An introduction to definitional equivalence and Morita-equivalence in the Many-Sorted First Order Logic
DOI:
https://doi.org/10.22370/sst.2020.8.4926Keywords:
logic, logical equivalence, signature, first orderAbstract
In this article we introduce the differences between the concepts of definitional equivalence and Morita-equivalence between theories, and the concept of logical equivalence between theories too, all of them under the Many-Sorted First Order Logic. In order to achieve this, in the first half of this text we focus on explaining the concepts of signature, structure and usual semantic we found in this logic. Next, we apply of these concepts to create the appropiate framework in order to present and improve the definitions of definitional equivalence and Morita-equivalence between theories regarding the articles that have already dealt with them before and that appear in our bibliography.
References
Barrett, T. W. y Halvorson, H. (2016). Morita equivalence. The Review of Symbolic Logic, 9(3):556–582.
Barrett, T. W. y Halvorson, H. (2017). Quine’s conjecture on many-sorted logic. Synthese, 194(9):3563–3582.
Halvorson, H. (2019). The Logic in Philosophy of Science. Cambridge: Cambridge University Press.
Hodges, W. (1993). Model Theory. Cambridge: Cambridge University Press.
Manzano, M. (1996). Extensions of first-order logic. Cambridge: Cambridge University Press.
Mceldowney, P. A. (2019). On morita equivalence and interpretability. The Review of Symbolic Logic, pages 1–28.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.