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Combining Expression and Content in Domains for Dialog Managers Bernd Ludwig

Gunther Gorzy Heinrich Niemannz FORWISS D-91058 Erlangen, Germany.

Abstract

by describing how inference is performed on the basis of such a framework. Following the approach by Hjelmslev [7], Eco [4] de nes two essential ingredients for any semiotic system (and, in particular, any natural language):  Expressiveness: what is the vocabulary, phonetics, and syntax of the language considered?  Content: what knowledge can be expressed by a given system? How (i.e. by which expressions) is this knowledge organised in the semiotic system? Obviously, the key problem is how to connect content, which exists a priori and virtually independently from any concrete language, and valid expressions. Russell [15] proposes to divide the vocabulary into two classes:  object words: de ne basic notions (in a train information scenario e.g. train, time, or station)  dictionary words: can be de ned using other words with already de ned meaning (e.g. departure time or arrival station) Trivially, there is an obvious analogy between object words and primitive concepts in description logics and dictionary words and derived concepts. We exploit this analogy to describe the application domain for a dialog manager by means of a terminology in DL. Doing this, we can de ne the meaning of basic and derived notions that are relevant in the domain under consideration.

We present work in progress on abstracting dialog managers from their domain in order to implement a dialog manager development tool which takes (among other data) a domain description as input and delivers a new dialog manager for the described domain as output. Thereby we will focus on two topics; rstly, the construction of domain descriptions with description logics and secondly, the interpretation of utterances in a given domain.

1 Introduction Current research on dialog management is guided by two dierent ideas: rstly, to describe the discourse structure that the dialog manager is able to handle by a nite automaton using possible utterances as transitions (e.g. [10]), and secondly, to view the detection of discourse structure as a parameter estimation problem and to use statistical models for the description of discourse structure (e.g. [12], [8]). Some serious problems remain with each of these approaches: rst of all, they do not integrate a user model. The nite state method imposes hard restrictions on \free dialog", as far as vocabulary, syntax and order of utterances are concerned. The statistical approach, on the other hand, suers from the sparse data problem and does not give theoretical insight into discourse theory. But as other researchers point out (see e.g. [13], [2]), it is important to explore the structure of discourse and the interactions of dialog and user model in order to obtain robust dialog systems. Studying the eect of natural language expressions on the state of discourse this paper tries to do a step in this direction by discussing the use of description logics for de ning any dialog domain formally and

2 Describing Partial Information in Dialog Contexts A key issue for dialog management is the handling of partial information provoked by \incomplete" utterances. By this notion we mean the fact that in

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the shared knowledge of the participants there is not enough information available to, e.g., answer a question posed by the speaker. For the sake of illustration, let us consider the query When does a train leave to Rome? The information given in this query is (only) partial as it is incomplete or insucient for the hearer to answer it. At least the station of departure is unknown and has to be asked for by the hearer if he wants to give some reasonable answer. We use First Order Partial Information Ionic Logic (FIL), as introduced by Abdallah [1], to handle situations of partial knowledge. FIL provides formulae (so called ionic formulae) like (f1 ; :::; k g;  ) meaning intuitively that  is true when it is plausible that  = f1 ; :::; k g (called justi cation set or justi cation context) is true, too. A formula of this type enables us to specify concepts or roles that are potentially partial in the sense discussed above. To give an example, we could say (fwant-dep(user; munich)g; dep-stat(munich)) The (informal) semantics of this formula would be: Munich is a departure-station if it is plausible that the user wants to depart from Munich, i.e. if the user has said this explicitly at some time earlier in the dialog.

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Justi cation Contexts and

log Plans

We obtain that the query \Is  true, and if it is, under what context?" follows from the given clauses under the justi cation context  = f1 ; :::; k g (and additional answer substitutions for variables, which have been omitted here). [11] describes that  is the set of dialog goals to be ful lled by the dialog manager in order to compute an answer to the user's question that respects his \personal situation" (formalized by justi cation contexts). As a consequence, the result of the inference process drives the system's dialog strategy.

