15.5-15.7, A Generative Inquiry Dialogue System

Notes taken from ‘A Generative Inquiry Dialogue System’ (2007), by Elizabeth Black and Anthony Hunter

5, Soundness and Completeness

5.1, The argument inquiry outcome of a dialogue is a function… if D is a well-formed argument inquiry dialogue with participants x1 and x2, then… (given D the outcome is the set of all arguments that can be constructed from the union of the commitment stores and whose claims are in the question store).

… The benchmark that we compare the outcome of the dialogue with is the set of arguments that can be constructed from the union of the two agents’ beliefs. So this benchmark is, in a sense, the ‘ideal situation’ where there are clearly no constraints on the sharing of beliefs.

5.2, Let D be a well-formed argument inquiry dialogue with participants x1 and x2. We say that D is sound if and only if… (when the outcome of the dialogue includes an argument, then that same argument can be constructed from the union of the two participating agents’ beliefs).

(Theorem 5.1) If D is a well-formed argument inquiry dialogue with participants x1 and x2, then D is sound. Proof: …

5.3, Let D be a well-formed argument inquiry dialogue with participants x1 and x2. We say that D is complete iff… (if the dialogue terminates at t and it is possible to construct an argument for a literal in the question store from the union of the two participating agents’ beliefs, then that argument will be in the outcome of the dialogue at t.)

(Theorem 5.2) If D is a well-formed argument inquiry dialogue with participants x1 and x2, then D is complete. Proof: …

6, Future work…

… We would like to allow more than two agents to take part in an argument inquiry dialogue…

We currently assume that an agent’s belief base does not change during a dialogue, and would like to consider the implication of dropping this assumption…

We would also like to further explore the benchmark which we compare our dialogue outcomes to…

… We would like to further investigate the utility of argument inquiry dialogues when embedded in dialogues of different types.

7, Conclusions…