Abstract: The first-order logic(FOL) approach to the foundation of spacial relativity has been elaborated in , , , . Besides foundation, these works elaborate a logic based conceptual analysis for special relativity, and reverse mathematics for space-time. The latter can be regarded as extending reverse geometry fo relativistic space-time.
In the present work we outline steps in generalizing the above FOL approach to foundation etc. of special relativity towards general relativity (GR). One of the key steps is making our FOL-theories for relativity local in the sense of GR. We show how to do this in such a way that we remain in the framework of FOL. Another step towards GR is to extend our theory to allow accelerated observers. Acceleration makes it possible to discuss some effects of gravity via Einstein's Equivalence Principle. Combining these two steps (localization, accelerated observers) makes it possible to develop a rather transparent, natural and simple FOL-theory going beyond SR.
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