{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T17:05:32Z","timestamp":1760547932371},"reference-count":50,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[1994,5,1]],"date-time":"1994-05-01T00:00:00Z","timestamp":767750400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Form. Asp. Comput."],"published-print":{"date-parts":[[1994,5]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>\n            We present a two-sorted algebra, called a\n            <jats:italic>Peirce algebra<\/jats:italic>\n            , of relations and sets interacting with each other. In a Peirce algebra, sets can combine with each other as in a Boolean algebra, relations can combine with each other as in a relation algebra, and in addition we have both a set-forming operator on relations (the Peirce product of Boolean modules) and a relation-forming operator on sets (a cylindrification operation). Two applications of Peirce algebras are given. The first points out that Peirce algebras provide a natural algebraic framework for modelling certain programming constructs. The second shows that the so-called\n            <jats:italic>terminological logics<\/jats:italic>\n            arising in knowledge representation have evolved a semantics best described as a calculus of relations interacting with sets.\n          <\/jats:p>","DOI":"10.1007\/bf01215410","type":"journal-article","created":{"date-parts":[[2005,2,25]],"date-time":"2005-02-25T15:22:43Z","timestamp":1109344963000},"page":"339-358","source":"Crossref","is-referenced-by-count":28,"title":["Peirce algebras"],"prefix":"10.1145","volume":"6","author":[{"given":"Chris","family":"Brink","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Cape Town, 7700, Rondebosch, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Katarina","family":"Britz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Cape Town, 7700, Rondebosch, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Renate A.","family":"Schmidt","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Cape Town, 7700, Rondebosch, South Africa"},{"name":"Max-Planck-Institut f\u00fcr Informatik, Saarbr\u00fccken, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","reference":[{"key":"e_1_2_1_2_1_2","volume-title":"Residuation Theory","author":"Blyth T. 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