TL;DR
This paper characterizes which IFG-formulas are equivalent to first-order formulas and demonstrates how the standard cylindric set algebra can be embedded into an IFG-cylindric set algebra, linking IFG logic to classical logic structures.
Contribution
It provides a complete characterization of IFG-formulas equivalent to first-order formulas and establishes an embedding of cylindric set algebras into IFG-cylindric set algebras.
Findings
Characterization of IFG-formulas equivalent to first-order formulas
Embedding of cylindric set algebra into IFG-cylindric set algebra
Bridges between IFG logic and classical first-order logic
Abstract
IFG logic is a variant of the independence-friendly logic of Hintikka and Sandu. We answer the question: ``Which IFG-formulas are equivalent to ordinary first-order formulas?'' We use the answer to show that the ordinary cylindric set algebra over a structure can be embedded into a reduct of the IFG-cylindric set algebra over the structure.
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