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Different properties ofthe accessibility functions (being injective, surjective, increasing, etc.) have been considered and axiomatic systems (called functional) which define these properties have been given. Only a few ofthese systems have been proved tobe complete. The aim ofthis paper is to make a progress in the study ofcompleteness for functional systems. For this end, we use indexes as names for temporal flows and give new proofs of completeness. Specifically, we focus our attention on the system which defines injectivity, because the system which defines this property without using indexes was proved to be incomplete in previous works. The only system considered which remains incomplete is the one which defines surjectivity, even ifwe consider a sequence ofnatural extensions ofthe previous one (\u00a9 2010 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200810038","type":"journal-article","created":{"date-parts":[[2010,1,15]],"date-time":"2010-01-15T18:26:22Z","timestamp":1263579982000},"page":"89-102","source":"Crossref","is-referenced-by-count":1,"title":["Analyzing completeness of axiomatic functional systems for temporal \u00d7 modal logics"],"prefix":"10.1002","volume":"56","author":[{"given":"Alfredo","family":"Burrieza","sequence":"first","affiliation":[]},{"given":"Inmaculada P.","family":"de Guzm\u00e1n","sequence":"additional","affiliation":[]},{"given":"Emilio","family":"Mu\u00f1oz\u2010Velasco","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2010,1,15]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"602","article-title":"MAT Logic: A temporal \u00d7 modal logic with non\u2010deterministic operators to deal with interactive systems in communication technologies","volume":"4140","author":"Aguilera G.","year":"2006","journal-title":"Lecture Notes in Artificial Intelligence"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"C.Areces andB.ten Cate Hybrid logics. 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