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Call a semantics for a language with variables absolute when variables map tofixed entities in the denotation. That is, a semantics is absolute when thedenotation of a variable a is a copy of itself in the denotation. We give atrio of lattice-based, sets-based, and algebraic absolute semantics tofirst-order logic. Possibly open predicates are directly interpreted as latticeelements / sets / algebra elements, subject to suitable interpretations of theconnectives and quantifiers. In particular, universal quantification "foralla.phi" is interpreted using a new notion of "fresh-finite" limit and using anovel dual to substitution.  The interest of this semantics is partly in the non-trivial and beautifultechnical details, which also offer certain advantages over existingsemantics---but also the fact that such semantics exist at all suggests a newway of looking at variables and the foundations of logic and computation, whichmay be well-suited to the demands of modern computer science.

Semantics out of context: nominal absolute denotations for first-order logic and computation