An algorithm for reasoning about equality

TL;DR: Two rewrite rules operating on a pair of equations E and a set of rules R, (E and R) are rewritten as follows: E = R and R = E + R.

TL;DR: This dissertation shows how standard decision procedures can be adapted so that they can produce detailed proofs of the proved predicates and also how these proofs can be encoded compactly and checked efficiently.

TL;DR: A practical procedure is presented for an extension of quantifier-free Presburger arithmetic that permits arbitrary unmterpreted predicate and function symbols and is powerful enough to encode the semantics of array operators as well as MAX, MIN, and ABSVALUE.

TL;DR: A novel procedure based on uninterpreted symbolic simulation for checking the scheduling step in high-level synthesis and its ability to efficiently handle loops and a wide range of loop transformations performed during scheduling is proposed.

TL;DR: This book discusses the semantics of Predicate Logic, and some of theorems of A. Robinson, Craig and Beth's treatment of Peano's Axiom System.

TL;DR: A simple algorithm for computing congruence closures of a relation on a graph in O(mn) time, where n is the number of vertices and m thenumber of edges in G.

TL;DR: This long-established text continues to expose students to natural proofs and set-theoretic methods and offers enough material for either a one- or two-semester course on mathematical logic.