A property $P$ is verifiable if, when it is true, it is possible to ascertain this fact via finite means.
An example would be ‘This program halts eventually’. If this statement is true then it can be confirmed in finite time simply by observing the program until such a time as it halts. If the statement is not true then this can never be ascertained through finite observation alone.
There is a logic of verifiable properties with the following connectives:
1. $\top$ is verifiable,
2. $\bot$ is verifiable,
3. If $P$ and $Q$ are verifiable then $P \wedge Q$ is verifiable,
4. If a family $P_i$ are verifiable then $\bigvee P_i$ is verifiable.
These satisfy all of the usual logical axioms (associativity, idempotence, commutativity and distributivity). The connective true $\top$ and false $\bot$ are the identities of $\wedge$ and $\vee$ respectively.
The opposite of a verifiable property is a [[Refutability|Refutable]] one.
Models of verifiable logic are [[Frame]]s and [[Topological Space]]s, where verifiable properties correspond to [[Open Set|Opens]].