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Use este identificador para citar ou linkar para este item: https://repositorio.ufba.br/handle/ri/14354
Tipo: Artigo de Periódico
Título: Abstract logics, logic maps, and logic homomorphisms
Título(s) alternativo(s): Logica Universalis
Autor(es): Lewitzka, Steffen
Autor(es): Lewitzka, Steffen
Abstract: What is a logic? Which properties are preserved by maps between logics? What is the right notion for equivalence of logics? In order to give satisfactory answers we generalize and further develop the topological approach of [4] and present the foundations of a general theory of abstract logics which is based on the abstract concept of a theory. Each abstract logic determines a topology on the set of theories. We develop a theory of logic maps and show in what way they induce (continuous, open) functions on the corresponding topological spaces. We also establish connections to well-known notions such as translations of logics and the satisfaction axiom of institutions [5]. Logic homomorphisms are maps that behave in some sense like continuous functions and preserve more topological structure than logic maps in general. We introduce the notion of a logic isomorphism as a (not necessarily bijective) function on the sets of formulas that induces a homeomorphism between the respective topological spaces and gives rise to an equivalence relation on abstract logics. Therefore, we propose logic isomorphisms as an adequate and precise notion for equivalence of logics. Finally, we compare this concept with another recent proposal presented in [2].
Palavras-chave: Primary 03B22
Secondary 54A99, 03G30
Abstract logics
Logic maps
Logic translations
Logic homomorphism
Universal logic
Topology
Institutions
Tipo de Acesso: Acesso Aberto
URI: http://repositorio.ufba.br/ri/handle/ri/14354
Data do documento: 2007
Aparece nas coleções:Artigo Publicado em Periódico (PGCOMP)

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