Abstract
This chapter describes the formal preliminaries for the RP-calculus. It discusses the basic notions for the RP-calculus and the notation used subsequently. The chapter presents an assumption that T is the set of well-formed terms over V, a set of variable symbols, the nonempty set of function symbols F, and the nonempty set of predicate symbols P. Then, a mapping from σ to T almost everywhere is called a substitution. Substitutions are extended as endomorphisms to mappings from T to T. Given a set D of terms or literals, one can call a substitution θ a unifier of D and say that D is unifiable. For a set of clauses S, S denotes the set of all ground instances of the clauses in S. Computing S for a given clause set S, T and IP will be minimal. This guarantees that T is the Herbrand Universe of S and AT is the Herbrand Base if one assumes in addition that that S contains no constant symbol at all.
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