A property $P$ is refutable if, when it is false, it is possible to ascertain this fact via finite means.
For instance ‘This computer program runs forever’. Slightly more hand-wavy examples are scientific theories.
There is a logic of refutability with the following connectives.
1. $\top$ is refutable,
2. $\bot$ is refutable,
3. If a family $P_i$ are verifiable then $\bigwedge P_i$ is refutable,
4. If $P$ and $Q$ are verifiable then $P \vee Q$ is refutable,
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 refutable property is a [[Verifiability|Verifiable]] one.
Models of the logic of refutability are given by the [[Closed Set]]s of a [[Topological Space]].