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We provide a system, based on graded monads, that synthesizes insights from these programs by formalizing individual discourse phenomena in terms of separate effects, or grades. Included are effects for introducing and retrieving discourse referents, non-determinism for indefiniteness, and generalized quantifier meanings. We formalize the behavior of individual effects, as well as the interactions between effects, in terms of algebraic laws tailored to the relevant discourse phenomena. The system we propose is thus modular and suggests a novel approach to integrating formal accounts of distinct semantic phenomena. Finally, we give an interpretation of the system into pure <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \\lambda $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03bb<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-calculus that respects the laws. Future work will aim to integrate more discourse phenomena using the same methodology, for example, presupposition and conventional implicature.\n<\/jats:p>","DOI":"10.1007\/s10849-022-09378-7","type":"journal-article","created":{"date-parts":[[2022,8,26]],"date-time":"2022-08-26T18:03:54Z","timestamp":1661537034000},"page":"219-245","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Algebraic Effects for Extensible Dynamic Semantics"],"prefix":"10.1007","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3675-3851","authenticated-orcid":false,"given":"Julian","family":"Grove","sequence":"first","affiliation":[]},{"given":"Jean-Philippe","family":"Bernardy","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,8,26]]},"reference":[{"key":"9378_CR1","doi-asserted-by":"publisher","unstructured":"Abel, A., & Bernardy, J.-P. (2020). 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