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Firstorder logic foundation of relativity theories
 In New Logics for the XXIst Century II, Mathematical Problems from Applied Logics, volume 5 of International Mathematical Series
, 2006
"... Abstract. Motivation and perspective for an exciting new research direction interconnecting logic, spacetime theory, relativity— including such revolutionary areas as black hole physics, relativistic computers, new cosmology—are presented in this paper. We would like to invite the logician reader to ..."
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Cited by 8 (8 self)
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Abstract. Motivation and perspective for an exciting new research direction interconnecting logic, spacetime theory, relativity— including such revolutionary areas as black hole physics, relativistic computers, new cosmology—are presented in this paper. We would like to invite the logician reader to take part in this grand enterprise of the new century. Besides general perspective and motivation, we present initial results in this direction.
Logic of spacetime and relativity theory
, 2006
"... 2.1 Motivation for special relativistic kinematics in place of Newtonian kinematics......................... 4 ..."
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Cited by 5 (3 self)
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2.1 Motivation for special relativistic kinematics in place of Newtonian kinematics......................... 4
AXIOMATIZING RELATIVISTIC DYNAMICS WITHOUT CONSERVATION POSTULATES
"... Abstract. A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within firstorder logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein’s famous E = mc 2 ..."
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Cited by 3 (3 self)
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Abstract. A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within firstorder logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein’s famous E = mc 2. The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and fourmomentum is also investigated. 1.
A logical analysis of the timewarp effect of general relativity,” in preparation
"... Abstract. Several versions of the Gravitational Time Dilation effect of General Relativity are formulated by the use of Einstein’s Equivalence Principle. It is shown that all of them are logical consequence of a firstorder axiom system of Special Relativity extended to accelerated observers. 1. ..."
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Cited by 2 (1 self)
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Abstract. Several versions of the Gravitational Time Dilation effect of General Relativity are formulated by the use of Einstein’s Equivalence Principle. It is shown that all of them are logical consequence of a firstorder axiom system of Special Relativity extended to accelerated observers. 1.
Vienna Circle and Logical Analysis of Relativity Theory
, 2009
"... 1 introduction In this paper we present some of our school’s results in the area of building up relativity theory (RT) as a hierarchy of theories in the sense of logic. We use plain firstorder logic (FOL) as in the foundation of mathematics (FOM) and we build on experience gained in FOM. The main a ..."
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1 introduction In this paper we present some of our school’s results in the area of building up relativity theory (RT) as a hierarchy of theories in the sense of logic. We use plain firstorder logic (FOL) as in the foundation of mathematics (FOM) and we build on experience gained in FOM. The main aims of our school are the following: We want to base the theory on simple, unambiguous axioms with clear meanings. It should be absolutely understandable for any reader what the axioms say and the reader can decide about each axiom whether he likes it. The theory should be built up from these axioms in a straightforward, logical manner. We want to provide an analysis of the logical structure of the theory. We investigate which axioms are needed for which predictions of RT. We want to make RT more transparent logically, easier to understand, easier to change, modular, and easier to teach. We want to obtain deeper understanding of RT. Our work can be considered as a casestudy showing that the Vienna
A GEOMETRICAL CHARACTERIZATION OF THE TWIN PARADOX AND ITS VARIANTS
, 807
"... Abstract. The aim of this paper is to provide a conceptual analysis of the twin paradox (TwP) within a firstorder logic framework. We give a geometrical characterization of TwP and its variants, for example, one without differential aging (NoTwP). It is shown that TwP is not equivalent to the assu ..."
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Abstract. The aim of this paper is to provide a conceptual analysis of the twin paradox (TwP) within a firstorder logic framework. We give a geometrical characterization of TwP and its variants, for example, one without differential aging (NoTwP). It is shown that TwP is not equivalent to the assumption of slowing down of moving clocks and NoTwP is not equivalent to the Newtonian assumption of the absoluteness of time. The connection of TwP and a symmetry axiom of Special Relativity is also studied. 1.
COMPARING RELATIVISTIC AND NEWTONIAN DYNAMICS IN FIRSTORDER LOGIC
"... In this paper we introduce and compare Newtonian and relativistic dynamics as two theories of firstorder logic (FOL). To illustrate the similarities between Newtonian and relativistic dynamics, we axiomatize them such that they differ in one axiom only. This one axiom ..."
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In this paper we introduce and compare Newtonian and relativistic dynamics as two theories of firstorder logic (FOL). To illustrate the similarities between Newtonian and relativistic dynamics, we axiomatize them such that they differ in one axiom only. This one axiom