (including standard First Order Logic) use a model theory • • based on Zermelo-Frankel set theory Terms in language correspond to entities in world • The domain of discourse (i.e., the part of the world being modelled) is • Meaning given by, e.g.: • represented as a set (often referred to as ! ) – Mapping to another formalism, such as FOL, with own well defined Objects in the world are interpreted as elements of ! semantics • – or a bespoke Model Theory (MT) – Classes/concepts (unary predicates) are subsets of ! MT defines relationship between syntax and interpretations – Properties/roles (binary predicates) are subsets of ! ! ! (i.e., ! 2 ) • – Can be many interpretations (models) of one piece of syntax – Ternary predicates are subsets of ! 3 etc. – Models supposed to be analogue of (part of) world The sub-class relationship between classes can be interpreted as set • inclusion ! E.g., elements of model correspond to objects in world – Formal relationship between syntax and models ! Structure of models reflect relationships specified in syntax – Inference can then be defined in terms of this Model Theory 19 20
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