Permissive-Nominal Logic (PNL) extends first-order predicate logicwith term-formers that can bind names in their arguments. It takes a semantics in (permissive-)nominal sets. In PNL, the ∀-quantifier or λ-binder are just term-formers satisfying axioms, and their denotation is functions on nominal atoms-abstraction. Then we have higher-order logic (HOL) and its models in ordinary (i.e. Zermelo–F...

An indexing technique for first-order predicate logic terms and literals is proposed. It exploits the lattice structure of terms, generated by the usual instance relation, to provide for a given “query term” fast access to all T-unifiable terms, T-instances (backward subsumption) and T-generalized terms (forward subsumption) where T is any finitary unification theory. In the best case one singl...