What does "fi" stand for? Call a statement A of a first-order language L logically true in the probabilistic sense if for all probability functions P, P(A) = 1. Where S is a set of statements of L, say that A is logically entailed by S in the probabilistic sense if, for all P, P(A) = 1 if P(B) = 1 for each member B of S. This sense of logical entailment is strongly sound and strongly complete: S fi A iff A is logically entailed by S in the probabilistic sense. And taking S to be ∅, we have fi A iff A is logically true in the probabilistic sense.
This is an abstract from a paper about Logic and Probability. I would really appreciate it if someone could shed some light on what exactly does "fi" represent above and where does it comes from. Is it logical consequence? Thank you.
 A: The "fi" seems to represent the entailment relation that mathematical logicians usually write "$\vdash$".
I found the exact text you quote, including "fi", in section 5.1 of a paper by A. Hájek, http://philrsss.anu.edu.au/people-defaults/alanh/papers/comp_logic.pdf, which cites H. Leblanc for the idea. And Leblanc states this particular result -- but now with "$\vdash$" -- as Theorems 100 and 105 of Handbook of Philosophical Logic (ed. Gabbay and Guenthner, Springer, 2013) vol 2, p. 100-102. (This is not exactly what Hájek cites, but was what I could find a Google Books preview of).
It is not clear whether representing $\vdash$ by "fi" is the result of a font problem (copy-pasting from a typeset paragraph where $\vdash$ is encoded as a glyph with the same codepoint that represents an fi-ligature in another font), or if Hájek deliberately decided that spelling "if" backwards would be a better symbol for entailment than the usual $\vdash$.
Looking closer, after the OP confirmed he was quoting Hájek, I would say it is probably a font problem. If we zoom in on the PDF I link above, we see that the symbol is definitely an "fi" ligature, whereas other appearances of the letters "fi" in the paper -- such as in the word "define" -- do not use ligatures.
