Ontologies Ontologies Modelling Static Knowledge Modelling Static Knowledge Modelling Dynamic Knowledge Modelling Dynamic Knowledge Summary Summary Where are we? Knowledge Engineering Last time . . . Semester 2, 2004-05 ◮ we attempted a transition from Knowledge Acquisition to Michael Rovatsos Knowledge Representation mrovatso@inf.ed.ac.uk Focus of the KR&R part of the module . . . ◮ representation of complex domain knowledge ◮ ontology reasoning systems ◮ dealing with uncertainty Today . . . Lecture 5 – Basics of Ontologies ◮ basics of ontologies 25th January 2005 ◮ formalising certain kinds of knowledge Informatics UoE Knowledge Engineering 1 Informatics UoE Knowledge Engineering 67 Ontologies Ontologies Modelling Static Knowledge Modelling Static Knowledge Modelling Dynamic Knowledge Modelling Dynamic Knowledge Summary Summary Ontologies Ontologies What are they good for? ◮ In toy domains, easy to describe relevant objects and ◮ Knowledge sharing and reuse (agreeing on a vocabulary) relationships to reason about ◮ Support of use of knowledge level vs. symbolic level ◮ In more complex domains, a principled way of structuring ◮ Make ontological commitments (decisions regarding the domain of discourse is required conceptualisation which relfect points of view) explicit ◮ Ontology ◮ Interaction problem: choice of knowledge representation ◮ philosophically speaking: a theory of nature of being or depends on problem to solve and inference mechanisms to existence be used ◮ practically speaking: a formal specification of a shared Many different representations, will use first-order logic (FOL) conceptualisation and discuss various knowledge modelling issues Informatics UoE Knowledge Engineering 68 Informatics UoE Knowledge Engineering 69
Ontologies Ontologies Modelling Static Knowledge Modelling Static Knowledge Modelling Dynamic Knowledge Modelling Dynamic Knowledge Summary Summary Example: Attribute Ladder Example: Concept Tree Informatics UoE Knowledge Engineering 70 Informatics UoE Knowledge Engineering 71 Ontologies Ontologies Modelling Static Knowledge Modelling Static Knowledge Modelling Dynamic Knowledge Modelling Dynamic Knowledge Summary Summary Example: Composition Ladder Example: Process Ladder Informatics UoE Knowledge Engineering 72 Informatics UoE Knowledge Engineering 73
Ontologies Ontologies Modelling Static Knowledge Modelling Static Knowledge Modelling Dynamic Knowledge Modelling Dynamic Knowledge Summary Summary Example: Process Map Example: State Diagram Informatics UoE Knowledge Engineering 74 Informatics UoE Knowledge Engineering 75 Upper Ontologies Upper Ontologies Ontologies Ontologies Categories Categories Modelling Static Knowledge Modelling Static Knowledge Physical Composition Physical Composition Modelling Dynamic Knowledge Modelling Dynamic Knowledge Measurements Measurements Summary Summary Substances and Objects Substances and Objects Upper Ontologies Categories General framework of concepts (convention: from top to bottom more specific) ◮ Categories play an important role in reasoning (although Anything individual objects are interacted with in practice) ◮ Representation through predicates ( Car ( X )) or through AbstractObject GeneralisedEvent reification ( Member ( X , Cars )) Set Number RepresentationalObject Interval Place PhysicalObject Process ◮ One way of defining categories: category = a collection of its members Category Sentence Measurement Moment Thing Stuff ◮ Inheritance most common relationship between categories Time Weight Animal Agent Solid Liquid Gas Human Informatics UoE Knowledge Engineering 76 Informatics UoE Knowledge Engineering 77
Upper Ontologies Upper Ontologies Ontologies Ontologies Categories Categories Modelling Static Knowledge Modelling Static Knowledge Physical Composition Physical Composition Modelling Dynamic Knowledge Modelling Dynamic Knowledge Measurements Measurements Summary Summary Substances and Objects Substances and Objects Categories Categories ◮ Subclasses inherit properties of super-classes ( OOP) ◮ Can use FOL to express all kinds of properties of ◮ Taxonomy : an ontology of categories induced by categories: ◮ Subclasses: Basset ⊂ Dog , Dog ⊂ Animal subclass relationships ◮ Describing properties/inferring class membership: ◮ Problems of multiple inheritance ∀ x Basset ( x ) ⇒ GoodScent ( x ), ◮ Example: The Nixon diamond ∀ x GoodScent ( x ) ⇒ Basset ( x ) Pacifist ◮ Category properties: Basset ∈ Species ◮ Further common