By Hans-Christian Schmitz (auth.)
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Extra resources for Accentuation and Interpretation
Let us assume that the speaker is well-informed and critical, so that the recipient can trust him and can assume that the speaker knows what he is talking about. The recipient therefore learns, ﬁrst, that p and, secondly that the speaker knows that p. Using the notation of Fagin et al. (1995), I write Ki ( p) for “the discourse participant i knows that p”. The index s stands for the speaker and the index r for the recipient. Now it holds that Ks ( p) ∧ Kr ( p) ∧ Kr (Ks ( p)). The recipient does not contradict the speaker 40 Accentuation and Interpretation and the speaker can therefore be certain of the effect of his assertion.
He knows how the recipient has updated his knowledge: Ks ( p) ∧ Kr ( p) ∧ Kr (Ks ( p)) ∧ Ks (Kr ( p)) ∧ Ks (Kr (Ks ( p))). The consequence of not contradicting the assertion can be calculated by the recipient; he knows which knowledge the speaker acquires: . . ∧ Kr (Ks (Kr ( p))) ∧ Kr (Ks (Kr (Ks ( p)))). And so on: The speaker knows which knowledge the recipient acquires and the recipient knows in turn which knowledge the speaker acquires, ad inﬁnitum. The discourse participants (speaker and recipient) are aware of each other’s knowledge of p.
E. a set of indices (so called possible worlds). t. M and TL iff σ M ⊆ I M . 12 I allow the formulation that not only propositions (meanings of declarative sentences) but also declarative sentences themselves can be known. 13 M is a reduced model, because the real world-index i ∗ , in relation to which the truth value of a sentence is determined, is lacking. Cf. deﬁnition A-10 in the appendix. – Why is M a reduced and not a complete model? – The holder of an information state must possess a model of TL in order to interpret the sentences of TL and to update his information state.
Accentuation and Interpretation by Hans-Christian Schmitz (auth.)