Cooperation between Top-Down and Bottom-Up Theorem Provers

05/27/2011
by   M. Fuchs, et al.
0

Top-down and bottom-up theorem proving approaches each have specific advantages and disadvantages. Bottom-up provers profit from strong redundancy control but suffer from the lack of goal-orientation, whereas top-down provers are goal-oriented but often have weak calculi when their proof lengths are considered. In order to integrate both approaches, we try to achieve cooperation between a top-down and a bottom-up prover in two different ways: The first technique aims at supporting a bottom-up with a top-down prover. A top-down prover generates subgoal clauses, they are then processed by a bottom-up prover. The second technique deals with the use of bottom-up generated lemmas in a top-down prover. We apply our concept to the areas of model elimination and superposition. We discuss the ability of our techniques to shorten proofs as well as to reorder the search space in an appropriate manner. Furthermore, in order to identify subgoal clauses and lemmas which are actually relevant for the proof task, we develop methods for a relevancy-based filtering. Experiments with the provers SETHEO and SPASS performed in the problem library TPTP reveal the high potential of our cooperation approaches.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

08/09/2018

Proof Simplification and Automated Theorem Proving

The proofs first generated by automated theorem provers are far from opt...
12/04/2017

Proceedings of the Fifth Workshop on Proof eXchange for Theorem Proving

This volume of EPTCS contains the proceedings of the Fifth Workshop on P...
08/23/2019

Proceedings Sixth Workshop on Proof eXchange for Theorem Proving

This volume of EPTCS contains the proceedings of the Sixth Workshop on P...
07/04/2021

Proceedings Seventh Workshop on Proof eXchange for Theorem Proving

This volume of EPTCS contains the proceedings of the Seventh Workshop on...
06/12/2018

Goal-Oriented Conjecturing for Isabelle/HOL

We present PGT, a Proof Goal Transformer for Isabelle/HOL. Given a proof...
05/23/2019

ENIGMAWatch: ProofWatch Meets ENIGMA

In this work we describe a new learning-based proof guidance -- ENIGMAWa...
04/27/2017

No, This is not a Circle

A popular curve shown in introductory maths textbooks, seems like a circ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.