One system using non-quantitative heuristics is PROSPECTOR.  The purpose of this system is to predict mineral deposits given geological information about a region.  Some of PROSPECTOR’s rules include the following.

RULE 1.
IF the igneous rocks in the region have a fine to medium grain size,
THEN they have a porphyritic texture (0.5).

RULE 2.
IF the igneous rocks in the region have a fine to medium grain size,
THEN they have a texture suggestive of a hypabyssal regional environment (2, 0.000001).

RULE 3. 
IF the igneous rocks in the region have a fine to medium grain size and they have a porphyritic texture,
THEN they have a texture suggestive of a hypabyssal regional environment (100, 0.0000001).

RULE 4.
IF the igneous rocks in the region have a texture suggestive of a hypabyssal regional environment,
THEN the region is a hypabyssal regional environment (65, 0.01).

RULE 5.
IF the igneous rocks in the region have a morphology suggestive of a hypabyssal regional environment,
THEN the region is a hypabyssal regional environment (300, 0.0001).

RULE 6. 
IF the region is a hypabyssal regional environment,
THEN the region has a favorable level of erosion (200, 0.0002).

RULE 7.
IF Coeval volcanic rocks are present in the region,
THEN the region has a favorable level of erosion (800, 1).

The system processes these and other rules much the way an expert geologist would  to examine the geological, geophysical and geochemical data to predict where ore-grade minerals could be found.  The numbers in parenthesis indicate measures of certainty with the conclusions that are built into the reasoning process.

PROSPECTOR rules were taken from Waterman, D.A., A Guide to Expert Systems, Reading, MA: Addison-Wesley Publishing Company, 1986, p.58.