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␈↓ ↓H␈↓α␈↓ αMINIMAL INFERENCE - A WAY FOR PROGRAMS TO JUMP TO CONCLUSIONS

␈↓ ↓H␈↓Abstract:␈α⊂We␈α∂present␈α⊂a␈α⊂new␈α∂mode␈α⊂of␈α⊂conjectural␈α∂reasoning␈α⊂in␈α⊂first␈α∂order␈α⊂logic.␈α⊂ A␈α∂minimality
␈↓ ↓H␈↓axiom␈α∂schema␈α∂expresses␈α∂the␈α∂conjecture␈α∂that␈α∂the␈α∂individuals␈α∂forced␈α∂to␈α∂exist␈α∂by␈α∂a␈α∂certain␈α⊂set␈α∂of
␈↓ ↓H␈↓axioms␈α⊂are␈α⊂all␈α⊂the␈α⊃individuals␈α⊂there␈α⊂are␈α⊂that␈α⊂also␈α⊃satisfy␈α⊂a␈α⊂given␈α⊂predicate.␈α⊂ We␈α⊃believe␈α⊂that
␈↓ ↓H␈↓minimal␈α⊃reasoning␈α⊃corresponds␈α⊃to␈α⊂a␈α⊃common␈α⊃human␈α⊃mode␈α⊂of␈α⊃conjectural␈α⊃reasoning␈α⊃and␈α⊂that
␈↓ ↓H␈↓intelligent␈α∩computer␈α∩programs␈α⊃will␈α∩also␈α∩need␈α⊃to␈α∩use␈α∩minimal␈α⊃reasoning.␈α∩ Yet␈α∩other␈α∩modes␈α⊃of
␈↓ ↓H␈↓minimal reasoning may be important.
␈↓ ↓H␈↓␈↓ εH␈↓ 91


␈↓ ↓H␈↓αIntroduction

␈↓ ↓H␈↓␈↓ α_We␈αwill␈α
argue␈αthat␈α
people␈αoften␈α
legitimately␈αdraw␈αconclusions␈α
from␈αa␈α
set␈αof␈α
assertions␈αthat
␈↓ ↓H␈↓go␈α∩beyond␈α∩the␈α∪logical␈α∩consequences␈α∩of␈α∪these␈α∩assertions.␈α∩ We␈α∪formalize␈α∩two␈α∩such␈α∪methods␈α∩of
␈↓ ↓H␈↓conjectural reasoning, but there may be others that will be useful in artificial intelligence.

␈↓ ↓H␈↓␈↓ α_The␈α
general␈α∞phenomenon␈α
is␈α
that␈α∞people␈α
often␈α
draw␈α∞conclusions␈α
from␈α
a␈α∞set␈α
␈↓↓A␈↓␈α∞of␈α
sentences
␈↓ ↓H␈↓that␈α
they␈α
will␈α
not␈α
draw␈α
from␈α
a␈α
more␈α
inclusive␈α
set␈α
␈↓↓B.␈↓␈α
 However,␈α
all␈α
mathematical␈α
logical␈αsystems
␈↓ ↓H␈↓have␈α∞the␈α∞property␈α∂that␈α∞any␈α∞consequence␈α∂of␈α∞␈↓↓A␈↓␈α∞is␈α∞also␈α∂a␈α∞consequence␈α∞of␈α∂any␈α∞␈↓↓B␈↓␈α∞such␈α∂that␈α∞␈↓↓A ⊂ B␈↓.
␈↓ ↓H␈↓This holds for both the semantic notion of entailment and the syntactic notion of deduction.

␈↓ ↓H␈↓John McCarthy
␈↓ ↓H␈↓Artificial Intelligence Laboratory
␈↓ ↓H␈↓Computer Science Department
␈↓ ↓H␈↓Stanford University
␈↓ ↓H␈↓Stanford, California 94305

␈↓ ↓H␈↓ARPANET: MCCARTHY@SU-AI

␈↓ ↓H␈↓␈↓εThis draft of IJCAI.2[S77,JMC] PUBbed at 12:17 on June 21, 1977.␈↓