A method for combining decision procedures for several theories into a single decision procedure for their combination is described, and a simplifier based on this method is discussed. The simplifier finds a normal form for any expression formed from individual variables, the usual Boolean

� Solving a linear (continues) system � Good old Gaussian Elimination for linear equations. � Feasibility test a-la Simplex for linear inequalities. � Fourir-Motzkin for linear inequalities. � Solving a linear (discrete) system � Branch and Bound for integer linear inequalities. � The Omega-Test method for integer linear inequalities.

OWL DL, a new W3C ontology language recommendation, is based on the expressive description logic SHOIN. Although the ontology consistency problem for SHOIN is known to be decidable, up to now there has been no known “practical ” decision procedure, i.e., a goal directed procedure that is likely

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ABSTRACT, The notion of the congruence closure of a relation on a graph ~s defined and several algorithms for computing it are surveyed A simple proof is given that the congruence closure algorithm provides a decision procedure for the quantifier-free theory of equality A decision procedure ts

The automata-theoretic approach is one of the most fundamental approaches to developing decision procedures in mathematical logics. To decide whether a formula in a logic with the tree-model property is satisfiable, one constructs an automaton that accepts all (or enough) tree models

UCLID is a tool for term-level modeling and verification of infinite-state systems expressible in the logic of counter arithmetic with lambda expressions and uninterpreted functions (CLU). In this paper, we describe a key component of the tool, the decision procedure for CLU.

STP is a decision procedure for the satisfiability of quantifier-free formulas in the theory of bit-vectors and arrays that has been optimized for large problems encountered in software analysis applications. The basic architecture of the procedure consists of word-level pre-processing algorithms

Abstract. We give a detailed survey of the Nelson-Oppen method for combining decision procedures, we show how Shostak's method can be seen as an instance of the Nelson-Oppen method, and we provide a generalization of the Nelson-Oppen method to the case of non-disjoint theories. 1 Introduction

ABSTRACT. The resolution principle, an automatic inference technique, is studied as a possible decision procedure for certain classes of first-order formulas It is shown that most previous resolution strategies do not decide satlsfiabihty even for "simple " solvable classes Two