4 From Notions to Vocabulary Natural languages normally oer the possibility to express the same notion by dierent synonyms. For example, one can say: When does the train leave to Rome? or, alternatively When does the train depart to Rome? In both cases, the notion of train departure is expressed. As we have inspected the EVAR1 corpus of train information dialogs, we could see that synonyms occur frequently, even in relatively simple domains as train information. Our hypothesis is that in much larger more complicated domains that allow for a greater variability of expressions and vocabulary there are even more synonyms for a certain abstract notion. To handle this phenomenon, we have to extend our domain description by adding formulae like SynC1 (x) _


_ SynCn (x) =) C (x) for any concept C and and its synonymic expressions SynCi (x) and, equally, SynR1 (x; y) _


_ SynRn (x; y) =) R(x; y) for any role R and its synonyms SynRi (x; y). Applying this idea to the two questions above we would have to introduce leave(x) _ depart(x) =) Depart(x) which \maps" the verbs leave and depart to the concept Depart.

Dia-

One of the interesting things about FIL is that it can be used to compute justi cation contexts that impose restrictions on the set of possible models for a formula  (for details, see [1]). This can be done by, e.g., resolution: Resolution in FIL works as in \normal" predicate logic. As far as ionic formulae are concerned, uni cation can assign justi cation contexts to variables: (f1 ; :::; k g;  ) and (;  ) can be uni ed under the substitution  = f1 ; :::; k g So we can write FIL programs analogously to PROLOG programs. For example: :

(f1 ; :::; k g;  )  ?  (; )

5 Integrating FIL and DL To combine the advantages of DL as a concept language for domain modelling and FIL as a tool for

? : ? :

1 EVAR is a publicly accessible information system on German Railway InterCity connections ([5]). The existing corpus of dialogs contains samples of \real world" data with \naive" users.

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whereas for role R and concepts C1 and C2 with C1 = 8R:C2 we have

describing partially de ned dialog contexts we de ne a mapping from DL to FIL that translates DL formulae into FIL formulae. Before translating the terminology that describes the application domain we mark a subset UserRel of the set of roles. UserRel is the set of all potentially partial roles, i.e. all roles that could eventually rely on information currently not available. Formally, any role that has the concept User as domain or range is a element of UserRel. Therefore, putting a role into UserRel or not is a decision which is made arbitrarily by the designer of the domain model and depends only on the analysis of the domain, but not on any theoretical or mathematical criterion. In the example (fwant-dep(user; munich)g; dep-stat(munich)) want-dep(x; y) would have to be included in UserRel as it can describe partial dialog contexts that we aim to handle dierently from \total" ones. By doing this, we want to exploit the expressiveness of ionic formulae to describe situations of partial information. More precisely, our aim is rstly to construct a domain model using DL, and secondly to incorporate such a model into the inference mechanism described in section 3. Therefore, we need a theoretical basis for the combination of DL and FIL. For a formal description of the connection of DL and FIL, we give a translation mapping  from DL to FIL which is sort of sensitive to UserRel de ned above. The mapping, of course, resembles Borgida's [3] and the one by [16] and actually is identical except of the names of roles: 8 y)g;R(x; y)); > > <  x; y:  (fR(x; R  (R) =  x; y:R(x; y); 2 UserRel > > : otherwise This says that all role names of a given TBox marked as partial are translated as ionic formulae, e.g.:  (want-dep) =  x; y:  (fwant-dep(x; y)g; want-dep(x; y)) All other symbols are translated to rst order formulae as usual by structural induction on the syntax of the DL. For example, given roles R, S1 , and S2 with R = S1 t S2 , the de nition of  is:  (R) =  x; y: (S1 )(x; y) _  (S2 )(x; y) Example:  (son t daughter) =  x; y: (son)(x; y) _  (daughter)(x; y)

 (C1 ) =  x:8y :  (R)(x; y) ?!  (C2 )(x)

Example:  (8son::male) =  x:8y :  (son)(x; y) !  (:male)(x)

