Splitting through New Proposition Symbols

Abstract

The splitting rule is a tableau-like rule, that is used in the resolution context. In case the search state contains a clause C(in1) V C(in2), which has no shared variables between C(in1) and C(in2), the prover splits the search state, and tries to refute C(in1) and C(in2) separately. Instead of splitting the state of the theorem prover, one can create a new proposition symbol α, and replace C(in1) V C(in2) by C(in1) V α and ¬α V C(in2). In the first clause α is the least preferred literal. In the second clause α is selected. In this way, nothing can be done with C(in2) as long as C(in1) has not been refuted.

This way of splitting simulates search state splitting only partially, because a clause that inherits from C(in1) V α cannot subsume or simplify a clause that does not inherit from C(in1). With search state splitting, a clause that inherits from C(in1) can in principle subsume or simplify clauses that do not derive from C(in1). As a consequence, splitting through new symbols is less powerfull than search state splitting. In this paper, we present a solution for this problem.