Combining decision procedures for the reals

Abstract. We address the general problem of determining the validity of boolean combinations of equalities and inequalities between real-valued expressions. In particular, we consider methods of establishing such assertions using only restricted forms of distributivity. At the same time, we explore ways in which "local" decision or heuristic procedures for fragments of the theory of the reals can be amalgamated into global ones. Let Tadd [Q] be the first-order theory of the real numbers in the language with symbols 0, 1, +, -, <, . . . , fa, . . . where for each a Q, fa denotes the function fa(x) = ax. Let Tmult [Q] be the analogous theory for the language with symbols 0, 1,

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Jeremy Avigad, Harvey Friedman
• Keywords: Boolean Combinations, CORR 2006, Education, General Problem, Theory