The X-ray absorption near-edge structures (XANES) at the F K-edge of alpha-AlF(3), beta-AlF(3) and a tetragonal AlF(3) phase are analysed by a combination of ab initio calculations with the FEFF8 code and a phenomenological discussion of local molecular orbital (MO) symmetries at the absorbing fluorine atoms. By means of a Walsh correlation diagram it is shown that the two intense absorption bands observed at the F K-edges of the AlF(3) polymorphs can be interpreted as transitions to anti-bonding MOs in [Al-F-Al]-units that have C(2v) and D(infinity h) point group symmetries. The energies of both anti-bonding orbitals are very insensitive to the angle between the Al-F bonds, which explains the close similarity of the XANES signatures from the three polymorphs. The FEFF8 analysis shows that the increased broadening of the XANES structure for beta-AlF(3) and the tetragonal AlF(3) phase is due to the superposition of the individual absorption spectra from the crystallographically distinct F species. The interpretation in terms of local MOs provides for the first time a "chemically intuitive" approach to investigations of solid fluorides by XANES spectroscopy and provides a simple conceptual framework for the discussion of the electronic structure in AlF(3) materials.