Reference in Dialogues and Shared Belief Revision

Reference in Dialogues and Shared Belief Revision Norihiro Ogatat�Tadayuki Matsuzawa� Akira Ishikawa;� Hisashi Komatsu t University of Tsukuba, DEC Japan, Sophia University, Hiroshima City University Abstract We shall show how to treat shared belief revision and reference management in the process of dialogues by distinguishing three types of discourse referents: (standard) discourse referents, shared discourse referents, and the shared belief referent, using an extended version of Discourse Representa- tion Theory, called Hyper-DRS, which can represent shared beliefs semantically in a notation based on hyper-sets (sets in non-well-founded set theory). 1 Introduction Belief sharing in dialogue necessarily involves circular structures, since shared beliefs have circular struc- tures. [1]'s theory of non-well-founded sets or hyper-sets makes it possible to encode such circular struc- tures in first-order fixed point equations, whose solution is guaranteed by his solution lemma. By adopting [1]'s theory, we extend the expressibility of Discourse Representation Structures, called Hyper-DRS(firstly proposed in [14, 13]), of [9, 8, 10, 2]'s Discourse Representation Theory, henceforth DRT. (See also [12] for another version of self-referential DRS and its semantics). This extension takes the form of introducing three new types of discourse referents, which we will show reflect our intuitions about dialogue processes. In this paper, we shall show how to treat shared belief revision and reference management in the process of dialogues by distinguishing three types of discourse referents: (standard) discourse referents, shared discourse referents, and the shared belief referent. Shared discourse referents play a role in preserving the topic of dialogues, and shared belief referents are used to convert circular propositions into first-order equational systems, and we can update and revise a circular proposition by hanging propositions on and taking propositions from shared discourse referents appearing in it. Thus, the three types of discourse referents are basic devices for the management of shared beliefs. In the context of shared belief revision, we can also characterize the three types of discourse referents in terms of the notion of accessibility and life span. The shared belief referent and standard discourse referents can not be accessed by both conversants. The conversants can access shared discourse referents, and each conversant can access standard discourse referents which are introduced by herself. Shared discourse referents and the shared belief referents can not be deleted and forgotten when shared beliefs are revised or deleted, i.e., the life span of shared belief referents is the longest in revision processes of discourse representation structures, and the life span of shared discourse referents is longer than that of standard discourse referents in their revision processes. Furthermore, we can explain the connection between shared belief revision, reference management, and dialogue process, and give a mothod of evaluation of dialogue in terms of successfulness in information sharing. As a result, our extended version of DRT with Hyper-DRS's can treat shared beliefs as first-order equational systems, which, being a finite representation of inherently infinite structures, allow us to simulate, and evaluate processes of shared belief revision and reference management in dialogue. In section 2 we consider …

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