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The central Kantian notion that we formalize is the<jats:italic>rule<\/jats:italic>. As we interpret Kant, a rule is not a declarative conditional stating what would be true if such and such conditions hold. Rather, a Kantian rule is a general procedure, represented by a conditional imperative or permissive, indicating<jats:italic>which acts must or may be performed<\/jats:italic>, given certain acts that are already being performed. These acts are not propositions; they do not have truth-values. Our formalization is related to the input\/ output logics, a family of logics designed to capture relations between elements that need not have truth-values. In this paper, we introduce KL<jats:sub>3<\/jats:sub>as a formalization of Kant\u2019s conception of rules as conditional imperatives and permissives. We explain how it differs from standard input\/output logics, geometric logic, and first-order logic, as well as how it translates natural language sentences not well captured by first-order logic. Finally, we show how the various distinctions in Kant\u2019s much-maligned Table of Judgements emerge as the most natural way of dividing up the various types and sub-types of rule in KL<jats:sub>3<\/jats:sub>. Our analysis sheds new light on the way in which normative notions play a fundamental role in the conception of logic at the heart of Kant\u2019s theoretical philosophy.<\/jats:p>","DOI":"10.1007\/s10992-019-09531-x","type":"journal-article","created":{"date-parts":[[2019,11,25]],"date-time":"2019-11-25T14:02:29Z","timestamp":1574690549000},"page":"613-680","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Formalizing Kant\u2019s Rules"],"prefix":"10.1007","volume":"49","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2131-8686","authenticated-orcid":false,"given":"R.","family":"Evans","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Sergot","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Stephenson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,11,25]]},"reference":[{"key":"9531_CR1","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1017\/S1755020310000341","volume":"4.02","author":"T Achourioti","year":"2011","unstructured":"Achourioti, T., & van Lambalgen, M. 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