Lecture 4 more patterns

Foundations of the Semantic WebLecture 4More Pattern and a ProblemClasses as ValuesCombining Necessary & Sufficient with Necessary conditions (General Inclusion Axioms - GICs): 

Foundations of the Semantic Web Lecture 4 More Pattern and a Problem Classes as Values Combining Necessary andamp; Sufficient with Necessary conditions (General Inclusion Axioms - GICs) Alan Rector

Part 1: Classes as Values: 

Part 1: Classes as Values In OWL DL nothing can be both a class and an individual In classic Protégé and most frame languages everything is an individual of something The class MetaClass is an instance of itself. In OWL-Full a class can also be an individual Why the problem? Paradoxes of self reference - undecidable statements are hard to avoid Russell Paradox: The class of all classes that are not instances of themselves. Liar Paradox (Epimenides paradox): Is the following statement true? 'This statement is false' The logic is trickier than it looks If you are interested in the theory look up Zermelo Frankel and/or Von Neuman set theory - or talk to our logician colleagues

The classic application: 

The classic application I want to index book / web pages / films … according to what they are ‘about’. The standard vocabulary for doing this in rdf is 'Dublin Core' - namespace usually abbreviated to 'dc:'

Using Classes as Property Values: 

Using Classes as Property Values subject dc:subject Animal African Lion Lion Tiger

Using Classes Directly As Values: 

Using Classes Directly As Values BookAboutAnimals

Cannot do this directly in OWL 1.0: 

Cannot do this directly in OWL 1.0 Will use ‘puns’s as weak solution in OWL 1.1 Best approximation in existing protégé Name a an individual for each class with a suffix or naming-convention, e.g. lower case. Provide the mirroring relation by hand or script There should be improved solutions coming

Approach 1: Considerations: 

Approach 1: Considerations Compatible with OWL Full and RDF Schema Outside OWL DL Because classes cannot be values in OWL-DL Nothing can be both a class and and instance

Approach 2: Hierarchy of Subjects: 

Approach 2: Hierarchy of Subjects

Hierarchy of Subjects: Considerations: 

Hierarchy of Subjects: Considerations Compatible with OWL DL Instances of class Lion are now subjects No direct relation between LionSubject and AfricalLionSubject Maintenance penalty Lion LionSubject rdf:type African Lion AfricanLionSubject rdf:type rdfs:subclassOf

Hierarchy of Subjects: 

Hierarchy of Subjects

Hierarchy of Subjects: Considerations: 

Hierarchy of Subjects: Considerations Compatible with OWL DL Subject hierarchy (terminology) is independent of class hierarchy (rdfs:seeAlso) Maintenance penalty Lion LionSubject rdf:type African Lion AfricanLionSubject rdfs:subclassOf Subject parentSubject rdfs:seeAlso

Apporach 3. Using members of a class as values: 

Apporach 3. Using members of a class as values

Protégé Examples of Approaches 2-3: 

Protégé Examples of Approaches 2-3

Representation in Protégé: 

Representation in Protégé

Class Hierarchy: Book about Lions: 

Class Hierarchy: Book about Lions

Inference: 

Inference

Book about SOME Lion: 

Book about SOME Lion

A Book about a Lion “Born Free”: 

A Book about a Lion 'Born Free'

Inference: 

Inference

Considerations: 

Considerations Compatible with OWL DL Interpretation: the subject is one or more specific lions, rather than the Lion class Can use a DL reasoner to classify specific books Manchester’s preferred solution … but others disagree

Part 2 Defined Classes with Necessary Conditions: 

Part 2 Defined Classes with Necessary Conditions OWL allows the same class to be defined and have additional necessary conditions Protégé OWL has made this easy to do

Defined classes with necessary conditions: 

Defined classes with necessary conditions What does it mean to have both kinds of restrictions Necessary and Sufficient Necessary Animal_with_fins = Animal AND has_limb_type Fins ==andgt; habitat_includes someValuesFrom Aquatic_habitat Vocabulary: 'Aquatic' - having to do with water.

Defined classes with necessary conditions: 

Defined classes with necessary conditions Effectively such classes are rules or axioms 'Any animal with fins, has a habitat that includes includes some Aquatic_habitat'

SubclassOf means “Necessarily implies”: 

SubclassOf means 'Necessarily implies' Protégé OWL necessary statements necessary implications Equivalent to subclass axioms In fact the interface will move the class under the subclass Very strong statement Any animal, without exception, that has fins lives in aquatic habitat Think about Toads - do their habitats include aquatic? The properties were phrased carefully Therefore defined classes with necessary statements are called 'General Inclusion Axioms' They are a general way of writing axioms about subsumption ('inclusion')

Subsumption means necessary implication - the classifier produces: 

Subsumption means necessary implication - the classifier produces

Debugging & GICs: 