properties of categories: ◮ Disjointness Quaker Republican ◮ Exhaustive decomposition ◮ Partition ◮ Exercise: describe these in FOL Nixon Informatics UoE Knowledge Engineering 78 Informatics UoE Knowledge Engineering 79 Upper Ontologies Upper Ontologies Ontologies Ontologies Categories Categories Modelling Static Knowledge Modelling Static Knowledge Physical Composition Physical Composition Modelling Dynamic Knowledge Modelling Dynamic Knowledge Measurements Measurements Summary Summary Substances and Objects Substances and Objects Physical Composition Measurements ◮ Quantitative measurements: mass, price, weight etc. ◮ Want to express physical composition of objects ◮ Price ( MyBasset ) = Pounds (500) = Euro (750) ◮ part-of relation (reflexive,transitive), ◮ Abstract objects: Pounds (500) is not a 500 pound e.g. PartOf ( Leg , Body ) amount of money/account balance ◮ How do we express a collection of concrete objects, e.g. a ◮ Each measurement value exists only once bag of apples? ◮ Qualitative measurements: focus on ordering ◮ Use of “set” problematic, since a set has no weight (is btw. different values, not the values themselves not an object itself) ◮ Example: use of rule ◮ Define “bunch”: ∀ x x ∈ s ⇒ PartOf ( x , BunchOf ( s )) ◮ Smallest object satisfying this condition ( logical ∀ x ∀ y Vehicle ( x ) ∧ Vehicle ( y ) ∧ Faster ( x , y ) ⇒ Prefer ( x , y ) minimisation ): sufficient (KB contains facts Faster ( Car , Bicycle )) rather ∀ y [ ∀ x x ∈ s ⇒ PartOf ( x , y )] ⇒ PartOf ( BunchOf ( s ) , y ) than getting speed measurements for each type of vehicle ◮ Area of qualitative physics Informatics UoE Knowledge Engineering 80 Informatics UoE Knowledge Engineering 81
Upper Ontologies Ontologies Ontologies Categories Modelling Static Knowledge Modelling Static Knowledge Situation Calculus Physical Composition Modelling Dynamic Knowledge Modelling Dynamic Knowledge Frame Problem Measurements Summary Summary Substances and Objects Substances and Objects Expressing Change ◮ Intuition: specify objects in the world and put them ◮ Straightforward way of capturing change: use time-steps together to obtain composite objects t in all predicates, and express change by reasoning about ◮ Problem of individuation (division into distinct object) subsequent time-steps: ◮ No problem for count nouns (cats, dogs, apples, planets) ∀ t Rains ( t ) ⇒ WetGround ( t + 1) ◮ But how about “stuff” (water, air, energy)? ◮ Alternatively, concentrate on situations brought about ◮ Example: Assume category Water by different actions situation calculus ◮ x ∈ Water ∧ PartOf ( x , y ) ⇒ y ∈ Water ◮ Situations are logical terms S 0 , S 1 , etc. ◮ x ∈ Water ⇒ BoilingPoint ( x , 100 o C ) ◮ Function Result ( a , s ) used to name situation that results ◮ But still problems: SaltWater subcategory of Water but from executing action a in s how about PintsOfWater ? ◮ Sometimes useful to extend this to sequences of actions ◮ Underlying problem: difference between intrinsic properties (properties of the substance, retained under Result ([ a | rest ] , s ) = Result ( rest , Result ( a , s )) subdivision) and extrinsic properties of objects Informatics UoE Knowledge Engineering 82 Informatics UoE Knowledge Engineering 83 Ontologies Ontologies Modelling Static Knowledge Situation Calculus Modelling Static Knowledge Situation Calculus Modelling Dynamic Knowledge Frame Problem Modelling Dynamic Knowledge Frame Problem Summary Summary Expressing Change Frame Problem ◮ Fluents = functions/predicates that vary from situation to situation (opposite: atemporal / eternal ◮ Problem: Effect axioms say what changes, but not what functions/predicates) stays the same! ◮ Describe actions by possibility and effect axioms: ◮ In the above example: How can we infer ◮ Possibility axiom: Preconditions ⇒ Poss ( a , s ) Clear ( A , Result ( Stack ( A , B ) , s )? ◮ Effect axiom: Poss ( a , s ) ⇒ Changes that result from the action ◮ Frame problem : Problem of representing all things that ◮ Example (blocks world): stay the same ◮ Possibility axiom: ◮ Expressing what does stay the same through frame ∀ s Clear ( A , s ) ∧ Clear ( B , s ) ⇒ Poss ( Stack ( A , B ) , s ) axioms is one possibility ◮ Effect axiom : ∀ s Poss ( Stack ( A , B ) , s ) ⇒ On ( A , B , Result ( Stack ( A , B ) , s )) ∧ ¬ Clear ( B , Result ( Stack ( A , B ) , s ) Informatics UoE Knowledge Engineering 84 Informatics UoE Knowledge Engineering 85
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