Towards a basis for human-computer dialogue. Bengt Nordström Chalmers, Göteborg

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1 Towards a basis for human-computer dialogue Bengt Nordström Chalmers, Göteborg

2 Goal We want to model dialogue systems in which a human interacts with a computer to build an object. From Wikipedia: A dialog system is a computer system intended to converse with a human, with a coherent structure. Dialog systems have employed text, speech, graphics, haptics, gestures and other modes for communication on both the input and output channel. Here I will ignore the problems of speech recognition and generation and abstract over the mode of interaction.

3 A dialogue is seen as the building of an object. The human fills in information which the computer needs. Typical examples are: Reservation system for trains, concerts, calendars, rooms, medical doctors,... Navigation systems Control center for TV, radio, mp3-players,... Editors for controlled languages like restaurant reviews recipies description of pharmaceuticals description of items for sale structure oriented editors for programs and formal proofs

4 Typical structure of a dialogue system speech input textual input syntax tree semantic representation system response content system response utterance system output speech recognition parsing semantic interpretation dialogue management generation speech synthesis

5 Checking correctness In all these systems there is a notion of syntactic correctness, which should be checked immediately after each input of the user. We will use a type system to express the syntactical correctness.

6 Some choices: System driven dialogue: The system decides the order to fill in the details. User driven dialogue: The user decides. explicit focus moving commands: up, down, left, right... assignment: any part of the object can be changed.

7 Objects are treated as directed graphs In principle, we have a graph like: q1 = c1 p1... pn...qn = cn r1... rn where p, q and r are placeholders and c are functional constants.

8 A simple example: We want to define the constant 2 : Nat and we assume that we have the constant 0 : Nat and s : Nat -> Nat: two :: Nat two := s q1 q1 := s q2 q2 := 0 -- declare the type of two -- the system can deduce that q1:nat -- the system can deduce that q2:nat How to introduce Nat, s and 0? Nat :: Set z :: Nat s :: q1 -> q2 -- the system deduces that q1, q2 are types q1 := El q3 -- the system deduces that q3:set q3 := Nat

9 The set of (thick) expressions are: e,t :: = t1... tn -> t' Set El e (c e1... en) q function types set types elements in a set application place holder

10 The set of thin expressions are: e,t :: = q1... qn -> q' Set El q (c q1... qn) q function types set types elements in a set application place holder

11 From a list of thin expressions to a thick expression: The translation is obvious: Suppose that r is a list of thin expressions, letting r e stand for the expression which e stands for: r (q1... qn -> i') = (r q1... r qn) -> r q' r (Set) = Set r (El q) = El (r q) r (c q1... qn) = c (r q1... r qn) r ( q ) = r d if (q = d) is in r q otherwise

12 Overview Starting from a state with expressions with place holders, like: c1 : t1; c1 = q1;...; cn : tn we want to use a series of commands to build up a new state c1 : t1; c1 = e1;...; cn : tn; c1 = en It is not necessary that all constants have a definiens. But in the end all holes must be filled in (place holders must be defined).

13 Commands q := e c :: e q :: e Refine the value of the place holder q, e is a thin expression. Introduce a new constant with its type. Introduce a new placeholder and its type. This is only used in bottom-up editing. The type e must not be a functional type

14 Type checking To type check a command of the shape q := e we always look up the type of q. It is an invariant of the system that all place holders have an expected type. Then we type check e:

15 Type checking an application q : Q in G c : Ts -> T in G Q = T in G G, q := c qs - G ; qs:ts; q = c rs Explanation: In order to type check the command q := c qs in G we: look up the type of q in G, call it Q look up the type of c in G, it has to have the shape Ts -> T check that Q = T in G Then we can update the state G with qs:ts (this update must be consistent with G) q = c rs (and make sure that no cycles are introduced)

16 Type checking El q type in G G, q := El q' - G ; q':set ; q = El q' Explanation: In order to type check the command q := El q' in G we: check that q is a type in G Then we can update the state G with q' : Set (this update must be consistent with G) q = El q' (and make sure that no cycles are introduced)

17 Type checking a function type q type in G G, q := Fun qs - G ; qs types ; q = Fun qs Explanation: In order to type check the command q := Fun qs in G we: check that q is a type in G Then we can update the state G with qs types (all elements in qs have to be types) q = Fun qsel q' (and make sure that no cycles are introduced)

18 Consistent updates The updates must be consistent in the sense that: No cycles in the definitions can be introduced An update of the shape G; q : A is only possible if q does not have a type in G or q already has the type A in G.

19 Summary: The user issues commands of the form q := e q :: e refine a place holder introduce a place holder The expressions e are thin expressions of the form e,t :: = q1... qn -> q' Set El q (c q1... qn) q

20 Summary (cont'd): Expressions are represented as directed graphs with placeholders as names for subexpressions. This makes it possible to build objects top-down bottom-up a combination of these This is absolutely essential when trying to mimic human dialogues.

21 Further work: Extend the language of objects and types to: dependent types some notion of a decidable subset type strategies for under-specified information (the system cannot deduce what placeholder to fill in) (Peter Ljunglöf)

22 Thanks to: Aarne Ranta, Computer Science, Chalmers Björn Bringert, Computer Science, Chalmers Peter Ljunglöv, Linguistics, University of Gothenburg Robin Cooper, Linguistics, University of Gothenburg for many interesting discussions on these topics!

Proof Documents: Presentation and Representation

Proof Documents: Presentation and Representation Bengt Nordström Computer Science, Chalmers and University of Göteborg National Institute of Advanced Industrial Science and Technology, Senri, Japan, April