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].
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J.-Y. Béziau, R.P. de Freitas, J.P. Viana. What is Classical Propositional Logic? (A Study in Universal Logic), Logica Studies 7, 2001.
C. Caleiro. Combining Logics. PhD thesis, IST, TU Lisbon, Portugal, 2000.
J. Czelakowski. Equivalential logics I, II, Studia Logica 40, pp. 227–236, 335–372.
D. Gabbay. What is a Logical System? Oxford University Press, 1994.
R. Goldblatt. Logics of Time and Computation. CSLI, 1992. Second edition.
F.J. Pelletier and A. Urquhart. Synonymous Logics, Journal of Philosophical Logic, 32, 2003, pp. 259–285.
S. Pollard. Homeomorphism and the Equivalence of Logical Systems, Notre Dame Journal of Formal Logic, 39, 1998, pp. 422–435.
A. Sernadas, C. Sernadas, and C. Caleiro. Synchronization of logics, Studia Logica, 59(2):217–247, 1997.
R. Wójcicki, Theory of Logical Calculi. Synthese Library, vol. 199, Kluwer Academic Publishers, 1988.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Birkhäuser Verlag Basel/Switzerland
About this paper
Cite this paper
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
Download citation
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
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)