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There are several first-order logic (FOL) axiomatizations of specialrelativity theory in the literature, all looking essentially different butclaiming to axiomatize the same physical theory. In this paper, we elaborate acomparison, in the framework of mathematical logic, between these FOL theoriesfor special relativity. For this comparison, we use a version of mathematicaldefinability theory in which new entities can also be defined besides newrelations over already available entities. In particular, we build aninterpretation of the reference-frame oriented theory SpecRel into theobservationally oriented Signalling theory of James Ax. This interpretationprovides SpecRel with an operational/experimental semantics. Then we makeprecise, "quantitative" comparisons between these two theories via using thenotion of definitional equivalence. This is an application of logic to thephilosophy of science and physics in the spirit of Johan van Benthem's work.

Comparing theories: the dynamics of changing vocabulary. A case-study in relativity theory