As it is shown by e.g. Borgida in [3], the mapping preserves satis ability of DL expressions that are translated into a FIL formula, as FIL is an extension of First Order Predicate Logic and the translation from FIL to FOPL only uses the FOPL \sublanguage" of FIL. I.e. if a formula has some model in DL, then it has one in FIL, too. On the other hand, if a FIL expression is satis able, then it is in DL, too, if no ionic formula is contained (see [16]). A ionic formula (R(; ); R(; )) is the translation of some role R 2 UserRel whose justi cation context R(; ) can have one of the following states of acceptance2:  +  R(; ) or ?R(; ): I.e. for any model M it is impossible that Mj 6j= R(; ) $ M j= :R(; ). This observation implies that either M j= R(; ) or R(; ) is unde ned. So j=  ( :: R : ) = (R(; ); R(; )) is no contradiction to j=  :: R : .  ?  R(; ) or +R(; ): in this case, analogously, either Mj6j= R(; ) or R(; ) is unde ned implying that  :: :R : is satis able. This follows from the notion of acceptance of ionic formulae as de ned in [1]. In any case,  preserves satis ability depending on the state of acceptance of justi cation contexts. Revisiting the sketch in section 3, we use UserRel for declaring which roles of a domain model eventually describe partial dialog contexts. The linguistic processor of the dialog manager computes DRT3 structures (see the example in section 8) containing conditions in FIL. Inference is performed 2 As FIL is a partial logic, an interpretation is a partial mapping from the set of well-de ned formulae to f0; 1g. The set of all possible FIL interpretations is partially ordered: f < g :, \g is less partial than f ". Given an interpretation f and justi cation context , one can try and nd interpretations g (f < g) which assign a truth value to  or still leave it unde ned. So (roughly speaking)  can be acceptable (g assigns 1 to : +  ), inacceptable (g assigns 0 to : ?  ), not acceptable (g does not assign 1 to : +), or not inacceptable (g does not assign 0 to : ?). See [1] for a full discussion. 3 For a introduction to DRT see [9].

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As one can see easily, there is an obvious relation between discourse strategy and the dierent possible cases of satis ability of ionic formulae|but a discussion of this topic is not part of this presentation.

by, e.g., resolution on the basis of the FIL translation of a domain model given in DL, and computes justi cation contexts describing information that is missing in the dialog history, but neccessary for processing the speaker's utterance. This information can then be obtained by asking the user for the elements in the justi cation contexts (thereby realizing a mixed-initiative dialog). The user, in turn, answering the new question assigns one of the states explained above to each question the system has posed. For further clari cation, we continue the example above: If the user initiates a dialog with the question When does a train leave to Rome? the system infers that any answer to this question depends on the justi cation context

6 Speci c and General Notions Another point to be mentioned here is also immediately visible from the examples given above: in general, there are two classes of utterances:  Utterances such as I want to depart from Milan. that are related directly to the application domain because all notions in this utterance have a well-de ned meaning in the train information domain.  Utterances such as Yes. that say something about the ongoing discourse as they refer to notions as acceptance or rejection of questions. But actually, these notions do not belong to the application domain, but to a socalled discourse domain. This discourse domain de nes all notions related to the discourse such as intentions, speech acts, and discourse obligations. In fact, one can consider the discourse domain as an abstraction or generalization of all application domains because it contains the notions that are common to all of them. This set of common notions can be characterized by their function for the dialog: they control the (further) course of the dialog (by stating \Could you repeat that", \Pardon?", \I think that ..."), while, in contrast, application speci c notions are used for asserting facts that have importance for the computation of solutions for the current dialog goal. For the interpretation of utterances (in order to compute such a solution) inference is done in the applicationindependent discourse domain as well as in the application domain. As a consequence of this observation we have de ne a appropriate model for each of these two domains.

