Abstract
The idea of solving problems in logic by first translating them to algebra, then using the powerful methodology of algebra for solving them, and then translating the solution back to logic, goes back to Leibnitz and Pascal. Papers on the history of Logic (e.g. Anellis-Houser [4], Maddux [14]) point out that this method was fruitfully applied in the 19th century not only to propositional logics but also to quantifier logics (De Morgan, Peirce etc. applied it to quantifier logics too). The number of applications grew ever since. (Though some of these remained unnoticed, e.g. the celebrated Kripke-Lemmon completeness theorem for modal logic w.r.t. Kripke models was first proved by Jónsson and Tarski in 1948 using algebraic logic.)
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Andréka, H., Németi, I., Sain, I. (1994). Applying Algebraic Logic to Logic. In: Nivat, M., Rattray, C., Rus, T., Scollo, G. (eds) Algebraic Methodology and Software Technology (AMAST’93). Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3227-1_3
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DOI: https://doi.org/10.1007/978-1-4471-3227-1_3
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