A casemarking system is considered to be symmetrical if it applies identically (in terms of number of cases and functions of those cases) to all types of nominals in the language. Asymmetry occurs when the case marking of a semantically or functionally defined group differs from the dominant casemarking system of the language.[1] Such groups most often include standalone personal (or other) pronouns, nouns, or both.
Types:
NoCase: The language does not use declension.
CasesystSym: Case marking is symmetrical; the number of cases is consistent across nominal types.
CasesystProg: Case marking is progressively asymmetrical; a limited group within nominals (such as pronouns) shows a greater number of cases than the majority of nominals.[2]
CasesystDegr: Case marking is degressively asymmetrical; a limited group within its nominals (such as pronouns or nouns within a defined lexical area) shows a smaller number of cases than the majority of nominals.
CasesystQual: Case marking is qualitatively asymmetrical; the differing groups display such a degree of divergence that cases within each system cannot be compared and thereby form incommensurable paradigms.[3]
[1] Asymmetry should not be confused with syncretism. In the case of syncretism, structurally identical forms reveal separate and distinguishable forms under the surface. In the case of asymmetry, however, any of the cases of one paradigm may be completely missing from the other. Furthermore, asymmetrical case marking refers only to semantically divergent groups; therefore, morphological divergence (such as difference between inflectional classes) does not constitute asymmetrical case marking, and nor do isolated and irregular exceptions.
[2] This describes the phenomenon in which the pronouns of certain languages (such as English) show two different case forms, while nouns do not show any case inflection.
[3] Pitjantjatjara, for example, shows split ergativity, with full nouns displaying ergative behavior and pronouns showing nominative behavior.