Journal of Philosophical Logic 50 (2):215-247 (2021)

Authors
Lorenzo Rossi
University of Salzburg
Jan Sprenger
University of Turin
Abstract
In Part I of this paper, we identified and compared various schemes for trivalent truth conditions for indicative conditionals, most notably the proposals by de Finetti and Reichenbach on the one hand, and by Cooper and Cantwell on the other. Here we provide the proof theory for the resulting logics DF/TT and CC/TT, using tableau calculi and sequent calculi, and proving soundness and completeness results. Then we turn to the algebraic semantics, where both logics have substantive limitations: DF/TT allows for algebraic completeness, but not for the construction of a canonical model, while CC/TT fails the construction of a Lindenbaum-Tarski algebra. With these results in mind, we draw up the balance and sketch future research projects.
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DOI 10.1007/s10992-020-09572-7
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References found in this work BETA

On Conditionals.Dorothy Edgington - 1995 - Mind 104 (414):235-329.
The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
A Counterexample to Modus Ponens.Vann McGee - 1985 - Journal of Philosophy 82 (9):462-471.
Basic Proof Theory.A. S. Troelstra - 2000 - Cambridge University Press.

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