want-dep(user; y): In order to process the justi cation context the system would ask Where do you want to depart from? A possible answer would be From Munich. making acceptable that want-dep(user; Munich) is true. This answer binds the variable y to Munich resulting in the assertions4: Munich :: Station Munich :: DepStation user :: want-dep : Munich These assertions are valid as satis ability between FIL and DL is preserved. See section 8 for a discussion of how these assertions are used in an example dialog. When asked Do you want to depart from Munich? the user could accept want-dep(user,Munich) simply by saying Yes. or reject the context by responding No. From Milan. thereby accepting implicitly the ionic formula

7 Pragmatic Meaning of Concepts and Roles

(want-dep(user; Milan); want-dep(user; Milan))

As discussed above, object words are described in

We use the FLEX notion for the syntax of DL expres- the DL model of the application domain by primisions:  :: A : !  2 A and  :: R : : ! (; ) 2 R. tive concepts and roles. 4

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While the inference process is on the way when interpreting an utterance, a truth value has to be assigned to the mapping (as de ned in section 5) of primitive concepts which correspond roughly to facts (as used, for example, in PROLOG). This assignment is the linkage between the logical model of the application and its implementation (the problem solving module): the assignment of a truth value is performed by evaluating the application speci c operation corresponding to the object word. This evaluation can also bind variables that are parameters of the operation to certain constants. In this way we can de ne an interface between dialog management and the pragmatics of the application which is by nature independent of a speci c domain and therefore allows for abstraction of the dialog manager from its underlying domaindependent problem solving component, linguistics, and discourse structure.

At, To, and From are implemented in the task problem solving component by the corresponding queries to a database. want-dep is in UserRel and is translated by

 (want-dep) =  u; s:  (fwant-dep(u; s)g;want-dep(u; s))

Furthermore, there are|among many others | the de nitions

9want-dep?1 :User \ Station = 9From:DepStation \ Train \ Depart = 9Time:At \ TrainFrom = 9Station:To \ TrainAtFrom

DepStation = TrainFrom TrainAtFrom TrainAtFromTo

8 Con guring the Knowledge of a Dialog Manager

The utterance When does a train depart to Rome? has (in DRT) the semantic representation 2 6 6 6 6 6 6 6 6 4

For the practical purpose of creating a dialog manager for a speci c task we have to carry out the following two steps (thereby making use of the foundations outlined so far): 1. The a priori given DL model for the discourse domain has to be adapted, extended, and specialized so that it de nes all notions which are of importance for the application. This can be done eectively by integrating two terminologies into one. 2. As far as the implementation for the task is concerned, the interface between the problem solving component and the dialog manager must devise a \realization" for each primitive notion that has been de ned in the DL application model. In the train information application that is considered throughout this paper, an appropriate terminology could|for example| include the following concepts and roles:  Train, Depart, Time, Station  At : Train  Time To : Train  ArrStation From : Train  DepStation want-dep : User  Station

t Rome Train(t) Depart(t) Time(x) Station(Rome) At(t; x) To(t; Rome)

3 7 7 7 7 7 7 7 7 5

Obviously, one can infer|on the basis of the concepts and roles given above|that any solution to the query 8t : TrainAtFromTo(t) depends on the justi cation context want-dep(user; s). Therefore, the dialog manager will update its discourse plan and ask for a departure station. This has been explained already in Sect. 5

9 Conclusions We have established a connection between DL and FIL in terms of satis ability via a mapping between formulae of each language. Furthermore, as an application of this result, we have constructed a subset UserRel of the set of roles in a given terminology that has been used to characterize mixed initiative dialog as a result of infering justi cation contexts, i.e. formulae of unde ned truth value, from user utterances. Finally, we have sketched how the declarative domain model and its corresponding implementation can be combined in a computationally eective way. 5

