The ability to target underspecified lexemes’ specifications for a rule feature, in which feature-filling is implemented by unification (e.g., Bale et al. 2014), ought to enable us to derive the traditional distinction (e.g., Lakoff 1970) between major rules (those for which non-application is exceptional) and minor rules (those for which application is exceptional), making this distinction purely descriptive of later feature-filling rules inserting unmarked rule features upon lexical insertion.

Let us suppose we have a rule R. Let us suppose that every formative is unified with  {+R} upon lexical insertion. Then, unification will fail only with formatives specified [−R], and these formatives will exhibit exceptional non-application. This describes the parade example of exceptions to a major rule: the failure of trisyllabic shortening in obesity (assuming obese is [−trisyllabic shortening]; see Chomsky & Halle 1968: §4.2.2).

Let us suppose instead that every formative is unified with {−R} upon lexical insertion. Then, unification will fail only with those formatives specified [+R], and these formatives will exhibit exceptional application, assuming they otherwise satisfy the phonological description of rule R. This describes minor rules.

This (admittedly quite sketchy at present) idea seems to address Zonneveld’s (1978: 160f.) concern that Lakoff and contemporaries did not posit any way to encode whether or not a rule was major or minor, except “transderivationally” via inspection of successful derivations. This also places the major/minor distinction—correctly, I think—in the scope of theory of productivity. More on this later.

References

Bale, A., Papillon, M., and Reiss, C. 2014. Targeting underspecified segments: a formal analysis of feature-changing and feature-filling rules. Lingua 148: 240-253.
Chomsky, N. and Halle, M. 1968. Sound Pattern of English. Harper & Row.
Lakoff, G. 1970. Irregularity in Syntax. Holt, Rinehart and Winston.
Zonneveld, W. 1978. A Formal Theory of Exceptions in Generative Phonology. Peter de Ridder.