Abstract
This paper studies the operations of public announcement of statements and public utterance of questions in the context of substructutral inquisitive epistemic logic. It was shown elsewhere that the logical laws governing the modalities of knowing and entertaining from standard inquisitive epistemic logic generalize smoothly to substructural logics. In this paper we show that the situation is different with the reduction axioms that in the standard setting govern the modality of public announcement/utterance. The standard reduction axioms depend on some features of classical logic that are not preserved in substructural logics. Using an additional auxiliary modality, we show how to overcome this obstacle and formulate an alternative set of reduction axioms for the public announcement/utterance modality that can be used even in the context of our general non-classical setting.
The work on this paper was supported by grant no. 18-19162Y of the Czech Science Foundation.
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Notes
- 1.
It is common to interpret the modality \([\varphi ]\) as public announcement of \(\varphi \). However, we will follow [4] in using the term “public utterance” instead of “public announcement”. The reason is that \(\varphi \) may represent a question, e.g. the question whether p or q, and it seems that there is an intuitive difference between announcing whether p or q and uttering whether p or q. The former indicates that an answer to the question is uttered, while the latter means only that the question itself is uttered, which corresponds better to what the modality \([\varphi ]\) is supposed to model.
- 2.
In the standard inquisitive epistemic logic, the letter K, instead of I, is used for this modality since it is interpreted as knowing that/whether. However, in our more general framework, we will not assume the specific features of knowledge, as for example factivity (the agent can know only what is true) so the letter I seems to be more appropriate.
- 3.
In the standard setting \(s \sqsubseteq t\) reduces to \(s \subseteq t\). In that case, the set of worlds s is informationally stronger than t since it excludes more possibilities.
- 4.
In [5], the logic generated by this system is called \(\mathsf {InqSE}\).
- 5.
It is discussed in detail in [5] why the distributivity axiom D1 is needed.
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Punčochář, V. (2020). Inquisitive Dynamic Epistemic Logic in a Non-classical Setting. In: Martins, M.A., Sedlár, I. (eds) Dynamic Logic. New Trends and Applications. DaLi 2020. Lecture Notes in Computer Science(), vol 12569. Springer, Cham. https://doi.org/10.1007/978-3-030-65840-3_13
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