{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,5,14]],"date-time":"2022-05-14T00:25:17Z","timestamp":1652487917836},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2004,8,5]],"date-time":"2004-08-05T00:00:00Z","timestamp":1091664000000},"content-version":"unspecified","delay-in-days":4,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2004,8]]},"abstract":"<jats:p>A formulation of lattice theory as a system of rules added to sequent calculus is given. The analysis of proofs for the contraction-free calculus of classical predicate logic known as <jats:italic>G3c<\/jats:italic> extends to derivations with the mathematical rules of lattice theory. It is shown that minimal derivations of quantifier-free sequents enjoy a subterm property: all terms in such derivations are terms in the endsequent.<\/jats:p><jats:p>An alternative formulation of lattice theory as a system of rules in natural deduction style is given, both with explicit meet and join constructions and as a relational theory with existence axioms. A subterm property for the latter extends the standard decidable classes of quantificational formulas of pure predicate calculus to lattice theory.<\/jats:p>","DOI":"10.1017\/s0960129504004244","type":"journal-article","created":{"date-parts":[[2004,10,13]],"date-time":"2004-10-13T17:31:27Z","timestamp":1097688687000},"page":"507-526","source":"Crossref","is-referenced-by-count":10,"title":["Proof systems for lattice theory"],"prefix":"10.1017","volume":"14","author":[{"given":"SARA","family":"NEGRI","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JAN","family":"VON PLATO","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2004,8,5]]},"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129504004244","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,31]],"date-time":"2019-03-31T18:53:23Z","timestamp":1554058403000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129504004244\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,8]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2004,8]]}},"alternative-id":["S0960129504004244"],"URL":"https:\/\/doi.org\/10.1017\/s0960129504004244","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,8]]}}}