Proposition 5 is in error, and should be deleted. Nothing later depends on it. (Due to Evan Goris)
FOIL Axiomatized, Studia Logica, 84:1--22, 2006. Electronic version at http://dx.doi.org/10.1007/s11225-006-9000-2. Click here for correction.
Possible world semantics for the first-order logic of proofs, in Annals of Pure and Applied Logic 165 (2014) 225-240, and for Possible world semantics for first-order LP, CUNY Ph.D. Program in Computer Science technical report TR-2011010, 2011. Click here for correction.