{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/40619"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/40619","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"A topological framework for program semantics","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Rewitzky, Ingrid Moira"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Brink, Chris"],"committee_chairs":[],"committee_members":[],"year":1995,"date_issued":"1995","date_published":"1995","updated_at":"2026-07-22T22:23:19Z","subjects":["Mathematics and Applied Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/40619","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Brink, Chris"]},{"key":"dc:creator","label":"Author","values":["Rewitzky, Ingrid Moira"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-10-25T12:06:35Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-10-25T12:06:35Z"]},{"key":"dc:date.issued","label":"Date","values":["1995"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:type","label":"Dc Type","values":["Thesis / Dissertation"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral","PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics and Applied Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/40619"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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. 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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."],"dc:identifier.uri":["http://hdl.handle.net/11427/40619"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:subject":["Mathematics and Applied Mathematics"],"dc:title":["A topological framework for program semantics"],"dc:type":["Thesis / Dissertation"],"dc:type.qualificationlevel":["Doctoral","PhD"]},"updated_at":"2026-07-22T22:23:19Z"}