adj. 1) inconsistent. 2) unmatching. 3) unable to live together as husband and wife due to irreconcilable differences. In no-fault divorce states, if one of the spouses desires to end the marriage, that fact proves incompatibility, and a divorce (dissolution) will be granted even though the other spouse does not want a divorce. The term also has the general meaning that two people do not get along with each other.