Um modelo algébrico para a lógica do muito
Arquivos
Data
2013-10-09
Autores
Vaine, Camila Augusta [UNESP]
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ISSN da Revista
Título de Volume
Editor
Universidade Estadual Paulista (Unesp)
Resumo
Esta dissertação trata, em um primeiro momento, de um estudo sobre quantificadores com seus aspectos históricos e algumas concepções sobre quantificadores generalizados, a saber, a concepção de Mostowski (1957), criada com o objetivo de formalizar alguns conceitos matemáticos, e a concepção de Barwise e Cooper (1981), que tem como objetivo aproximar a lógica da linguagem natural. A partir daí, Sette, Carnielli e Veloso (1999) introduziram um sistema lógico, a lógica dos ultrafiltros, para formalizar a noção de “geralmente” ou “quase todos”, através da introdução de um novo quantificador generalizado na linguagem clássica de primeira ordem. Em continuidade, Grácio (1999) apresentou uma ampla família de sistemas lógicos, a família das lógicas moduladas, determinados por novos quantificadores. Dentre as lógicas moduladas estudadas por Grácio, destacamos a Lógica do Muito, que se caracteriza por estender a lógica clássica através da introdução de um novo quantificador generalizado na sua sintaxe. Por outro lado, Halmos (1962) estuda as álgebras monádicas e apresenta a interpretação dos quantificadores universal e existencial nestas álgebras. Neste trabalho, desenvolvemos uma álgebra monádica e uma lógica monádica do muito, com base nos trabalhos de Halmos, com o intuito de apresentar outro modelo algébrico para a lógica do muito. Por fim, mostramos que a lógica do muito é correta e completa, em relação a álgebra monádica do muito apresentada
This dissertation presents a study of quantifiers with their historical development and some conceptions about generalized quantifiers, namely the designed by Mostowski (1957), which was created with the purpose of formalizing some mathematical concepts, and in a complementary way, the notion of Barwise and Cooper (1981), which aims to link logic and natural language. In 1999, Sette, Carnielli and Veloso introduced a logical system, the logic of ultrafilters, in order to formalize the notion of generally or almost all through the introduction of a new generalized quantifier into the language of classical first order logic. Furthermore, Grácio (1999) presented a wide family of logical systems, named modulated logics determined by new quantifiers. Among the modulated logics studied by Grácio, we take the Logic of Many, which is characterized by extending the classical logic by introducing a new generalized quantifier in its syntax for the notion of “many”. On the other hand, Halmos (1962) studied the monadic algebras associated with classical logic and presented the interpretation of universal and existential quantifiers in these algebras. In this dissertation, we develope a monadic algebra of many and monadic logic of many, based on the work of Halmos for to presenting a different algebraic model for the Logic of Many. Finally, we show that the logic of many is sound and complete in relation to the presented in this dissertation monadic algebra of many
This dissertation presents a study of quantifiers with their historical development and some conceptions about generalized quantifiers, namely the designed by Mostowski (1957), which was created with the purpose of formalizing some mathematical concepts, and in a complementary way, the notion of Barwise and Cooper (1981), which aims to link logic and natural language. In 1999, Sette, Carnielli and Veloso introduced a logical system, the logic of ultrafilters, in order to formalize the notion of generally or almost all through the introduction of a new generalized quantifier into the language of classical first order logic. Furthermore, Grácio (1999) presented a wide family of logical systems, named modulated logics determined by new quantifiers. Among the modulated logics studied by Grácio, we take the Logic of Many, which is characterized by extending the classical logic by introducing a new generalized quantifier in its syntax for the notion of “many”. On the other hand, Halmos (1962) studied the monadic algebras associated with classical logic and presented the interpretation of universal and existential quantifiers in these algebras. In this dissertation, we develope a monadic algebra of many and monadic logic of many, based on the work of Halmos for to presenting a different algebraic model for the Logic of Many. Finally, we show that the logic of many is sound and complete in relation to the presented in this dissertation monadic algebra of many
Descrição
Palavras-chave
Álgebra, Lógica, Linguagem e lógica
Como citar
VAINE, Camila Augusta. Um modelo algébrico para a lógica do muito. 2013. 111 f. Dissertação (mestrado) - Universidade Estadual Paulista Júlio de Mesquita Filho, Faculdade de Filosofia e Ciências de Marília, 2013.