Axioms for Equivalential Calculus ========================================================= Rules: (S) The substitution rule is defined in a standard way. (D) $E\alpha\beta, \alpha\vdash \beta$ (RD) $E\alpha\beta, \beta\vdash \alpha$ ========================================================= Rules: S+D --------------- Sets of axioms: A1. Epp A2. EEpqEqp A3. EEEpqEqrEpr (wajsberg1932) (cf. Yoshinari1966) W1a. EEEpqrEpEqr W2a. EEpqEqp (wajsberg1932)(cf. Yoshinari1966) W1b. EEpEqrErEqp W2b. EEEpppp (wajsberg1937) W1a'. EEpEqrEEpqr (lesniewski1929) W2a. EEpqEqp -------------- Single axiom: (wajsberg1932) EEEpEqrEErssEpq (wajsberg1932) EEEEpqrsEsEpEqr Bryman EEpEqrEEqEsrEsp (sobocinski1932) EEpEqrEEpErsEsq (sobocinski1932) EEpEqrEEpEsrEsq (sobocinski1932) EEpEqrEEpErsEqs (lukasiewicz1939) EEpEqrEEqErsEsp (lukasiewicz1939) EEsEpEqrEEpqErs -------------- Single 11 characters long axiom: (lukasiewicz1939) YQL. EEpqEErqEpr YQF. EEpqEEprErq YQJ. EEpqEErpEqr (meredith1963) UM. EEEpqrEqErp XGF. EpEEqEprErq WN. EEpEqrErEpq YRM. EEpqErEEqrp YRO. EEpqErEErqp PYO. EEEpEqrrEqp PYM. EEEpEqrqErp (kalman1978) XGK. EpEEqErpErq (wos1983) XHK. EpEEqrEEprq XHN. EpEEqrEErpq (wos2003) XCB. EpEEEpqErqr