Debugging andamp; GICs If a definition implies that something is classified under it that conflicts with its necessary conditions The classifier will not show the classification It will just show that the class is unsatisfiable but will not move it. Therefore, although powerful, such constructs can be hard to debug

Part 3:A Ridiculously Brief Glance at Representing Time & Space: 

Part 3: A Ridiculously Brief Glance at Representing Time andamp; Space

Extents, Intervals, and Ordering: 

Extents, Intervals, and Ordering 'Extent' is a general term for a point, interval, area, volume, etc. in space and/or time Time comes with natural coordinates Many spatial measures are also laid out with coordinates Timed is concerned with points and interval Space with points, intervals, areas, and volumes Most temporal and spatial reasoning beyond OWL

A few things you should knowAxioms of Ordering of time or lines: 

A few things you should know Axioms of Ordering of time or lines For points in an ordered one-dimensional space Anti-symmetry Xandlt;Y  ¬(Yandlt;X) Transitivity Xandlt;Y andamp; Yandlt;Z  Xandlt;Z Totality Xandlt;Y  Yandlt;X  X=Y

For an Ordered One Dimensional SpaceRelations between Intervals: 

For an Ordered One Dimensional Space Relations between Intervals The 'Allen Calculus' specifies the results of combining intervals. There are precisely 13 possible combinations including symmetries (6 * 2 + 1)

Exercise: 

Exercise Using the diagrams on the previous slide, write down the axioms that should apply to the relations between intervals r1(X,Y) andamp; r2(Y,Z)  r?(X,Z) e.g. before(X,Y) andamp; before(Y,Z)  before(X,Z)

Points and Intervals : 

Points and Intervals Time representations are either point based or interval based A point can be viewed as: An interval of zero length One of the set of ordered things that make up an interval. Points can be: Contained in intervals The start or end of the interval start(I) or end(I)

Classic Situation CalculusTime, Situations, and Fluents: 

Classic Situation Calculus Time, Situations, and Fluents Situation = a cross section of time Representation as parameter 'The radio was on at 9:00' on(radio, S9:00) Representation by fluents (things that can be true in situations) 'the radio was on at 9:00' true_in(s9:00, on(radio))

Basic Assumptions: 

Basic Assumptions There is an integral measure clock time The differential measure of clock time is duration Intervals of clock times are sets of clock times 'Kenedy was president throughout 1962' S Î year_1962 « kennedy=value_in(S, president(us)) Intervals of clock times have durations

Events, States and Fluents: 

Events, States and Fluents Fluents refer to time points and may be of three types: Things that can have values - states NB 'state' is used differently by other authors! Things that can occur - events Things that change things - processes Davis defines processes as a special case of state which can be active or inactive

Processes and EventsAlternative View: 

Processes and Events Alternative View Processes have duration and correspond to intervals and have positive duration. Events correspond to points and have zero duration. States have values and may hold those values and have a duration but the duration may be zero. In most ontologies states must correspond to intervals, though the intervals may be of zero length.

What is an event? A process?: 

What is an event? A process? He sat down at three o’clock sharp. He sat down slowly and carefully. He was so stiff that it took him nearly a half a minute to sit down He sat down before the meeting. The birthday party took place on Tuesday The birthday party lasted three hours. The birthday party was the biggest event of the season

Situations and OWL/DLs: 

Situations and OWL/DLs Full situation calculus beyond OWL or DLs and even to attempt it need concrete data types Can use the idea of a situation If using an event-based view of time The class of situations in which someone is sitting down at 18:00 Sitting_at_1800  Situation and (hasFluent someValuesFrom SittingProcess ) and (occursAt someValuesFrom (Event and occursAt value 1800)))

Situations and OWL/DLs (cont): 

Situations and OWL/DLs (cont) if using an interval based view of time Sitting_between_1800_and_1801 ≡ Situation and (hasFluent someValuesFrom SittingProcess) and (occurs_during someValuesFrom (Interval and (hasStartTime value 1800) and (hasEndTime value 1801)))

Snaps and Spans 3D and 4D viewsYet another View : 

Snaps and Spans 3D and 4D views Yet another View Another version is to index by time A 'span' is entire history of an entity through time Spans are intrinsically four dimensional A 'snap' is a cross section of a span at a point in time. Qualities of continuants are dependent on the SNAP and change in the course of a SPAN e.g. an Apple can be green in one SNAP and red in a later SNAP A 'situation' is a piece of situated information in a 4-D universe; a 'Snap' is a three D section of a 4 d entity Due to Barry Smith et al (google 'Barry Smith')

Slide41: 

single-cell zygote multi-cell zygote morula early blastocyst gastrula new born infant adolescent young adult

The Futureof Time in OWL : 

The Future of Time in OWL Might also represent ordering of time or intervals, but most useful applications require both concrete domains and individuals highly speculative at this time but description logics are closely related to formally to temporal logics, so …