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D Goforth - COSC 4117, fall Ontology: structure of knowledge E.g. java programming ontology – object-oriented design: class/object inheritance and interfaces part-of hierarchy API message-passing sequential execution, threads
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OntologyApplying logic to the real world
D Goforth - COSC 4117, fall 2006 2
Real world knowledge
general knowledge /common sense reasoning
domain expertise /specific knowlege
problem /facts
example: understand a news reportlanguage and world knowledge; specific situation and terminology interpret story
D Goforth - COSC 4117, fall 2006 3
Ontology: structure of knowledge E.g. java programming ontology –
object-oriented design: class/object inheritance and interfaces part-of hierarchy API message-passing sequential execution, threads
D Goforth - COSC 4117, fall 2006 4
Ontology: structure of knowledge general knowledge: what top-level
structure? Anything
(like class Object)
AbstractObject(eternal)
GeneralizedEvent(time-limited existence)
D Goforth - COSC 4117, fall 2006 5
Upper Ontology
General knowledge
Domain knowledge
Problem facts and questions
Ontology in Knowledge base
“Abstract objects”
“Generalized events”
Categories (ontology)
Logic (sentences)
D Goforth - COSC 4117, fall 2006 7
Representing Knowledge how ‘deep’?
shallow – as predicate: Terrier(x)
deep ‘reification’category with meaning structure: Terriers ⊆ Dogs,
Dogs ⊆ Mammals Member (x, Terriers)
D Goforth - COSC 4117, fall 2006 8
Categories like set theory – easy to reason with
in FOL subcategories / subsets categories of categories intersections, unions, disjoint sets,
partitions
D Goforth - COSC 4117, fall 2006 9
Reasoning about categories disjoint subcategories – no common
objects NO: x Students, x Employed YES:x Mazdas, x Mercedes
x Mazdas ⇒ ~(x Mercedes) x Mercedes ⇒ ~(x Mazdas)
D Goforth - COSC 4117, fall 2006 10
Reasoning about categories exhaustive decomposition – all
objects of a category belong to at least one of the subcategories Namedstreets Cityroutes Numberedroads Cityroutes x Cityroutes ⇒ (x Namedstreets)
(x Numberedroads)(could be both named and numbered)
D Goforth - COSC 4117, fall 2006 11
Reasoning about categories Partitioning a category
subcategories are disjoint subcategories form exhaustive decompositione.g.,Players are teammates or opponents:Players = Teammates OpponentsTeammates Opponents = {}
D Goforth - COSC 4117, fall 2006 12
Physical objects properties
things – a pile of sand measurable / quantities
vs stuff - sand
intrinsic qualities
PhysicalObjects
StuffThings
D Goforth - COSC 4117, fall 2006 13
Situation calculus in specific domain
(TimedEvents vs AbstractObjects) some objects are ‘fluent’
functions and properties can change over time (position, orientation, etc)
some objects are ‘eternal’ existence and properties remain fixed
during period of reasoning (more efficient)(recall wumpus world example)
D Goforth - COSC 4117, fall 2006 14
GeneralizedEvents – the time problem
objects in this hierarchy have time property physical objects events processes intervals
‘fluent’ (“fleeting”) vs ‘eternal’ abstract objects
D Goforth - COSC 4117, fall 2006 15
Situation calculusuniverse is defined as
sequence of ‘situations’ ‘actions’ are like
inferences: preconditions – required
facts in current situation effects – facts that are
true in subsequent situation if action is applied
situa
tion
S 3
precondition effectaction
situa
tion
S 2
situa
tion
S 1
situa
tion
S 0
D Goforth - COSC 4117, fall 2006 16
Situation calculus - example blocks world
tabletop and three blocks actions and situations
A BC
eternal Table(x) Block(x)
fluent On(x,y,s) ClearTop(x,s)
s is situation variable
objects/terms in FOL
D Goforth - COSC 4117, fall 2006 17
Situation calculus - example actions are functions (objects) situations are objects
A BC
PutOn(x,y) preconditions:
ClearTop(x,s) ClearTop(y,s) V
Table(y) effect:
On(x,y,Result(PutOn(x,y),s))
D Goforth - COSC 4117, fall 2006 18
Situation calculus - example each situation is a function of the
previous one – Result function
A BC
Result(a,s) preconditions:
action a can be applied at s effect:
Result is next situation after a is applied at s
D Goforth - COSC 4117, fall 2006 19
T
Situation calculus - example e.g. KB:
function PutOn(x,y) ∀x (~∃y On(y,x,s)) ⇒ ClearTop(x,s) ∀x,y,s ClearTop(x,s) ^
(ClearTop(y,s) v Table(y) => On(x,y,Result(PutOn(x,y),s))
constants: A, B, C, T, S0, S1, S2,… Table(T), Block(A), Block(B), Block(C) On(A,B,S0), On(B,C,S0), On(C,T,S0)
ABC
S0
D Goforth - COSC 4117, fall 2006 20
T
Situation calculus - example action: PutOn(A,T)
preconditions: ClearTop(A,S0),Table(T) effect: On(A,T,Result(PutOn(A,T),S0))
BUT…what happens to other fluents?
some propagated, some not ABC
S1
A
D Goforth - COSC 4117, fall 2006 21
T
Situation calculus - example ‘On’ axiom: ∀x,y,z,a,s On(x,y,Result(a,s)) [ClearTop(x,s)^(ClearTop(y,s)vTable(y))^
a= PutOn(x,y)
v [ On(x,y,s)^~(a=PutOn(x,z))]
CS1
A
AB