{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:52:04Z","timestamp":1750308724000,"version":"3.41.0"},"reference-count":43,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2013,11,1]],"date-time":"2013-11-01T00:00:00Z","timestamp":1383264000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Comput. Logic"],"published-print":{"date-parts":[[2013,11]]},"abstract":"<jats:p>Logical relations are a central concept used to study various higher-order type theories and occur frequently in the proofs of a wide variety of meta-theorems. Besides extending the logical relation principle to more general languages, an important research question has been how to represent and thus verify logical relation arguments in logical frameworks.<\/jats:p>\n          <jats:p>We formulate a theory of logical relations for Dependent Type Theory (DTT) with \u03b2 \u03b7-equality which guarantees that any valid logical relation satisfies the Basic Lemma. Our definition is syntactic and reflective in the sense that a relation at a type is represented as a DTT type family but also permits expressing certain semantic definitions. We use the Edinburgh Logical Framework (LF) incarnation of DTT and implement our notion of logical relations in the type-checker Twelf. This enables us to formalize and mechanically decide the validity of logical relation arguments. Furthermore, our implementation includes a module system so that logical relations can be built modularly. We validate our approach by formalizing and verifying several syntactic and semantic meta-theorems in Twelf. Moreover, we show how object languages encoded in DTT can inherit a notion of logical relation from the logical framework.<\/jats:p>","DOI":"10.1145\/2536740.2536741","type":"journal-article","created":{"date-parts":[[2013,12,4]],"date-time":"2013-12-04T14:04:47Z","timestamp":1386165887000},"page":"1-34","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Logical relations for a logical framework"],"prefix":"10.1145","volume":"14","author":[{"given":"Florian","family":"Rabe","sequence":"first","affiliation":[{"name":"Jacobs University Bremen, Bremen, Germany"}]},{"given":"Kristina","family":"Sojakova","sequence":"additional","affiliation":[{"name":"Carnegie Mellon University, Pittsburgh, PA"}]}],"member":"320","published-online":{"date-parts":[[2013,11,28]]},"reference":[{"volume-title":"Workshop on Mechanizing Metatheory.","year":"2009","author":"Atkey R.","key":"e_1_2_1_1_1"},{"volume-title":"Proceedings of the Conference on Computer Science Logic","year":"2012","author":"Atkey R.","key":"e_1_2_1_2_1"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(90)90151-7"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/1863543.1863592"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0956796812000056"},{"key":"e_1_2_1_6_1","unstructured":"Bertot Y. and Cast\u00e9ran P. 2004. 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