[13 December 2010]

When I took an introductory course in symbolic logic, all those many years ago, we used a textbook (Richard C. Jeffrey, *Formal logic: its scope and limits* [New York: McGraw-Hill, 1967], in case you’re curious) which presented a proof method based on proof trees, which had the nice property that for valid inferences it’s guaranteed to terminate, and that for invalid inferences it will never terminate with a false positive. Allen Renear informs me that the locus classicus for proof trees is Raymond M. Smullyan, *First-order logic* (2d ed. New York: Dover, 1995), which I have been reading lately with pleasure.

All the theorem provers I’ve read about, however, seem to require more or less active participation and guidance from the user; like the proof-tree method, they produce a proof only when a proof exists, but unlike the proof-tree method they aren’t guaranteed to find a proof if one exists.

So I’ve been wondering: why aren’t there automatic theorem provers based on the proof-tree method?

Or are there?

Claus Huitfeldt calls my attention to a paper by Adolfo Gustavo Serra Seca Neto and Marcelo Finger (from 2005? not sure) which describes a ‘multi-strategy’ theorem prover called MSTP. In their introduction, Neto and Finger do say that “most” automatic theorem provers use different approaches (which makes me feel a

littlebetter), but the discussion does mention several provers which use proof trees.