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It is controversial whether monotonicity (especially upward monotonicity) is blocked under attitude verbs expressing obligation or desire. This debate tends to focus on whether the classical semantics for these verbs is correct. The difficulty is that we cannot determine this by intuitive data as both sides of the argument have plenty prima facie examples of how monotonicity can be rejected or left unaffected, e.g. Ross's paradox and Asher's puzzle of desire. So it may not be a bad idea to study other kinds of modality. We look at the monotonic reasoning under epistemic verbs. In this talk, I will present joint work with Maria Aloni, in which we aim to determine whether monotonic inferences are problematic in epistemic contexts. We present a puzzle showing that monotonicity under the verb 'know' may be problematic from the perspective of pragmatics, and then we propose an analysis w.r.t. predicates. We will then develop the Quantified Bilateral State-based Modal Logic (QBSEL, by Aloni & van Ormondt 2021) to capture this pragmatic analysis formally.