Olá João. Muitíssimo obrigado pelos links, achei muito interessante!
Vou usar também, em minhas aulas de Lógica, como exemplo de utilização da lógica de primeira ordem nos fundamentos da ciência. Abraço, Ricardo. Em 7 de maio de 2010 11:29, Joao Marcos <[email protected]> escreveu: > Dois novos artigos do arXiv.org que podem ser de interesse para quem > trabalha com a axiomatização de teorias físicas contemporâneas. > > JM > > > ---------- Forwarded message ---------- > > ------------------------------------------------------------------------------ > Submissions to: > Logic > received from Wed 5 May 10 20:00:00 GMT to Thu 6 May 10 20:00:00 GMT > > ------------------------------------------------------------------------------ > > %-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%- > > ------------------------------------------------------------------------------ > \\ > arXiv:1005.0960 (*cross-listing*) > Date: Thu, 6 May 2010 10:07:45 GMT (28kb) > > Title: A logic road from special relativity to general relativity > Authors: Hajnal Andr\'eka, Judit X. Madar\'asz, Istv\'an N\'emeti and > Gergely > Sz\'ekely > Categories: gr-qc math-ph math.LO math.MP > \\ > We present a streamlined axiom system of special relativity in first-order > logic. From this axiom system we "derive" an axiom system of general > relativity > in two natural steps. We will also see how the axioms of special relativity > transform into those of general relativity. This way we hope to make > general > relativity more accessible for the non-specialist. > \\ ( http://arxiv.org/abs/1005.0960 , 28kb) > > ------------------------------------------------------------------------------ > \\ > arXiv:1005.0973 (*cross-listing*) > Date: Thu, 6 May 2010 10:55:35 GMT (347kb) > > Title: First-Order Logic Investigation of Relativity Theory with an > Emphasis on > Accelerated Observers > Authors: Gergely Sz\'ekely > Categories: gr-qc math-ph math.LO math.MP > Comments: PhD thesis E\"otv\"os Lor\'and University > \\ > This thesis is mainly about extensions of the first-order logic > axiomatization of special relativity introduced by Andr\'eka, Madar\'asz > and > N\'emeti. These extensions include extension to accelerated observers, > relativistic dynamics and general relativity; however, its main subject is > the > extension to accelerated observers (AccRel). One surprising result is that > natural extension to accelerated observers is not enough if we want our > theory > to imply certain experimental facts, such as the twin paradox. Even if we > add > the whole first-order theory of real numbers to this natural extension, it > is > still not enough to imply the twin paradox. Nevertheless, that does not > mean > that this task cannot be carried out within first-order logic since by > approximating a second-order logic axiom of real numbers, we introduce a > first-order axiom schema that solves the problem. Our theory AccRel nicely > fills the gap between special and general relativity theories, and only one > natural generalization step is needed to achieve a first-order logic > axiomatization of general relativity from it. We also show that AccRel is > strong enough to make predictions about the gravitational effect slowing > down > time. Our general aims are to axiomatize relativity theories within pure > first-order logic using simple, comprehensible and transparent basic > assumptions (axioms); to prove the surprising predictions (theorems) of > relativity theories from a few convincing axioms; to eliminate tacit > assumptions from relativity by replacing them with explicit axioms > formulated > in first-order logic (in the spirit of the first-order logic foundation of > mathematics and Tarski's axiomatization of geometry); and to investigate > the > relationship between the axioms and the theorems. > \\ ( http://arxiv.org/abs/1005.0973 , 347kb) > > %%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%% > > %%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%--- > For general information on the new math archive (partitioned by > keyword subject classification), see http://arXiv.org/new/math.html > For subscribe options to combined math archives, > e-mail To: [email protected], Subject: subscribe > _______________________________________________ > Logica-l mailing list > [email protected] > http://www.dimap.ufrn.br/cgi-bin/mailman/listinfo/logica-l > -- Dr. Ricardo Pereira Tassinari - Departamento de Filosofia UNESP - Faculdade de Filosofia e Ciências - Marília Homepage: http://www.marilia.unesp.br/ricardotassinari
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