By Stefan Minica
ISBN-10: 9057762293
ISBN-13: 9789057762291
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Extra resources for Dynamic Epistemic Logic of Questions and Inquiry
Example text
Ri), for all i. ]Ri6 for all i Moreover, our language can express basic laws of interrogative reasoning. ][ ! 2 and proceed to giving a dynamic logic. 4 Here we assume that each world has a unique nominal i naming it. This generalizes standard definitions of entailment restricted to factual questions. 6 Again, this generalizes notions of compliance restricted to propositional formulas. 2. 3 25 Dynamic Logic of Informational Issues We have seen that effects of asking questions are not always easy to keep straight, but also, that there is an interesting structure to management operations on models.
The latter choice involves a slightly delicate issue of mutual recursion, which is similar to that for DEL in general. We continue by specifying the way such structures transform given issue epistemic models which provide the underlying changing entities for specific questioning actions. 2. Definition. [Product Update] Given any arbitrary epistemic-issue struca a a a ture M = ( W, ∼, ≈, V , w), and action-issue structure γ = ( E, ∼, ≈, pre , e) the a a update product M ⊗ γ = M⊗γ = ( W⊗ , ∼⊗ , ≈⊗ , V⊗ , (w, e)) is defined by: – W⊗ = {(w, e) | w ∈ W, e ∈ E, M |=w pre(e)}, V⊗ (w, e) = V (w), a a a a a a – ∼⊗ = {((w, e), (w′ , e′ )) | w, w′ ∈ W, e, e′ ∈ E, w ∼ w′ , e ∼ e′ }, – ≈⊗ = {((w, e), (w′ , e′ )) | w, w′ ∈ W, e, e′ ∈ E, w ≈ w′ , e ≈ e′ }, If we need to work with sets of distinguished events, as indicated earlier, we take all pairs of an earlier distinguished world and the (unique) answer event supported by it.
9 Extension to other types of questions, such as Wh-questions are possible but they would need a predicate-logical version of the static epistemic logics. 3. 10 Some common multi-agent preconditions: (1) ‘b asks ϕ’ presupposes ¬Kb ϕ ∧ ¬Kb ¬ϕ: that is, the questioner must not know the answer to the question she asks, (2) ‘b asks ϕ to a’ presupposes Kb (Ka ϕ ∨ Ka ¬ϕ): that is, the questioner must consider it possible that the questionee knows the answer. These make sense for truly informative Gricean questions, and there may be other preconditions.
Dynamic Epistemic Logic of Questions and Inquiry by Stefan Minica
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