Paramodulation and Theorem-Proving in First-Order Theories with Equality

Abstract

A term is an individual constant or variable or an n-adic function letter followed by n terms. An atomic formula is an n-adic predicate letter followed by n terms. A literal is an atomic formula or the negation thereof. A clause is a set of literals and is thought of as representing the universally-quantified disjunction of its members. It will sometimes be notationally convenient1 to distinguish between the empty clause □, viewed as a clause, and ‘other’ empty sets such as the empty set of clauses, even though all these empty sets are the same set-theoretic object ø. A ground clause (term, literal) is one with no variables. A clause C’ (literal, term) is an instance of another clause C (literal, term) if there is a uniform replacement of the variables in C by terms that transform C into C’.KeywordsAtomic FormulaUnit ClauseEmpty ClauseGeneral ClauseResolution ProofThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.