Sistemas EsquemÃticos de DeduÃÃo Natural: um Estudo Prova-TeÃrico / Schematic Natural Deduction Systems: A Proof-Theoretical Study

AUTOR(ES)
FONTE

IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia

DATA DE PUBLICAÇÃO

12/03/2010

RESUMO

The term Theory Test was introduced by Hilbert to identify the study of formal proofs. Research in this area can be classified into: a) Proof Theory of reductive or interpretational, whose goal is to demonstrate, among other things, the consistency of mathematics using only methods finitistas, b) Structural Proof Theory, where the structural characteristics of the formal proofs are investigated by means of deductive systems as Natural Deduction and Sequent Calculus. Prawitz through Theory Proof set a Theory of Meaning for constants logics and proposed schematic introduction rules and elimination to characterize the propositional connectives. Schroeder-Heister settings Prawitz extended and formalized the use of rules as hypotheses, making possible the use of separate calculations for assumptions of calculations for logical constants. We are not interested in the investigation of schematic rules to give meaning to the logical constants. We intend to actually set schematic standardization procedures, based on such schematic rules? Attic, in order to identify sufficient conditions for a system to be normalizÃvel. These results are relevant to the Abstract Theory of Evidence, a term used to identify the study of the conditions abstract and general to the proof-theoretical analysis of formal systems. Abstract Theory of Evidence do not study specific logical calculations, but families of calculations instances of rules schematic. Our proposal is therefore based on rules schematic rules can be instantiated for concrete, in particular, by introducing rules modal operators. We prove also theorems NormalizaÃÃoo Weak and Strong systems defined in schematic funÃÃoo schematic of our rules, we obtain sufficient conditions for a system instance is normalizÃvel these rules, we define a procedure that normalizes deductions concrete evidence and compare our standards with evidence schematic standards for systems defined in the literature.

ASSUNTO(S)

logica matematica teoria da prova teoria abstrata da prova sistemas de deduÃÃo natural sistemas esquemÃticos de deduÃÃo natural teoremas de normalizaÃÃo theory of evidence abstract theory of evidence natural deduction systems system schematics natural deduction theorems for standardization teoria das demonstraÃÃes teoria dos sistemas anÃlise de sistemas

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