The Philosophy of Automated Theorem Proving

ph i losoph ica l level i t addresses the quest ion of whether var ious practi t ioners of automated theorem prov ing have a coherent posi t ion. Consider a person who argues that natural deduct ion is better than resolution-based systems, e.g., Bledsoe (1971) or Pelletier (1982). Whyever wou ld a person be even tempted to argue this unless he thought that the goal of automated theorem prov ing was to approach "the real sys tem" — that is, unless he were a Realist. Af ter a l l , it is patent ly obv ious that T H I N K E R is better at emulat ing proofs in the KM system than any reso lu t ion-emulat ing system; and that any resolut ion-emulat ing system is better than T H I N K E R at producing proofs of a resolution system. The same sort of Real ist reasoning must have been in Wang 's m i n d when he inveighed against the Logic Theorist and in favour of h is consecution-style method (Wang 1960, p.246). But not everyone seems to be a Real ist in this sense. These who , l i ke the designers of the Logic Theorist, bel ieve that they are invest igat ing how people reason in the context of a g i ven system ( s tudy ing subs t i tu t ion in to par t icu lar ax ioms, reasoning backward f r o m certain goals dictated by part icular ax ioms, and the l i ke) can be taken to be Nomina l i s ts — at least insofar as they wou ld be qu i t e unconcerned w i t h the results of a system where proofs take a dif ferent f o rm. A n d I have spoken w i t h various practit ioners in the f ie ld who wou ld vehement ly deny the existence of any