Categorical Abstract Algebraic Logic: Meet-Combination of Logical Systems
The widespread and rapid proliferation of logical systems in several areas of computer science has led to a resurgence of interest in various methods for combining logical systems and in investigations into the properties inherited by the resulting combinations. One of the oldest such methods is fib...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/126347 |
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| _version_ | 1832567635331514368 |
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| author | George Voutsadakis |
| author_facet | George Voutsadakis |
| author_sort | George Voutsadakis |
| collection | DOAJ |
| description | The widespread and rapid proliferation of logical systems in several areas of computer science has led to a resurgence of interest in various methods for combining logical systems and in investigations into the
properties inherited by the resulting combinations. One of the oldest such methods is fibring. In fibring the shared connectives of the combined logics inherit properties from both component logical systems, and this leads often to inconsistencies. To deal with such undesired effects, Sernadas et al. (2011, 2012) have recently introduced a novel way of combining logics, called meet-combination, in which the combined connectives share only the common logical properties they enjoy in the component systems. In their investigations they provide a sound and concretely complete calculus for the meet-combination based on available sound and complete calculi for the component systems. In this work, an effort is made to abstract those results to a categorical level amenable to categorical abstract algebraic logic techniques. |
| format | Article |
| id | doaj-art-1d4c69910b364f55b3dd61268bd62992 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-1d4c69910b364f55b3dd61268bd629922025-02-03T01:00:57ZengWileyJournal of Mathematics2314-46292314-47852013-01-01201310.1155/2013/126347126347Categorical Abstract Algebraic Logic: Meet-Combination of Logical SystemsGeorge Voutsadakis0School of Mathematics and Computer Science, Lake Superior State University, Sault Sainte Marie, MI 49783, USAThe widespread and rapid proliferation of logical systems in several areas of computer science has led to a resurgence of interest in various methods for combining logical systems and in investigations into the properties inherited by the resulting combinations. One of the oldest such methods is fibring. In fibring the shared connectives of the combined logics inherit properties from both component logical systems, and this leads often to inconsistencies. To deal with such undesired effects, Sernadas et al. (2011, 2012) have recently introduced a novel way of combining logics, called meet-combination, in which the combined connectives share only the common logical properties they enjoy in the component systems. In their investigations they provide a sound and concretely complete calculus for the meet-combination based on available sound and complete calculi for the component systems. In this work, an effort is made to abstract those results to a categorical level amenable to categorical abstract algebraic logic techniques.http://dx.doi.org/10.1155/2013/126347 |
| spellingShingle | George Voutsadakis Categorical Abstract Algebraic Logic: Meet-Combination of Logical Systems Journal of Mathematics |
| title | Categorical Abstract Algebraic Logic: Meet-Combination of Logical Systems |
| title_full | Categorical Abstract Algebraic Logic: Meet-Combination of Logical Systems |
| title_fullStr | Categorical Abstract Algebraic Logic: Meet-Combination of Logical Systems |
| title_full_unstemmed | Categorical Abstract Algebraic Logic: Meet-Combination of Logical Systems |
| title_short | Categorical Abstract Algebraic Logic: Meet-Combination of Logical Systems |
| title_sort | categorical abstract algebraic logic meet combination of logical systems |
| url | http://dx.doi.org/10.1155/2013/126347 |
| work_keys_str_mv | AT georgevoutsadakis categoricalabstractalgebraiclogicmeetcombinationoflogicalsystems |