If I have two propositions $p$ and $q$, what is the simplest standard notation for expressing that they are logically consistent with each other—in other words, that no contradiction can be derived from assuming them both.
Something like $\,p,q \,\nvdash\! \bot$ seems clunky, especially if we use the notation many times, and $p \parallel q$ has unwanted connotations from geometry. Are there better options?
META: This is a very basic question about mathematical notation. From perusing the various Stack Exchange sites, it appears math.se is the best place to ask it, but feel free to correct me if I'm wrong.
Best Answer
I'm sorry to disappoint your expectations, but the widely used notation to say that two propositions $p$ and $q$ are consistent with each other is $p,q \not\vdash \bot$ or $\text{Con}(\{p,q\})$. This is the same notation used more in general to say that a set $\Gamma$ of propositions is consistent ($\Gamma \not\vdash \bot$ or $\text{Con}(\Gamma)$).
As far as I know, there is no special (and widely used) notation for consistency of just two propositions.