10 Future Research

[9] Kamp, Hans and Reyle, Uwe: From Discourse to Logic, Kluwer, Dordrecht 1993 [10] Larsen, Lars Bo: Development and Evaluation of a Spoken Dialogue for a Telephone Based Transaction System, in: Proc. EUROSPEECH 95, Madrid, 1995, pp. 1973{1976 [11] Ludwig, Bernd: Partielle Logik in Semantik und Diskurs, Diplomarbeit, Universitat Erlangen-Nurnberg 1997 [12] Moeller, Jens-Uwe: DIA-MOLE: An Unsupervised Learning Approach to Adaptive Dialogue Models for Spoken Dialogue Systems, in: Proc. EUROSPEECH 97, Rhodes, Greek, pp. 2271-2274 [13] Ward, Karen and Novick, David G.: On the Need for a Theory of Integration of Knowledge Sources for Spoken Language Understanding, in: Proceedings of the AAAI-94 Workshop on the Integration of Natural Language and Speech Processing, Seattle, 1994, pp. 23{30 [14] Poesio, Massimo: Discourse Interpretation and the Scope of Operators, Ph.D. Thesis, Computer Science Dept., University of Rochester 1994 [15] Russell, Bertrand: The Object Language, in: Russell, B.: An Enquiry into Meaning and Truth, Allen and Unwin, London 1950 [16] Schmolze, J.G. and Israel, D.: KL-ONE: semantics and classi cation, in Research in Knowledge Representation for NL Understanding, Tech Report 5421, BBN Laboratories 1983 [17] Schnaittinger, Klemens and Hahn, Udo: Constraining the Acquisition of Concepts by the Quality of Heterogeneous Evidence, in: Proceedings of the 21st Annual German Conference on Arti cial Intelligence (LNAI 1303), Springer, Berlin 1997, pp. 255{266 [18] Traum, David: A Computational Theory of Grounding in Natural Language Conversation , Ph.D. Thesis, Computer Science Dept., University of Rochester 1994

Recent discourse theories such as [18] consider the construction of the so called common ground a key problem in discourse understanding. Evidence from a muber of experiments shows that humans perform domain reasoning while adding new items to the common ground (see e.g. [14]). Currently, we are studying the use of domain descriptions and DL reasoning services as a tool for classifying the function (grounding speech act) of items that are added to the common ground as a means of simulating inference by humans in spoken dialog. Closely related is the topic of disambiguation of underspeci ed utterances in given contexts. Cooperating with several industrial partners we want to generate domain models for dierent domains. For the acquisition of \synonym knowledge" we will apply learning techniques from these corpora. General work on DL learning (see e.g. [6]) as well as work on the combination of DL and linguistic processing (as done in [17]) will have to be considered.

References

[1] Abdallah, Nait: The Logic of Partial Information, Springer, New York 1995 [2] Agarwal, Rajeev: Towards a PURE Spoken Dialogue System for Information Access, in: Proceedings of the ACL/EACL Workshop on Interactive Spoken Dialog Systems: Bringing Speech and NLP Together in Real Applications, Madrid, Spain, pp. 90{97, 1997 [3] Borgida, Alex: On the Relative Expressiveness of Description Logics and Predicate Logics, Arti cial Intelligence, volume 82 (1996), pp. 353{367 [4] Eco, Umberto: La ricerca della lingua perfetta nella cultura europea, Laterza, Rom, Bari 1993 [5] Eckert, Wieland and Niemann, Heinrich: Semantic Analysis in a Robust Spoken Dialog System, in: Proc. Int. Conf. on Spoken Language Processing, Yokohama, 1994, pp. 107{110 [6] Frazier, Michael and Pitt, Leonard: CLASSIC learning, Machine Learning, 25 (1996), pp. 151{194 [7] Hjelmslev, Louis:, Omkring sprogteoriens grundlaeggelse, Munksgaard, Kopenhagen 1943; engl. Prolegomena to a Theory of Language, Univ. of Wisconsin Press, Madison 1961 [8] Jurafsky, D., Bates, R., Coccaro, N., Martin,

R., Meteer, M., Ries, K., Shriberg, E., Stolcke, A., Taylor, P., and Van Ess-Dykema, C.: Automatic Detection of Discourse Structure for Speech Recognition and Understanding., in: Proc. 1997 IEEE Workshop on Speech Recognition and Understanding, Santa Barbara, 1997

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