Metalinguistic Focus in P-HYPE Semantics Luke Edward Burke Abstract P-HYPE is a hyperintensional situation semantics in which hyperinten- sionality is modelled as a ‘side effect’, as this term has been understood in natural language semantics [8, 42], and in functional programming [21]. In [5], we com- bine [2]’s perspective-sensitive semantic theory with a hyperintensional situation semantics, HYPE [28], using monads from category theory in order to ‘upgrade’ an ordinary intensional semantics to a possible hyperintensional counterpart. In [6] we expand our semantic theory to capture cases of intra-sentential anaphora. We here supplement the framework with the pointed power set monad so that we can account for certain cases of hyperintensionality involving metalinguistic focus [29] which seem to resist treatment in P-HYPE as it stands. This gives a mini case study in how to combine monads together in order to integrate different side effects in one language, one of the advantages of monads as a tool in compositional semantics. 1 Introduction Hyperintensional semantic theories, as we are understanding them in this paper, are semantic theories that sometimes distinguish the semantic values of sentences that express logical and mathematical truths (or falsities), where by ‘logical truths’ we are referring to the validities of classical logic. Such sentences are often assigned the same semantic value in semantic theories of natural language based on standard possible world semantics [18]. L. E. Burke (B ) Department of Philosophy, The University of London, Gower Street, WC1E 6BT London, England University College London, London, England Foundations of Computer Science, The University of Bamberg, An der Weberei 5 (ERBA), 96047 Bamberg, Germany Universität Bamberg, Bamberg, Germany e-mail: l.burke@ucl.ac.uk; luke.burke@uni-bamberg.de © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. Giordani and J. Malinowski (eds.), Logic in High Definition, Trends in Logic 56, https://doi.org/10.1007/978-3-030-53487-5_10 203