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The Modelling We Do

The Modelling We Do. Enrico Motta. Modelling Primitives Classes Slots Instances Relations Functions Rules Axioms. Reasoning Services Query Answering (Ask) Constraint Checking (Tell). Class Modelling. Intensional vs Extensional Definitions Classes as Objects of Discourse

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The Modelling We Do

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  1. The Modelling We Do Enrico Motta

  2. Modelling Primitives Classes Slots Instances Relations Functions Rules Axioms Reasoning Services Query Answering (Ask) ConstraintChecking(Tell)

  3. Class Modelling • Intensional vs Extensional Definitions • Classes as Objects of Discourse (def-class person) (def-instance enrico person) (def-class guideline-user-type () ?x :iff-def (or (subclass-of ?x generic-care-giver ) (= ?x patient)))

  4. Constraints on Class Definitions (def-class project (activity) ?x((has-leading-organization :type organization) (involves-organization :type organization :min-cardinality 1)(has-project-leader :type person)(has-project-member :type person :min-cardinality 1)(funding-source :type organization)(has-web-address :type URL)(addresses-generic-area-of-interest :type generic-area-of-interest)):constraint (and (forall ?y (=> (has-leading-organization ?x ?y) (involves-organization ?x ?y))) (forall ?y (=> (has-project-leader ?x ?y) (has-project-member ?x ?y)))))

  5. Relations (in addition to slots) (def-relation PROJECT-INVOLVES-ORGANIZATION-UNIT (?p ?u) "It is sufficient that somebody in unit ?u works in project ?p" :constraint (and (project ?p)(organization-unit ?u)) :sufficient (and (project ?p)(organization-unit ?u) (has-project-member ?p ?x) (works-in-unit ?x ?u)))

  6. Functions (def-function filter (?l ?rel) -> ?sub-l "Returns all the elements in ?l which satisfy ?rel" :body (if (null ?l) ?l (if (holds ?rel (first ?l)) (cons (first ?l) (filter (rest ?l) ?rel)) (filter (rest ?l) ?rel)))) Holds Holds (?rel ?arg1…..?argn) iff (?rel ?arg1…..?argn)

  7. Functions (def-function EXTENSION (?r) -> ?set "The extension of a relation is the set of all tuples for which the relation holds. This is a kind of operational definition, which retrieves the set of all tuples for which the relation is predicated in the current KB. This function is restricted to defined relations only" :constraint (defined-relation ?r) :body (if (= (the-schema ?r) ?list) (eval-setofall ?list (cons ?r ?list))))

  8. Rules are also useful • Used for inferences (no constraint checking) • Separate from ontological definitions • Allow modular extensions of definitions (def-rule rule-for-collaborating#1 ((collaborates-or-collaborated-with ?p1 ?p2) if (or (and (involved-in-projects ?p1 ?project) (or (has-project-leader ?project ?p2) (has-project-member ?project ?p2))) (and (or (technology ?d) (document ?d)) (has-author ?d ?p1) (has-author ?d ?p2))) (not (= ?p1 ?p2))))))

  9. Axioms Used for additional constraint checking (def-axiom agrees-and-disagrees-are-mutually-inconsistent (forall (?a ?y) (not (exists (?x1 ?x2 ?z ?z2) (and (agrees ?x1 ?y ?z) (disagrees ?x2 ?y ?z2) (member ?a ?x1) (member ?a ?x2))))))

  10. Formulas as values (def-class classification-task (goal-specification-task) ?task ((has-goal-expression (:default-value (kappa (?task ?sols) (forall ?sol (=> (member ?sol (role-value ?task 'has-solutions)) (admissible-solution ?sol (apply-match-criterion (role-value ?task 'has-match-criterion) (role-value ?task 'has-observables) ?sol) (role-value ?task 'has-solution-admissibility-criterion)))))))

  11. Things we would also like to have • Comprehensive meta-level • Clean way to annotate individual statements (def-relation criticises (?person ?statement) • Mechanisms to define inference schemas • E.g., new inheritance mechanisms for different part-of relations

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