{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T19:48:19Z","timestamp":1762458499716,"version":"3.32.0"},"reference-count":6,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":9323,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1988,9]]},"abstract":"<jats:p>Ordinary equational logic is a connective-free fragment of first-order logic which is concerned with total functions under the relation of ordinary equality. In [AN] (see also [AN1]) and in [Cr] it has been extended in two equivalent ways into a near-equational system of logic for partial functions. The extension given in [Cr] deals with partial functions under two relationships: a relationship of existence-dependent existence and one of existence-dependent Kleene equality. For the language that involves both relationships a set of rules was given that is complete. Those rules in the set that involve only existence-dependent existence turned out to be complete for the sublanguage that involves this relationship only. In the present paper we give a set of rules that is complete for the other sublanguage, namely the language of partial functions under existence-dependent Kleene equality.<\/jats:p><jats:p>This language lacks a certain, often needed, power of expressing existence and fails, in particular, to be an extension of the language that underlies ordinary equational logic. That it possesses a fairly simple complete set of rules is therefore perhaps more of theoretical than of practical interest. The present paper is thus intended to serve as a supplement to [Cr] and, less directly, to [AN]. The subject is further rounded out, and some contrast is provided, by [Rob]. The systems of logic treated there are based on the weaker language in which partial functions are considered under the more basic relation of Kleene equality.<\/jats:p>","DOI":"10.2307\/2274574","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:27:13Z","timestamp":1146954433000},"page":"834-839","source":"Crossref","is-referenced-by-count":7,"title":["A system of logic for partial functions under existence-dependent kleene equality"],"prefix":"10.1017","volume":"53","author":[{"given":"H.","family":"Andr\u00e9ka","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"W.","family":"Craig","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"I.","family":"N\u00e9meti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200042067_ref004","unstructured":"Craig William , Near-equational and equational systems of logic for partial functions, this Journal (to appear)."},{"key":"S0022481200042067_ref002","unstructured":"Andr\u00e9ka H. , Corrections of a calculus of equations for partial algebras (to appear)."},{"key":"S0022481200042067_ref003","doi-asserted-by":"crossref","DOI":"10.1515\/9783112720875","volume-title":"A model theoretic oriented approach to partial algebras","author":"Burmeister","year":"1986"},{"key":"S0022481200042067_ref001","article-title":"Generalization of the concept of variety and quasivariety to partial algebras through category theory","volume":"204","author":"Andr\u00e9ka","year":"1983","journal-title":"Dissertationes Mathematicae\/Rozprawy Matematyczne"},{"key":"S0022481200042067_ref005","unstructured":"Robinson Anthony , Equational logic of partial functions under Kleene equality: a complete and an incomplete set of rules, this Journal (to appear)."},{"key":"S0022481200042067_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF01191787"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200042067","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,8]],"date-time":"2025-01-08T21:16:27Z","timestamp":1736370987000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200042067\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1988,9]]},"references-count":6,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1988,9]]}},"alternative-id":["S0022481200042067"],"URL":"https:\/\/doi.org\/10.2307\/2274574","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"type":"print","value":"0022-4812"},{"type":"electronic","value":"1943-5886"}],"subject":[],"published":{"date-parts":[[1988,9]]}}}