Representation

The user's beliefs, knowledge and intentions are represented by means of a modal logic whose main modal operators are Bel (the belief operator), K (the knowledge operator), Goal (the basic operator used for expressing the purposes of an agent), Know-about (expressing the knowledge about the concepts of the domain), Knowif (expressing that an agent knows the truth value of a condition [Allen1983]), Knowref (expressing that an agent knows the referent of a description [Allen1983]), Know-act (expressing that a user knows the structure of an action: e.g. its preconditions, decomposition, etc), Intend1 and Intend2 (which, respectively, specify that an agent is committed to performing an action or achieving a condition by means of some action [Cohen and Levesque1990]).

Formally:

a)

Bel is the modal belief operator and it is axiomatized with the Weak S5 logic.

b)

K(agt,x) Bel(agt,x) x.

c)

Goal(agt,x) identifies the possible worlds where x is true as corresponding to agt's desires.

d)

Know-about(agt,conc) K(agt, concept(conc))

e)

Knowif(agt,pred) (pred Bel(agt,pred)) ( Bel())

f)

Knowref(agt, ref, descr) K() ( Bel(agt, )

g)

Intend1(agt,act) means that agt has the persistent goal that action act is executed and agt is aware of that (i.e. s/he does not execute act accidentally) [Cohen and Levesque1990].

h)

Intend2(agt,cond) means that agt has the persistent goal to achieve the condition cond and s/he is committed to some action for making cond true [Cohen and Levesque1990].

The domain knowledge of an agent may be characterized in the following way:

- Beliefs and knowledge about the facts in the domain. E.g: the user IS (for Information Seeker) knows/believes that Professor Smith is the teacher of Geometry:

K(IS, teacher-of(Smith, Geometry)) / Bel(IS, teacher-of(Smith, Geometry))

- Knowledge about the concepts in the domain. E.g: the user knows about the computer concept.

Know-about(IS, conc( computer))

- Beliefs and knowledge about the structure of the concepts in the domain (relationships among the concepts of the domain). E.g: the user knows/believes that the ``Professor'' concept is a subconcept of ``Department employee''.

K(IS, x (Professor(x) Department-employee(x))) /

Bel(IS, x (Professor(x) Department-employee(x)))

- Beliefs and knowledge about the structure of the actions in the domain. E.g: the user knows that, in order to talk to Prof.Smith, s/he must phone him and fix an appointment. Then s/he must go to his office (at the time of the appointment) and talk to him.

In order to deal with the last kind of information, we introduce the modal operator Know-act, defined below.

i)

Know-act(agt,act)  Know-env(agt,act) 

		 (.decomp(act,d)  K(agt, decomp(act,d))) 


		 (.in-decomp(a,d)  Know-env(agt,a))

where

 Know-env(agt,act)  Know-restr(agt,act)  
Know-constr(agt,act) 

		 Know-prec(agt,act)  Know-post(agt,act)

Know-restr(agt,act) .restr(act,x) Bel(agt, restr(act,x))

Know-constr(agt,act) .constr(act,x) Bel(agt, constr(act,x))

Know-prec(agt,act) .prec(act,x) Bel(agt, prec(act,x))

Know-post(agt,act) .post(act,x) Bel(agt, post(act,x))

The above modal operators have the following intuitive meaning: Know-env expresses the fact that agents know the ``environment'' of an action, that is, its preconditions, restrictions on the parameters, constraints and postconditions. Know-act expresses the fact that agents have complete knowledge of an action: that is, they know the environment and the decomposition of the action. Notice that agents are supposed to know only the environment of the steps in the decomposition of the main action: in fact, to require that they also know their decompositions would be a strong hypothesis, involving complete knowledge of the actions at each level in the decomposition of the main action. The requirement that agents know that d is the decomposition of act implies, in particular, that they know the order of the actions in d, because d is intended as an ordered sequence of actions. The meaning of Know-restr, know-constr, know-prec and know-post is, at this point, self-explanatory. Moreover, decomp(act,d) means that d is the decomposition of action act; in-decomp(a,d) states that action a is part of the decomposition d; restr(act,x), constr(act,x), prec(act,x) and post(act,x) specify, respectively, that x is a restriction, constraint, precondition or postcondition of act.

The UM is a collection of modal formulae of the type defined above and is built during the analysis of the dialogue by means of the activation of stereotypes and application of UM acquisition rules. Each stereotype contains three kinds of information: the prototypical individuals' beliefs about the world description and about specific facts, their goals and their knowledge about the actions defined in the plan library. Figure shows the contents of the Student and Beginner-student stereotypes ( Student is more general than Beginner-student, that inherits features from it). Stereotypes are activated by their triggers or, in alternative, because a strictly related stereotype is activated (e.g. Student is activated by the activation of Beginner-student).

  
Figure: Two example stereotypes