∙ 𝑅𝑒 is a set of continuous temporal relaxations for some episodes with free con-straints in𝑅𝐸.
∙ ∆′𝑡 is a relaxation for∆𝑡, and ∆′𝑡≥∆𝑡.
∙ 𝑁𝑎𝑙𝑙𝑜𝑐 is a TPNU that grounds all episodes with probabilistic durations using fixed lower and upper bounds.
∙ 𝐸′ is a set of episodes that encodes the traversal activities between locations, generated by the routing function. Each 𝑒′ ∈ 𝐸′ encodes the traversal time associated with an agent’s movement between locations specified in𝐴, following the order defined by 𝑆.
A feasible solution to a cc-pTPN provides a grounded and controllable STPU. We can also separate the solutions into two categories, strongly controllable and dynami-cally controllable, based on the type of execution strategies a solution can enable.
Given an over-subscribed cc-pTPN, there is usually more than one valid resolution to it due to the continuous property of temporal and chance constraint relaxations.
It is important to prioritize the resolutions and enumerate only preferred ones of lower cost for the users. In addition, finding a good resolution usually requires a considerable amount of negotiation since the users may not have encoded all their requirements in the input problem. BCDR needs to learn about them through the interaction before reaching an agreement with the user.
adjustments to the timing requirements, if necessary. We extend the variable repre-sentation for their activities to be parameterized, which include domain constraints that encode the meanings as sets of semantic queries. These semantic queries capture the user requirements on the state that cannot be encoded by only using temporal constraints, and describe allowed values for the domain of these variables.
Leave Office
18:00 Arrive Home
< 210 mins (SI) Arrive
Cinema Leave
Cinema Comedy Movie (SI)
Arrive Restaurant
Leave Restaurant Chinese Restaurant (SI,CR)
(movie m) ∧ (genre g) ∧ (hasGenre m g) ∧(surface g ’Comedy’)
(restaurant r) ∧ (cuisine c) ∧ (servesCuisine r c) ∧(surface c ’CHINESE’)
Figure 2-15: A TPN for Simon’s trip
For example, the extended TPN for Simon and Christian’s travel problem is shown in (Figure 2-15), which again encodes the two activities for dinner and movie, as well as the temporal requirements over the trip departure and completion times. The two activities requested by them are associated with a set of semantic queries that encode the genre and cuisine requirements. When implemented with SparQL, these queries can be expressed as the following (m.05p553 and m.01xw9 are Freebase Machine IDs for entity Comedy film and Chinese food):
∙ Comedy Movie:
SELECT ?m WHERE{ //select subject ?m that meets the following triples
?m ns:type.object.type ns:film.film. //subject ?m is of type film
?g ns:type.object.type ns:film.film_genre. //subject ?g is of type genre
?m ns:film.film.genre ?g. //?m has genre ?g
FILTER (?g =<http://rdf.freebase.com/ns/m.05p553>).} //?g is object m.05p553
∙ Chinese Restaurant:
SELECT ?r WHERE{
?r ns:type.object.type ns:dining.restaurant.
?c ns:type.object.type ns:dining.cuisine.
?r ns:dining.restaurant.cuisine ?c.
FILTER (?c = <http://rdf.freebase.com/ns/m.01xw9>).}
Given the domain constraints of the variables for dinner and movie, we pass their semantic queries to a knowledge base, which can search through multiple data sources and retrieve candidate options for the activities. These options will then be encoded as alternative episodes for the activities and added to the TPN. For example, the expanded TPN for Simon and Christian’s outing trip is shown in Figure 2-16.
Leave Office
18:00 Arrive Home
< 210 mins 20:00 Joy
at AMC 16 (124 mins) 19:30 Norm of the
North at AMC 20 (90 mins)
Panda Express (30 mins)
Magic Wok (30 mins)
Figure 2-16: An expanded TPN with alternative activity candidates
Due to the long travel times to and from the candidate Chinese restaurants, no solution can be found that meets all temporal requirements. Hence the system engages Simon and Christian, and initiates a discussion about possible resolutions for their
problem.
DA: Simon, you may have dinner at Magic Wok then watch the 8pm Joy at AMC 16. However, due to the length of the movie you won’t be back home until 10:34pm. Is that OK?
Simon: No, I must arrive home by 9:30pm.
DA: OK, then Simon can you leave office 30 minutes earlier? If so you may watch Norm of the North at 7:30pm, and arrive home at 9:30pm.
Simon: No I cannot leave office before 6pm.
DA: Simon and Christian, How about eating at Sunny Bowl, a Ko-rean restaurant? It is closer and Simon can make the 7:30pm movie without leaving any earlier.
Christian: That’s fine.
Simon: Sounds good. Thank you.
In this example, Simon cannot change the departure and arrival times. As a result, he rejected the first two proposals. Previous approaches would have failed at this step, as no more temporal relaxation can be found that resolves the conflicts between long travel times to the restaurants and movie start times. However, the domain relaxation extension to BCDR weakens the domain constraints for the restaurant variable, such that three new options became available for his trip (Figure 2-17). In this case, BCDR discovered a close alternative, Korean, for the cuisine requirement of restaurant. It then queried the knowledge base to retrieve additional candidate restaurants, and found one that is closer to their home and satisfies all temporal constraints (Figure 2-18).
This example demonstrates the desired behavior of domain relaxation: it allows BCDR to resolve over-subscribed travel plans through relaxing the domain con-straints, and actively searching for candidates that are not encoded in the original problem. It gives the users more flexibility in resolving their over-subscribed plans when they cannot compromise on the temporal requirements.
CHINESE RESTAURANT
?r ns:type.object.type ns:dining.restaurant.
?c ns:type.object.type ns:dining.cuisine.
?r ns:dining.restaurant.cuisine ?c.
FILTER (?c = <http://rdf.freebase.com/ns/m.01xw9>).
KOREAN RESTAURANT
FILTER (?c = <http://rdf.freebase.com/ns/m.048vr>).
{Panda Express, Magic Wok}
{Sunny Bowl, Bibimbowl, Jang Su Jang}
KNOWLEDGE BASE
Relaxing Cuisine Constraint
+
Figure 2-17: Domain relaxation for the restaurant cuisine
18:00
Leave Office < 210 mins Arrive Home
19:30 Norm of the North at AMC 20 (90 mins) Sunny Bowl (30 mins)
Drive to AMC 20 [25,30]
Drive to Sunny Bowl
[15,20]
Drive Home [20,25]
(a) Simon’s trip
17:45
Leave Office < 180 mins Arrive Home
Sunny Bowl (30 mins) Drive to
Sunny Bowl [25,35]
Drive Home [30,45]
(b) Christian’s trip
Figure 2-18: A solution enabled by relaxed cuisine constraint