Domain‐independent Temporal Reasoning With Recurring Events

Abstract

Numerous examples of temporal reasoning involve a process of abstraction from the number of times an event is to occur or the number of times events stand in a temporal relation. For example, scheduling a recurring evenf such as one's office hours may consider things like the relative temporal ordering of the ofice hours and anumber of other events in a given work day. The number of times office hours will actually be held may be unknown, even irrelevant.at the time of scheduling them. The objective of this article is to formulate a domain-independent framework for reasoning about recurring events and their relations. To achieve this end, we propose an ontology of recurrence based on the model-theoretic structure underlying collective predication using plural noun phrases. We offer a calculus of binary temporal relations for temporal collections based on a well-defined transformation of interval temporal relations into recurrence relations. Finally, we describe a reasoning framework based on manipulating knowledge stored in temporal relation nerworks, which is in turn a specialization of the CSP (constraint satisfaction problem) framework. The reasoner manipulates recurrence relations in the network to determine the network's consistency or to generate scenarios.The work here is motivated by the observation that many applications of temporal reasoning seem to require manipulation of recurring events. This section provides examples from scheduling, planning, and managing temporal data for illustration.First, consider a scheduling problem. In certain domains such as telescope observation scheduling (Drummond et al. 1994), an effective scheduler should be responsive to the tendency for a schedule to "break" during execution. Breakage is due to the temporal uncertainty of the initial knowledge about the durations of events to be scheduled. This uncertainty can be measured in terms of statistical data that characterize the mean and standard deviation of the duration of each event. These data are generated from observations of repeated executions of the events. Hence the effective scheduling and rescheduling of future events (as a result of schedule failure during execution) requires a representation and manipulation of recurring events.More generally, planning and scheduling tasks might involve constraints in which the number and even the ordering of the events are unspecified. For example, consider the constraint on a schedule imposed by the sentence Office hours should be held once a week on teaching days, preferably before the hour one's classes begin to meet. A schedule satisfying this constraint will be an assignment to recurring events (classes, office hours), the number of which may be unknown. Furthermore, from the information specified in the sentence All classes are held in the morning it is possible to infer, again with no knowledge of the number of events involved, the proposition expressed by Office hours will always be held in the morning. A formal characterization of the temporal entity assigned to thes...

Toward a comprehensive treatment of temporal constraints about periodic events

“…On the other hand, approaches in the AI field (including Refs. 1,35,36,39,42,46,47, and 75) mainly focused on qualitative temporal constraints between classes of events only (such as the one in Example 1) without taking into account perioddependent constraints (as in .…”

Recursive representation of periodicity and temporal reasoning

“…This is done until the last triple in RepSpec is reached (else branch of if statement in step 4), then the procedure unfoldNode is called (step 6) to continue the unfolding on the child node in the STP tree. Finally, unfoldRep adds to the STP (steps 7-12) the constraints corresponding to the semantic assumptions of the construct: -the repetitions must be included in a time procedure classConsistency(T : CKB) (1) initialize S to an empty STP (2) unfoldNode(root(T), S) (3) S' := FloydWarshall(S) (4) return S' procedure unfoldNode(X : STPNode, S : STP) (1) add to S the placeholder class C X (2) forall C A | C A is not a repeated class in X do (3) add to S the class C A od (4) forall C R | C R is a repeated class in X do (5) let RepSpec = (R 1 , …, R n ) be the repetition specification of class C R (6) C sub := unfoldRep(X, C R , RepSpec) (7) add to S the constraints that C sub ⊆ C X od (8) for each monadic constraint in X do (9) add the constraint to the corresponding classes in S (10)for each binary constraint in X do (11) add the constraint to the corresponding classes in S return C X procedure unfoldRep(X : STPNode, S : STP, C : Class, RepSpec = < R 1 , R 2 ,…, R n >) (1) add to S the placeholder class C 1 (2) let R 1 = <nRep 1 , IT 1 , constrs 1 > (3) for r := 1 to nRep 1 do (4) if R 1 is not the last one in RepSpec then (5) C sub,r := unfoldRep(X, C, (R 2 , …, R n )) else (6) C sub,r := unfoldNode(child(C, X)) od (7) add to S the constraint that duration of C 1 is IT 1 (8) add to S the constraints that C sub,i ⊆ C 1 , i = 1, …, nRep 1 (9) add to S the constraints that C sub,i+1 is after C sub,i , i = 1, …, nRep 1 -1 (10)add to S the possible constraint fromStart in constrs 1 in R 1 between C 1 and C sub,1 (11)add to S the possible constraint toEnd in constrs 1 in R 1 between C sub,nRep1 and C 1 (12)add to S the constraints inBetween and inBetweenAll in constrs 1 in R 1 between C sub,i and C sub,i+1 , i = 1, …, nRep 1 -1 return C 1 -each repetition must be included in the I-Time (step 8); -the repetitions must not overlap (step 9); -the repetitions must follow the possible pattern in repConstraints (steps 10-12). It is possible to test the consistency of the resulting STP S (step 3 of procedure classConsistency) by propagating the constraints using the Floyd-Warshall's all-pairs shortest path algorithm.…”

“…Morris et al ( [10,11,12]) dealt only with qualitative constraints between repeated events. Repeated events are used as "classes" of events, with different quantifiers relating them.…”

Symbolic user-defined periodicity in temporal relational databases

“…For instance, within the artificial intelligence community, most attention has been devoted to the treatment of qualitative temporal constraints (e.g., "before") between events which repeat in time (see, e.g., [25], [26], [28], [33], [40], [43]). On the other hand, approaches in classical temporal logic (see, e.g., [1], [30]) deal with truth and validity of logical formulae, specifying how predicates change value over time.…”