Theorem Proving Using Equational Matings and Rigid E-Unifications

Loading...
Thumbnail Image
Penn collection
Technical Reports (CIS)
General Robotics, Automation, Sensing and Perception Laboratory
Degree type
Discipline
Subject
GRASP
Funder
Grant number
License
Copyright date
Distributor
Related resources
Author
Narendran, Paliath
Raatz, Stan
Snyder, Wayne
Contributor
Abstract

In this paper, it is shown that the method of matings due to Andrews and Bibel can be extended to (first-order) languages with equality. A decidable version of E-unification called rigid E-unification is introduced, and it is shown that the method of equational matings remains complete when used in conjunction with rigid E-unification. Checking that a family of mated sets is an equational mating is equivalent to the following restricted kind of E-unification. Problem: Given →/E = {Ei | 1 ≤ i ≤ n} a family of n finite sets of equations and S = {〈ui, vi〉 | 1 ≤ i ≤ n} a set of n pairs of terms, is there a substitution θ such that, treating each set θ(Ei) as a set of ground equations (i.e. holding the variables in θ(Ei) "rigid"), θ(ui) and θ(vi) are provably equal from θ(Ei) for i = 1, ... ,n? Equivalently, is there a substitution θ such that θ(ui) and θ(vi) can be shown congruent from θ(Ei) by the congruence closure method for i 1, ... , n? A substitution θ solving the above problem is called a rigid →/E-unifier of S, and a pair (→/E, S) such that S has some rigid →/E-unifier is called an equational premating. It is shown that deciding whether a pair 〈→/E, S〉 is an equational premating is an NP-complete problem.

Advisor
Date Range for Data Collection (Start Date)
Date Range for Data Collection (End Date)
Digital Object Identifier
Series name and number
Publication date
1992-07-21
Volume number
Issue number
Publisher
Publisher DOI
Journal Issue
Comments
University of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-88-15.
Recommended citation
Collection