Dialogue Modeling

Task-Oriented Dialogues Online appointment manager

– Schedules and co-ordinates meetings between people

User : Can you schedule a meeting with John on Tuesday?

System : John is free from 2pm to 4pm.User : How about Thursday?System : 10am?User : Fine, thanks.

How could the system work?

How can it understand the requests?

What knowledge does it need?

What reasoning must it do?

Plan-based Inference Use knowledge about people and

about the nature of requests to conduct the dialogue

Use predicate logic to perform the inference, and direct the dialogue

Lecture Outline

1. Intuition behind reasoning

2. Formal definitions of belief and desire in predicate calculus

3. Inference rules for belief and desire

4. Work through the process for the first line of the dialogue!

Indirect Requests “Can you schedule a meeting with John on Tuesday?”

There are many other ways to make the same request:

– “Can I meet with John on Tuesday?”[ question the ability to perform the action]

– “I want to meet John on Tuesday.”[ mention the speaker’s desire to perform the action.]

Top-Level intuition A request is made, whose surface

level interpretation doesn’t make sense according to Grice’s Maxims. It can only be interpreted as really representing a deeper indirect dialogue act.

“Can I go to the bathroom”

Detailed Reasoning“Can you schedule a meeting with John on Tuesday?”

1. X has asked a question about whether I have the ability to perform an action

2. I assume that X is being cooperative, and his utterance has some aim.

3. X knows I can perform the action, and there is no alternative explanation for interest in my theoretical abilities.

Detailed Reasoning …4. Therefore, X probably has some other illuctionary

motive.

5. A preparatory condition for a directive is that the hearer be able to perform the action.

6. X has asked whether I am prepared for the action of scheduling appointments.

7. We are in a dialogue where scheduling appointments is a common action.

8. Therefore, X wants to schedule an appointment.

But this is informal…

How can we formalize this line of reasoning?

Lecture Outline

1. Intuition behind reasoning

2. Formal definitions of belief and desire in predicate calculus

3. Inference rules for belief and desire

4. Work through the process for the first line of the dialogue!

Propositional Logic Informally,

– Variables either true or false– Connected with and (^), or (V), not (~),

Implies (->)

– Example formulas A ^ B (A and B) (A ^ B) -> (A V B)

Predicate Calculus Functions introduced :

– E.g. Happy(A) New operators :

– forall, exists Allows statements like

– exists(a) : happy(a) There exists someone who is happy

– forall(x) : grad_student(x) -> coffee_addict(x) All grad students are coffee addicts

What needs to be modeled?

S believes p– B(S,P)

S knows P– Know(S,P) = P ^ B(S,P)

S knows whether P– KnowIF(S,P) = Know(S,P) V Know(S,~P)

S wants A– W(S,P) e.g. P = ACT(H)

Exploring the model… Two actors H(earer) and S(peaker)

– W(H,B(S,P)) = H wants S to believe P an act of convincing

– Schedule(H,S,X) = the hearer schedules S for an appoint at X time– KnowIf(H,S,CanDo(X)) = hearer knows whether

the Speaker can do something– InformIf(H,S,X) = hearer informs the speaker

whether X is true or not true– S.Request(S,H,X) = speaker makes a direct

request of the hearer

Surface Meaningin Predicate Logic

So for the statement– “Can you schedule a meeting with John

on Tuesday?”

The predicate logic form would be :

S.Request(S,H,InformIf(H,S,CanDo(H,Schedule(X))))

So how do we get to the deeper meaning –

The Indirect Request

Lecture Outline

1. Intuition behind reasoning

2. Formal definitions of belief and desire in predicate calculus

3. Inference rules for belief and desire

4. Work through the process for the first line of the dialogue!

Action Schema ScheduleMeeting(A,B,T,D)

– Constraints : Person(A) ^ Person(B) ^ TimeOfDay(T) ^ Day(D) ^ Building(Q)

– Precondition : Free(A,T,D) ^ Free(A,T,D)

^ HasRoom(Q)– Effect : ~Free(A,T,D) ^ ~Free(A,T,D)– Body : BookRoom(T,D)

Relevant Speech Acts for Indirect Speech 1

Inform(S,H,P) : informs the hearer by causing the hearer to believe that the speaker wants them to know something– Constraints : Speaker(A) ^ Hearer(H) ^

Proposition(P)– Precondition : Know(S,P) ^ W(S,Inform(S,H,P)– Effect : Know(H,P)– Body : B(H, W(S,Know(H,P)))

Relevant Speech Acts for Indirect Requests 2

InformIF(S,H,P) used to inform the hearer whether a proposition is true or not– Constraints : Speaker(S) ^ Hearer(H) ^

Proposition(P)– Precondition : Know(S,P) ^

W(S,InformIF(S,H,P)– Effect : KnowIf(H,P)– Body : B(H, W(S, KnowIf(H,P)))

Relevant Speech Acts for Indirect Requests 3

Request(S,H,ACT) directive speech act requesting an action be performed– Constraints : Speaker(S) ^ Hearer(H) ^

Act(A) ^ H is an agent of ACT– Precondition : W(S,Act(H))– Effect : W(H,Act(H))– Body : B(H,W(S,Act(H)))

Started from

“Can you schedule a meeting with John on Tuesday”

Now must go from :

S.Request(S,H,InformIf(H,S,CanDo(H,Schedule(X)))

Request(S,H,Schedule(X))

But How?

Specialized Dialogue “Plausible”

Inference Rules PI.AE : If Y is an effect of action X, and

H believes that S wants X done, then it is plausible that H believes S wants Y to be true

PI.PA : If X is a precondition of action Y, and H believes S wants X to obtain, then plausible that H believes S wants Y to be done

Specialized Dialogue “Plausible”

Inference Rules (cont.) PI.BA : If X is part of the body of Y,and

H believes S wants X done, then plausible that S wants Y done

PI.KP : If H believes S wants to KnowIF(P) then H believes S wants P to be true

E1.I – these rules can be combined recursively

Lecture Outline

1. Intuition behind reasoning

2. Formal definitions of belief and desire in predicate calculus

3. Inference rules for belief and desire

4. Work through the process for the first line of the dialogue!

We start with… S.Request(S,H,InformIf(H,S,CanDo(H,

Schedule(X)))– Speaker is requestion to know if the hearer is

able to perform the scheduling job Then use PI.AE

– B(H,W(S, InformIf(H,S,(CanDo(H, Schedule(X)))– The hearer believes that S wants the hearer to

inform whether or not the hearer can carry out the scheduling task

B(H,W(S, InformIf(H,S,(CanDo(H, Schedule(X)))

Now PI.AE (again)– B(H,W(S,KnowIf(H,S,(CanDo(H, Schedule(X)))– The hearer believes that S wants to know

whether or not the hearer can carry out the scheduling task

B(H,W(S,KnowIf(H,S,(CanDo(H, Schedule(X)))

PI.KP– B(H,W(S,CanDo(H,Schedule(X)))

– Hearer believes that the speaker wants the hearer to be able to do the task

– (otherwise the speaker wouldn’t ask about it)

B(H,W(S,CanDo(H,Schedule(X)))

PI.PA– B(H,W(S,Schedule(X)))– The hearer realizes that S wants to

schedule X

B(H,W(S,Schedule(X)))

PI.BA– Request(H,S,Schedule(X))

– Hearer understands that S is making a request to schedule a meeting.

1 line down 5 to go… These list of plausible inferences not

complete, nor are the action schemas More are needed Furthermore, the method for searching the

space to find the right chain of inferences is under specified (here)

But – we’ve shown a formal method for the intuition established at the beginning