README⤓ .txt 2026-10-22T182136.000 000000000008872 Logics that drop the structural rule of exchange, so that the order of hypotheses is significant and cannot be permuted. Implication splits into two directed forms—one seeking its argument on the left, one on the right—and the resulting calculi are non-commutative.
Categorial Grammar⤓ .md 2026-10-22T090631.000 000000000038320 Ajdukiewicz (1935), Bar-Hillel, Lambek. Categories and slashes. Function-argument structure. Syntax as logic. Foundation of type-logical grammar.
Displacement Calculus⤓ .md 2026-08-20T101614.000 000000000045480 Morrill, Valentín and Fadda introduced the displacement calculus D (2011), developing a line of work by Morrill from 2010. It is a conservative extension of the Lambek calculus with connectives for discontinuity. Where Lambek's calculus is the logic of concatenation, D is the logic of concatenation together with intercalation — the operation that inserts one expression into a marked position inside another. Foundation for type-logical treatments of discontinuous constituency.
Full Lambek Calculus⤓ .md 2026-10-22T180154.561 000000000000888 Lambek's syntactic calculus (1958) supplies the residuated core; the additives and constants were added and the family systematized by Ono and Komori (1985) and Ono (1993, 2003). Galatos, Jipsen, Kowalski, and Ono, Residuated Lattices: An Algebraic Glimpse at Substructural Logics (2007), is the standard reference and the reason FL is the base of the field rather than one system in it.
Lambek Calculus⤓ .md 2026-10-22T092433.000 000000000037576 Joachim Lambek (1958). Syntactic calculus for categorial grammar. Non-commutative residuated structure. Types as syntactic categories. Foundation for type-logical grammar.
Lambek-Grishin⤓ .md 2026-10-22T092436.000 000000000035168 Grishin (1983), Moortgat and Kurtonina. Symmetric Lambek. Both products and coproducts. Interaction principles. Foundation for symmetric categorial grammar.
Non-commutative Logic⤓ .md 2026-08-20T102201.000 000000000037392 Lambek calculus (1958) for linguistics. Non-commutative linear logic (Abrusci 1991). Order of hypotheses matters. Models syntactic structure. Foundation for categorial grammar.
Ordered Logic⤓ .md 2026-08-20T102255.000 000000000035576 Ordered (non-commutative) logic from Lambek calculus (1958) and later work. No exchange rule: order of hypotheses matters. Models resource order, linguistic word order. Part of substructural logic family. Categorical: non-symmetric monoidal categories.
Pregroup Grammar⤓ .md 2026-10-22T180154.561 000000000000832 Joachim Lambek (1999, 2008), a later reformulation of his 1958 syntactic calculus. Replaces the residuated (implicational) structure of the Lambek calculus with a pregroup: an ordered monoid with left and right adjoints. A non-commutative, order-based type logic for natural-language syntax.
CRITERIA⤓ .txt 2026-10-22T182134.000 000000000006632 Not sufficient: Dropping weakening or contraction while keeping exchange (Linear, Affine, Relevant). A commutative substructural base.