Abstract

AbstractAVATAR is an elegant and effective way to split clauses in a saturation prover using a SAT solver. But is it refutationally complete? And how does it relate to other splitting architectures? To answer these questions, we present a unifying framework that extends a saturation calculus (e.g., superposition) with splitting and embeds the result in a prover guided by a SAT solver. The framework also allows us to study locking, a subsumption-like mechanism based on the current propositional model. Various architectures are instances of the framework, including AVATAR, labeled splitting, and SMT with quantifiers.

Highlights

  • One of the great strengths of saturation calculi such as superposition [1] is that they avoid case distinctions

  • We provide that missing piece, in the form of a splitting framework, and use it to show the completeness of an AVATAR-like architecture

  • As we developed the framework, we faced some tension between constraining the SAT solver’s behavior and the saturation prover’s

Read more

Summary

Introduction

One of the great strengths of saturation calculi such as superposition [1] is that they avoid case distinctions. This extends the base calculus with splitting and inherits the base’s completeness It works on A-clauses or A-formulas C ← A, where A is a set of propositional literals. We can prove the dynamic completeness of an abstract prover, formulated as a transition system, that implements the splitting calculus This ignores a vital component of AVATAR: the SAT solver. This refines the locking model-guided prover of the fourth layer with the given clause procedure, which saturates an A-formula set by distinguishing between active and passive A-formulas. We make another discovery: Selecting A-formulas fairly is not enough to guarantee completeness.

Preliminaries
Splitting Calculi
Model-Guided Provers
A Unifying Splitting Framework 351
Locking Provers
AVATAR-Based Provers
Application to Other Architectures
Conclusion

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.