Abstract
In this paper we summarize concepts from earlier work and demonstrate how infinite sequential games can be used to model strategic conversations. Such a model allows one to reason about the structure and complexity of various kinds of winning goals that conversationalists might have. We show how to use tools from topology, set-theory and logic to express such goals. We then show how to tie down the notion of a winning condition to specific discourse moves using techniques from Mean Payoff games and discounting. We argue, however, that this still requires another addition from epistemic game theory to define appropriate solution and rationality underlying a conversation.
The authors thank ERC grant 269427 for supporting this research.
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Notes
- 1.
We note that this is a simplification of SDRT which also countenances complex discourse units (cdus) and another set of edges in the graph representation, linking cdus to their simpler constituents. These edges represent parthood, not rhetorical relations. We will not, however, appeal to cdus here.
- 2.
Note that [3] considers the discounting as a function of the history rather than a constant factor which, arguably, better reflects real-life situations. We stick to a constant discounting factor here for the simplicity of presentation. The main concepts remain the same.
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Asher, N., Paul, S. (2017). Conversation and Games. In: Ghosh, S., Prasad, S. (eds) Logic and Its Applications. ICLA 2017. Lecture Notes in Computer Science(), vol 10119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54069-5_1
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