{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T20:29:20Z","timestamp":1761596960000},"reference-count":23,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":5763,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1998,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study logical systems for reasoning about equations involving recursive definitions. In particular, we are interested in \u201cpropositional\u201d fragments of the <jats:italic>functional language of recursion<\/jats:italic> FLR [18, 17], i.e., without the value passing or abstraction allowed in FLR. The \u201cpure,\u201d propositional fragment FLR<jats:sub>0<\/jats:sub> turns out to coincide with the <jats:italic>iteration theories<\/jats:italic> of [1]. Our main focus here concerns the sharp contrast between the simple class of valid identities and the very complex consequence relation over several natural classes of models.<\/jats:p>","DOI":"10.2307\/2586843","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:01:17Z","timestamp":1146938477000},"page":"451-478","source":"Crossref","is-referenced-by-count":19,"title":["The logic of recursive equations"],"prefix":"10.1017","volume":"63","author":[{"given":"A. J. C.","family":"Hurkens","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Monica","family":"McArthur","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiannis N.","family":"Moschovakis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lawrence S.","family":"Moss","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Glen T.","family":"Whitney","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200015012_ref009","unstructured":"\u00c9sik, Zolt\u00e1n , Completeness of park induction, Theoretical Computer Science , to appear."},{"key":"S0022481200015012_ref006","volume-title":"Automata, languages, and programming","author":"de Barker","year":"1973"},{"key":"S0022481200015012_ref017","volume-title":"Proceedings of the 10th International Congress of Logic, Methodology and the Philosophy of Science","author":"Moschovakis","year":"1995"},{"key":"S0022481200015012_ref003","volume-title":"Mathematical foundations of programming semantics '93","author":"Bloom","year":"1994"},{"key":"S0022481200015012_ref023","unstructured":"Whitney, G. 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