Por favor, use este identificador para citar o enlazar este ítem:
https://repositorio.ufba.br/handle/ri/14883
metadata.dc.type: | Artigo de Periódico |
Título : | Construction of a canonical model for a first-order non-Fregean logic with a connective for reference and a total truth predicate |
Otros títulos : | Logic Journal of the IGPL |
Autor : | Lewitzka, Steffen |
metadata.dc.creator: | Lewitzka, Steffen |
Resumen : | Logics with quantifiers that range over a model-theoretic universe of propositions are interesting for several applications. For example, in the context of epistemic logic the knowledge axioms can be expressed by the single sentences ∀x.(Kix → x), and in a truth-theoretical context an analogue to Tarski's T-scheme can be expressed by the single axiom ∀x.(x:true ↔ x). In this article, we consider a first-order non-Fregean logic, originally developed by Sträter, which has a total truth predicate and is able to model propositional self-reference. We extend this logic by a connective ‘<’ for propositional reference and study semantic aspects. φ < ψ expresses that the proposition denoted by formula ψ says something about (refers to) the proposition denoted by φ. This connective is related to a syntactical reference relation on formulas and to a semantical reference relation on the propositional universe of a given model. Our goal is to construct a canonical model, i.e. a model that establishes an order-isomorphism from the set of sentences (modulo alpha-congruence) to the universe of propositions, where syntactical and semantical reference are the respective orderings. The construction is not trivial because of the impredicativity of quantifiers: the bound variable in ∃x.φ ranges over all propositions, in particular over the proposition denoted by ∃x.φ itself. Our construction combines ideas coming from Sträter's dissertation with the algebraic concept of a canonical domain, which is introduced and studied in this article. |
Palabras clave : | Non-Fregean logic Propositional quantifiers Impredicativity Propositional (self-) reference Truth theory |
metadata.dc.rights: | Acesso Aberto |
URI : | http://repositorio.ufba.br/ri/handle/ri/14883 |
Fecha de publicación : | 2012 |
Aparece en las colecciones: | Artigo Publicado em Periódico (IME) |
Ficheros en este ítem:
Fichero | Descripción | Tamaño | Formato | |
---|---|---|---|---|
Steffen Lewitzka.pdf | 286,59 kB | Adobe PDF | Visualizar/Abrir |
Los ítems de DSpace están protegidos por copyright, con todos los derechos reservados, a menos que se indique lo contrario.