De Finettian Logics of Indicative Conditionals Part II: Proof Theory and Algebraic Semantics

Abstract In Part I of this paper, we identified and compared various schemes for trivalent truth conditions indicative conditionals, most notably the proposals by de Finetti (1936) Reichenbach (1935, 1944) on one hand, Cooper ( Inquiry , 11 295–320, 1968) Cantwell Notre Dame Journal Formal Logic 49 245–260, 2008) other. Here provide proof theory resulting logics using tableau calculi sequent calculi, proving soundness completeness results. Then turn to algebraic semantics, where both have substantive limitations: allows completeness, but not construction a canonical model, while fails Lindenbaum-Tarski algebra. With these results in mind, draw up balance sketch future research projects.