Abstract
When can we say that two distinct logical systems are, nevertheless, essentially the “same”? In this paper we discuss the notion of “sameness” between logical systems, bearing in mind the expressive power of their associated spaces of theories, but without neglecting their syntactical dimension. Departing from a categorial analysis of the question, we introduce the new notion of equipollence between logical systems. We use several examples to illustrate our proposal and to support its comparison to other proposals in the literature, namely homeomorphisms [7], and translational equivalence (or synonymity) [6].
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This work was partially supported by FCT and EU FEDER, namely, via the Projects POCTI/2001/MAT/37239 FibLog and POCTI/MAT/55796/2004 QuantLog of CLC. The second author was also supported by FCT under the PhD grant SFRH/BD/18345/2004/SV7T.
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© 2007 Birkhäuser Verlag Basel/Switzerland
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Caleiro, C., Gonçalves, R. (2007). Equipollent Logical Systems. In: Beziau, JY. (eds) Logica Universalis. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8354-1_6
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DOI: https://doi.org/10.1007/978-3-7643-8354-1_6
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8353-4
Online ISBN: 978-3-7643-8354-1
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