On a New Semantics for First-Order Predicate Logic
Hajnal Andréka, Johan van Benthem and István Németi	

Abstract:
Aldo Antonelli has proposed a new semantics for first-order predicate
logic that treats quantifiers using non-standard power sets. In this
note, we analyze and clarify this decidable semantics, explore the
resulting weak logical systems in terms of their semantics and proof
theory, and sharpen up connections with the guarded fragment of
first-order logic, with earlier logics of generalized quantifiers, and
with modal neighborhood semantics.

Note: This is an invited commentary to appear in the "Journal of Philosophical Logic".

Keywords: first-order logic, generalized quantifier, generalized semantics, guarded fragment, neighborhood semantics, modal logic