关于“full first-order logic”术语含义的技术问询

Hey there! Great question—it’s so annoying when authors toss around jargon without spelling it out, right? Let’s break down what "full first-order logic" means in categorical logic and mainstream logic literature.

First off, the "full" here almost always refers to the complete, standard version of first-order logic, set apart from restricted fragments or stripped-down variants. Here’s what that typically includes:

• Predicate symbols of all arities (not just 1-place/monadic predicates, which show up in simpler fragments)
• Function symbols (including constants, which count as 0-ary functions)
• Both universal (∀) and existential (∃) quantifiers, no restrictions on their use
• The full suite of propositional connectives: ∧ (and), ∨ (or), ¬ (not), → (implies), ↔ (if and only if)
• Usually the equality symbol (=) — sometimes authors will specify "full first-order logic with equality" to be extra clear, since some variants leave out equality

You’ll often see this term when someone’s contrasting it with limited versions, like:

• Monadic first-order logic (only 1-place predicates, no functions)
• First-order logic without function symbols
• Fragments that restrict quantifier use (like existential-only logic)

Occasionally, in niche categorical contexts, "full" might refer to using standard full semantics instead of something like Henkin semantics, but that’s a way less common usage. The core idea is always that you’re working with the complete, untruncated system of first-order logic, not a simplified subset.

备注：内容来源于stack exchange，提问作者IllogicalUser