1 research outputs found
Studies in the completeness and efficiency of theorem-proving by resolution
Inference systems Τ and search strategies E for T are distinguished from proof procedures β = (T,E)
The completeness of procedures is studied by studying
separately the completeness of inference systems and of
search strategies. Completeness proofs for resolution
systems are obtained by the construction of semantic
trees. These systems include minimal α-restricted
binary resolution, minimal α-restricted M-clash resolution
and maximal pseudo-clash resolution. Certain refinements
of hyper-resolution systems with equality axioms are
shown to be complete and equivalent to refinements of
the pararmodulation method for dealing with equality.
The completeness and efficiency of search strategies
for theorem-proving problems is studied in sufficient
generality to include the case of search strategies for
path-search problems in graphs. The notion of theorem-proving problem is defined abstractly so as to be dual to
that of and" or tree. Special attention is given to
resolution problems and to search strategies which generate
simpler before more complex proofs.
For efficiency, a proof procedure (T,E) requires
an efficient search strategy E as well as an inference
system T which admits both simple proofs and relatively
few redundant and irrelevant derivations. The theory
of efficient proof procedures outlined here is applied
to proving the increased efficiency of the usual method
for deleting tautologies and subsumed clauses. Counter-examples
are exhibited for both the completeness and
efficiency of alternative methods for deleting subsumed
clauses.
The efficiency of resolution procedures is improved
by replacing the single operation of resolving a clash
by the two operations of generating factors of clauses
and of resolving a clash of factors. Several factoring
methods are investigated for completeness. Of these the
m-factoring method is shown to be always more efficient
than the Wos-Robinson method