More defining

Bijan Parsia

Constraints and Definitions

• We have relations between classes:
• C SubClassOf B
• C is a sufficient condition of B
• One way to be a B is to be a C
• B is a necessary condition of C
• If x is a C, then x is a B
• C EquivalentTo B
• C is a necessary and sufficient condition of B (and vice versa)
• When C and B are (always) names this is trivial
• But we can use class expressions in place of either
• Definitions and constraints can interact
• In surprising ways

Some definitions

Class: Father
    EquivalentTo:
        Male
        and (parentOf some owl:Thing)
Class: Carnivore
    EquivalentTo:
        (eats some Animal)
        and (eats only Animal)

Definitions have consequences

• Some are obvious:
Class: Father
    SubClassOf:
        Male
(But note that they are not equivalent.)
• Some are less so:
• Class: Carnivore   
    SubClassOf:
        Animal
• (Because of an axiom about eats)

A Functional Description

• The system has two operators
• ASK and TELL
• We can describe behavior of the system "externally"
• I.e., by responses to certain ASKs after specific TELLs
• ASK takes a state and a sentence and returns yes or no
• TELL takes a state and a sentence and returns a new state
• We can also use this to conceptualize user interaction
• This is a very constrained interface
• It allows represenation independant specification
• But, suitibly liberallized, does not ensure it

Methodology Implications

• In our situation:
• The KR system is a file + Protege + a reasoner
• Well TELL it things via the interface
• ASKing is enabled by a command
• So consider that the updating has to be independant of the reasoning
• We have a set of canonical ASKs
• I.e., all the atomic subsumptions
• The system is reactive
• We react to the system
• From dealing with inconsistencies
• To being stimulated to reflect
• Bottom-up style
• We think in terms of individuals and their relations

Taking Stock

• We started with a domain you all know a lot about
• As was shown by all the terms you threw up
• We elicited that knowledge in a very raw form
• We are refining what we elicited
• Three langauges for representing that knowledge
• English
• Nodes and arcs (semantic nets)
• And OWL (using Protege and Manchester syntax)
• We have some sense of what KR is
• And next class we're going to reflect on that

Next Coursework

• On Moodle (or should be)
• Provide definitions and constraints
• We are more concerned with your learning the system and language than a particular outcome
• Feel free to modify things to make your definitions nicer
• You have no application, so we can't hope for more
• We are aiming for a degree of richness
• Where we characterize that roughly by number and sophistication of entailments
• Due 16-10-2007