Abstract
In this paper, we model the behavior of an epistemic agent that faces a deliberation against a background of oughts, beliefs and information. We do this by introducing a dynamic epistemic logic where ought operators are defined and release of information makes beliefs and oughts co-vary. The static part of the logic extends single-agent Conditional Doxastic Logic by combining dyadic operators for conditional beliefs and oughts that are interpreted over two distinct preorders. The dynamic part of the logic introduces concurrent upgrade operators, which are interpreted on operations that change the two preorders in the same way, thus generating the covariation of beliefs and oughts. The effect of the covariation is that, after receiving new information, the agent will change both her beliefs and her oughts accordingly, and in deliberating, she will pick up the best states among those she takes to be the most plausible.
The author wishes to thank two anonymous reviewers and Ilaria Canavotto, Davide Grossi, Carlo Proietti for their helpful comments. Research for this paper was carried while the author was a Marie Curie IE Fellow with the WADOXA project at the Institute of Logic, Language and Computation, University of Amsterdam (2015–2016).
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Notes
- 1.
- 2.
Also, we do not presuppose that the deliberating agent has a particular position with respect to the issue in question (for instance, some kind of authority). We attribute deliberation to any agent that can assess what ought to be the case on the ground of believed circumstances.
- 3.
- 4.
A preorder \(\mathcal {R}\) is connected if \(\forall s,s'\in S: \mathcal {R}(s,s')\) or \(\mathcal {R}(s',s)\). It is upward well-founded if, for every \(U\ \subseteq \ S\), if \(U \ne \emptyset \), then
—the set of the ‘most \(R \)’ among the states in U is nonempty. Here, 
, and \(\tilde{\mathcal {R}}(s,s')\) is short for ‘\(\mathcal {R}(s,s')\) and 
’. - 5.
We omit the definition for the Boolean constructions, which is standard.
- 6.
That is, their valuations do not vary across states in S of a given model \(\mathcal {M}\).
- 7.
Of course, we could also define \(\mathcal {K}\phi \) as \(\mathcal {O}^{\lnot \phi }\bot \). However, given the conceptual nexus between knowledge and belief, we prefer the definition above.
- 8.
- 9.
Two states s and \(s'\) are equally good if \(R_{\mathcal {O}^{}}(s,s')\) and \(R_{\mathcal {O}^{}}(s',s)\). They are equally plausible if \(R_{\mathcal {B}^{}}(s,s')\) and \(R_{\mathcal {B}^{}}(s',s)\).
- 10.
Unless, of course, there is another formula \(\theta \) such that \(\{\mathcal {B}^{\top }\theta ,\mathcal {O}^{\theta }\psi ,\mathcal {O}^{\top }\psi \}\).
- 11.
Under this reading, the validity of \(\mathcal {O}^{\phi }\phi \) does not cause any concern, even in cases where \(\mathcal {O}^{\top }\lnot \phi \) is satisfied: the best among the scenarios where Jones steals something are still scenarios where he steals something.
- 12.
As for the missing arrows, remember that concurrent upgrade \(\upuparrows p\) leaves relations within the p- and \(\lnot p\)-zones as they were in Fig. 1.
- 13.
These prove especially interesting. In contrast to announcements of factual formulas, announcements of \(\top \),\(\bot \), or any (true or false) modal formula in \(\mathcal {L}_{}\) cannot change the initial model \(\mathcal {M}\). An interesting case holds when Moore sentences are (unsuccessfully) announced. We will not face these cases here, and we refer the reader to [9] for them.
- 14.
As for the missing arrows and curves, remember that concurrent upgrade \(\upuparrows s\) leaves relations within the s- and \(\lnot s\)-zones as they were in Fig. 3. This helps with the missing arrows.
- 15.
Just to get a concrete feeling of this: the fact (or information) that Jones steals does not make stealing (by Jones) norm-abiding.
- 16.
This reading relies on the fact that \(\mathcal {K}\) is a universal modality in our framework, to the effect that the above definition equates with \([\![d]\!]^{\mathcal {M}}\ \subseteq \ [\![\phi ]\!]^{\mathcal {M}}\) in our framework. The definition extends perfect knowledge of the agent to the new deontic component.
- 17.
Any model \(\mathcal {M}\) satisfying \(\mathcal {K}(d\rightarrow p)\) and \([\upuparrows \lnot p]\mathcal {B}^{\top }\lnot p\) fails to satisfy \([\upuparrows \lnot p](\mathcal {B}^{\top }\lnot p\rightarrow \Box \lnot p)\). Indeed, since d and p contains no modal operators, the interpretation of d and p does not change in the upgraded model, to the effect that \([\![d]\!]^{\mathcal {M}^{\upuparrows p}}\ \subseteq \ [\![p]\!]^{\mathcal {M}^{\upuparrows p}}\).
—the set of the ‘most 
, and 
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Ciuni, R. (2017). Conditional Doxastic Logic with Oughts and Concurrent Upgrades. In: Baltag, A., Seligman, J., Yamada, T. (eds) Logic, Rationality, and Interaction. LORI 2017. Lecture Notes in Computer Science(), vol 10455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55665-8_21
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