An "incomplete proof" is a collection of ideas for how one might go about finding a particular proof.
In an incomplete proof, there are two DirectedAcyclicGraphs:
- The graph of the possible, branching from the premises of the desired theorem
- The graph of the desired, merging toward the conclusions of the desired theorem
The connections, or arcs, in these graphs may be lemmas or theorems (i.e., steps of conventional logic). Also permissible are:
- Arcs which represent other IncompleteProofs
- Arcs which represent conjectures
IncompleteProofTechnique describes a method for using IncompleteProofs to find conventional proofs.
Example
References
- Michael Nielsen's [exposition] of how the incomplete proof could apply to a broader scientific context.