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A Glimpse to the Logic of Provability


Academic year: 2022

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A Glimpse to the Logic of Provability (Un Vistazo a la L´ogica Demostrativa)

Erick Ju´arez-Guti´errez Department of Physics and Mathematics, Institute for Engineering and Technology,

Autonomous University of Juarez, JU ´AREZ, CHIHUAHUA, 32310, MEXICO


Abstract. The logic of provability has its origin in an article published by Kurt G¨odel in 1933, where there is a provability of the Intuitionistic Propositional Logic of LEJ Brouwer (founder), whose objective is to determine what arithmetic theory can be expressed with a language restricted on demonstrative predicates.

In this logic the modality⇤, “it is necessary that”, is going to be interpreted asit must be proven that. The need for this logic is that in classical logic it is limited to adenunciativelanguage. Therefore, we do not have theneedmodality; that is, in the Logic of Provability, the modalitymust be proven that. In this report, the main objective is to introduce what this logic is, its language, axioms, rules of inference, well-formed formulas, which theorems exist, as well as a conclusion about its advantages and disadvantages.

Resumen:La L´ogica Demostrativa tiene su origen en un art´ıculo publicado por Kurt G¨odel en el a˜no 1933, donde se da unademostrabilidadde la L´ogica Proposi- cional Intuicionista de L. E. J. Brouwer (fundador), tiene como objetivo determi- nar qu´e teor´ıa aritm´etica se puede expresar con un lenguaje restringido sobre predicados demostrativos. En esta l´ogica la modalidad⇤(es necesario que) va a ser interpretada comodebe ser demostrado que. La necesidad de esta l´ogica reside que en la L´ogica Cl´asica solamente se limita al lenguajedenunciativo. Por lo tanto, no tenemos las modalidadnecesidad; esto es en la L´ogica Demostrativa, la modalidaddebe ser demostrado que. En este reporte, se tiene como objetivo principal introducir lo que es esta l´ogica, su lenguaje, axiomas, reglas de infer- encia, f´ormulas bien formadas, cu´ales teoremas existen, as´ı como una conclusi´on sobre sus ventajas y desventajas.


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