DELIVERABLE Task Taxonomies for Knowledge Content

Plan(x) → Plan(x) ∧ ∀yz. ((Role(y) ∧ Uses(x,y)) → (Endurant(z) ∧ Selects(y,z))) ∧ ∀wk. ((Task(w) ∧ Uses(x,w)) → (Perdurant(k) ∧ Selects(w,k))) only states general restrictions over plan components and situation elements. We need to express acondition by which an instance of an abstract plan specifies instances of plan components, but noinstances of situation elements, e.g. that manager selects some (if any) instance of person. A circumstantial plan has all components selecting named individuals from the ground ontology (e.g.only specific persons, specified resources, a finite number of time intervals and space regions, etc.): CircumstantialPlan(x) =df Plan(x) ∧ ∀y. (Concept(y) ∧ Uses(x,y)) → ∃z. Entity(z) ∧ Selects(y,z)* *provided that z is a named entity, and not a skolemized individual (this is relevant only for thelanguages allowing skolemization btw). A saturated plan is a plan that cannot be executed twice, since it defines spatio-temporal parametersrestricted to one value, e.g. one of its tasks selects an event that is valued by a definite temporal valuein a definite space region: METOKIS 507164D07 – Task taxonomies for knowledge content Version 1.1Page 35 of 102SaturatedPlan(x) =df Plan(x) ∧ ∃y,z. Parameter(y) ∧ Parameter(z) ∧ Uses(x,y) ∧ Uses(x,z) ∧ ∃t,s.ValuedBy(y,t) ∧ TimeInterval(t) ∧ ¬∃t1. TimeInterval(t1) ∧ ValuedBy(y,t1) ∧ t?t1 ∧ ValuedBy(z,s) ∧ SpaceRegion(s) ∧ ¬∃s1. SpaceRegion(s1) ∧ ValuedBy(y,s1) ∧ s?s1 Of course, in the case of maximal spatio-temporal regions, a saturated plan tends to approximate anabstract plan from the execution viewpoint, but these worst cases are unavoidable when dealing withmaximality. Plan executions are situations that proactively satisfy a plan (cf. definition of P-SAT above): PlanExecution(x) =df Situation(x) ∧ ∃y. Plan(y) ∧ P-SAT(x,y) Subplan executions are parts of the whole plan execution: ∀p1,p2,s1,s2. (Plan(p1) ∧ Plan(p2) ∧ ProperPart(p1,p2) ∧ P-SAT(p1,s1) ∧ P-SAT(p2,s2)) →ProperPart(s1,s2) A goal situation is a situation that satisfies a goal: GoalSituation(x) =df Situation(x) ∧ ∃y. Goal(y) ∧ SAT(x,y) Opposite to the case of subplan executions, a goal situation is not part of a plan execution: GoalSituation(x) → ∀y,p,s. (Goal(y) ∧ SAT(x,y) ∧ Plan(p) ∧ ProperPart(p,y) ∧ P-SAT(s,p)) →