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http://hdl.handle.net/10119/9221
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| Title: | Interpolation Properties, Beth Definability Properties and Amalgamation Properties for Substructural Logic |
| Authors: | Kihara, Hitoshi
Ono, Hiroakira |
| Issue Date: | 2009-01-08 |
| Publisher: | Oxford University Press |
| Magazine name: | Journal of Logic and Computation |
| Volume: | 20 |
| Number: | 4 |
| Start page: | 823 |
| End page: | 875 |
| DOI: | 10.1093/logcom/exn084 |
| Abstract: | This paper develops a comprehensive study of various types of interpolation propertiesand Beth definability properties for substructural logics, and their algebraic characterizationsthrough amalgamation properties and epimorphisms surjectivity. In general, substructural logicsare algebraizable but lack many of the basic logical properties that modal and superintuitionisticlogics enjoy (cf. [7]). In this case, careful examination is necessary to see how these logical and algebraic properties are related. To describe these relations exactly, many variants of interpolation properties and Beth definability properties, and also corresponding algebraic properties, are introduced. Because of their generality, the results reported here hold not only for substructural logics, but can be extended to a more general setting such as abstract algebraic logic [1], [6]. |
| Rights: | © The Author, 2009. Published by Oxford University Press. This is a pre-copy-editing, author-produced PDF of an article accepted for publication in JOURNAL OF LOGIC AND COMPUTATION following peer review. The definitive publisher-authenticated version JOURNAL OF LOGIC AND COMPUTATION (2009) 20(4): 823-875 is available online at: http://dx.doi.org/10.1093/logcom/exn084 |
| URI: | http://hdl.handle.net/10119/9221 |
| Material Type: | author |
| Appears in Collections: | z4-10-1. 雑誌掲載論文 (Journal Articles)
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| KOipap-final.pdf | | 532Kb | Adobe PDF | View/Open |
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