Representatain and combination of logics: conceptual questions

Author(s)

Alberto Leopoldo Batista Neto

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Filosofia e Ciências Humanas
• Defense date: 2007-04-26

Examining board members

Marcelo Esteban Coniglio; Hercules de Araujo Feitosa; Itala Maria Loffredo D'Ottaviano

• Advisor: Marcelo Esteban Coniglio

Abstract

In order to accomplish an elucidation of the fundamental concepts involved in the study of the combinations between logics, we undertake an analysis of the problem of the general representation of logical systems (with an emphasis on the central concept of logical consequence) together with that of the establishment of an appropriate notion of translation or morphism between the logical systems defined in a certain fashion, on which basis we can ground some of the combination techniques, specially that of algebraic fibring. Such techniques are defined and presented in their most relevant features, and we find, in the particular case of fibring, problems such as collapsing and anticollapsing. The solution for these seem to rest on the choice of adequate forms of representing logics in general and translating logics into others. A modeltheoretic presentation shows itself appropriate for some representations of logics in general (such as Hilbert calculi), although they are not for some others (such as multipleconclusion systems). Notwithstanding, two of the most promising attempts to solve, in particular, the problem of the anticollapsing of algebraic fibring metatranslations and elementary transfers , are definable within that framework. Transfers including elementary transfers have been defined in [17] and we here present a representation of metatranslations as an specific kind of transfers (AU)