Talk:Rational consequence relation

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	Logic

RMO generalizes CMO ?

It seems to me that rule RMO ${\frac {p\vdash r\quad \quad p\not \vdash \lnot q}{p\land q\vdash r}}$ is a generalization of rule CMO ${\frac {p\vdash r\quad \quad p\vdash q}{p\land q\vdash r}}$ . For, if $p\vdash q$ holds, then, assuming consistency, $p\not \vdash \lnot q$ also holds. Therefore, I wonder why both rules are required. - Jochen Burghardt (talk) 15:57, 14 October 2023 (UTC)[reply]