Agreement classes and target genders

This file defines the agreement classes of a language's nouns and the target genders of its agreement targets, and classifies the map between the target genders of two numbers, in the lattice of partitions.

An agreement class is a set of nouns that take the same agreement forms on every target in every morphosyntactic form, and the controller genders of a language are its agreement classes. The forms a target shows are its target genders, and the agreement classes are the meet of the partitions they induce; there may be fewer target genders than controller genders, Romanian having three of the latter over two of the former in each number. The partitions of the genders by two numbers' target genders are equal, as in French, the singular's strictly finer, as in German, or incomparable, as in Romanian or Lak. A strictly finer plural would distinguish more target genders, which Greenberg's universal 37 excludes.

Main definitions

• Gender.agreementClasses: the kernel of the noun-level agreement map.
• Gender.targetGenders: the range of the agreement map restricted to one target.
• Gender.Parallel, Gender.Convergent, Gender.Crossed: the partitions of two numbers' target genders are equal, the first strictly finer, or incomparable.

Main results

• Gender.agreementClasses_eq_iInf, Gender.faithful_iff_iInf_eq_bot: the agreement classes are the meet of the targets' partitions, and controller genders are faithful exactly when that meet is discrete.
• Gender.card_quotient_agreementClasses: the controller genders are as many as the agreement map has values.
• Gender.card_range_le_prod: the controller genders are at most the product over the targets of the target genders.
• Gender.agreementClasses_eq_ker_of_faithful: under faithful agreement mediated by an assignment, the agreement classes are the assignment's genders.
• Gender.convergent_or_parallel_or_convergent_or_crossed: every map between two numbers' target genders is parallel, crossed, or convergent in one direction.
• Gender.Convergent.card_range_lt: a convergent map distinguishes strictly fewer target genders in the second number.
• Morphology.Polar.faithful, Morphology.Polar.parallel: a polar exponent of gender and number separates the genders and is a parallel system.

Implementation notes

• The index T of the agreement map is whatever the map is restricted to: a target category, a morphosyntactic form, or a pair of the two, so that target genders can be counted per target as well as per number across targets.
• An assignment N → G gives every noun one controller gender, the Canonical Gender Principle of Corbett & Fedden 2016.
• The relations between two numbers take any controllers; the fragments state them of their genders rather than their nouns.
• The kernel of a map is the syncretism of Morphology/Paradigm/Basic.lean, read here over the controllers a target agrees with rather than over the cells of a paradigm.
• Subgenders, agreement classes differing on a minority of forms, inquorate genders, small closed classes whose pattern mixes other genders, and overdifferentiated targets are the steps from agreement classes to controller genders that remain to be defined; until then the agreement classes of a fragment are its controller genders only when the fragment records no such class.

References

• Corbett 1991, Gender formalized
• Zaliznjak 1964, K voprosu o grammatičeskix kategorijax roda i oduševlennosti v sovremennom russkom jazyke
• Corbett & Fedden 2016, Canonical gender
• Greenberg 1963, Some Universals of Grammar with Particular Reference to the Order of Meaningful Elements formalized
• Corbett 1998, Morphology and Agreement formalized