On Deciding Subsumption Problems

Abstract

Subsumption is an important redundancy elimination method in automated deduction. A clause D is subsumed by a set $$\mathcal{C}$$ of clauses if there is a clause C ? $$\mathcal{C}$$ and a substitution ? such that the literals of C? are included in D. In the field of automated model building, subsumption has been modified to an even stronger redundancy elimination method, namely the so-called clausal H-subsumption. Atomic H-subsumption emerges from clausal H-subsumption by restricting D to an atom and $$\mathcal{C}$$ to a set of atoms. Both clausal and atomic H-subsumption play an indispensable key role in automated model building. Moreover, problems equivalent to atomic H-subsumption have been studied with different terminologies in many areas of computer science. Both clausal and atomic H-subsumption are known to be intractable, i.e., ? p 2 -complete and NP-complete, respectively. In this paper, we present a new approach to deciding (clausal and atomic) H-subsumption that is based on a reduction to QSAT2 and SAT, respectively.