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A topological framework for program semantics
Program semantics can be viewed relationally as in relational semantics, algebraically as in predicate transformer semantics, logically as in information systems and order-theoretically as in denotational semantics. This can be compared to a common situation in non-classical logics. Namely, a logic...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2024
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| _version_ | 1867613299321864192 |
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| access_status_str | Open Access |
| author | Rewitzky, Ingrid Moira |
| author2 | Brink, Chris |
| author_browse | Brink, Chris Rewitzky, Ingrid Moira |
| author_facet | Brink, Chris Rewitzky, Ingrid Moira |
| author_sort | Rewitzky, Ingrid Moira |
| collection | Thesis |
| description | Program semantics can be viewed relationally as in relational semantics, algebraically as in predicate transformer semantics, logically as in information systems and order-theoretically as in denotational semantics. This can be compared to a common situation in non-classical logics. Namely, a logic can often be presented as a formal deductive system, as an algebra and as a relational structure, with each of the presentations derivable from each of the other two. The central hypothesis of this thesis is that this situation can serve as a paradigm for unifying the various versions of program semantics. Starting with a relational semantics based on certain ordered topological spaces, called Priestley spaces, and invoking the techniques of Priestley duality, an algebraic. a logical and an order-theoretic presentation of program semantics are derived. Each of these four presentations are also derivable from each of the other three. The topological model of program semantics based on Priestley spaces thus serves as a unifying framework for other versions of program semantics, essentially as in the logic-algebra-semantics paradigm. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/40619 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:55.830Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/40619 A topological framework for program semantics Rewitzky, Ingrid Moira Brink, Chris Mathematics and Applied Mathematics Program semantics can be viewed relationally as in relational semantics, algebraically as in predicate transformer semantics, logically as in information systems and order-theoretically as in denotational semantics. This can be compared to a common situation in non-classical logics. Namely, a logic can often be presented as a formal deductive system, as an algebra and as a relational structure, with each of the presentations derivable from each of the other two. The central hypothesis of this thesis is that this situation can serve as a paradigm for unifying the various versions of program semantics. Starting with a relational semantics based on certain ordered topological spaces, called Priestley spaces, and invoking the techniques of Priestley duality, an algebraic. a logical and an order-theoretic presentation of program semantics are derived. Each of these four presentations are also derivable from each of the other three. The topological model of program semantics based on Priestley spaces thus serves as a unifying framework for other versions of program semantics, essentially as in the logic-algebra-semantics paradigm. 2024-10-25T12:06:35Z 2024-10-25T12:06:35Z 1995 2024-07-12T06:20:25Z Thesis / Dissertation Doctoral PhD http://hdl.handle.net/11427/40619 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science |
| spellingShingle | Mathematics and Applied Mathematics Rewitzky, Ingrid Moira A topological framework for program semantics |
| thesis_degree_str | Doctoral |
| title | A topological framework for program semantics |
| title_full | A topological framework for program semantics |
| title_fullStr | A topological framework for program semantics |
| title_full_unstemmed | A topological framework for program semantics |
| title_short | A topological framework for program semantics |
| title_sort | topological framework for program semantics |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/40619 |
| work_keys_str_mv | AT rewitzkyingridmoira atopologicalframeworkforprogramsemantics AT rewitzkyingridmoira topologicalframeworkforprogramsemantics |