Samson Abramsky and Mehrnoosh Sadrzadeh (2014), in C. Casadio, B. Coecke, M. Moortgat and P. Scott (eds.), Categories and Types in Logic, Language, and Physics, LNCS 8222, Springer, pp. 1–13 — ARXIV-1403.3351, DOI-10.1007/978-3-642-54789-8_1
Key takeaways
- The construction. Objects are pairs (L, X) of a finite vocabulary of relation symbols and a finite set of variables; a morphism is an inclusion of vocabularies with any function on variables, so it can include, relabel or identify referents. F(L, X) is the set of deductive closures of consistent finite sets of literals over X in L, and restriction along f pulls a literal ±A(x) back exactly when ±A(f(x)) holds. A basic DRS is a section.
- Semantic unification is gluing. A cover is a jointly surjective family fᵢ : (Lᵢ, Xᵢ) → (L, X) with L the union of the Lᵢ; a gluing is a section s over (L, X) restricting to each sᵢ. Proposition 1: if a gluing exists it is unique (the deductive closure of the pushed-forward literals). So “the intelligence of the semantic unification operation is in the choice of cover”: DRT’s merging of referents is the cover, and the gluing condition checks that the merge is semantically correct.
- What blocks a gluing. With disjoint vocabularies, as in all the linguistic examples, only inconsistency: “John owns a donkey. It is grey” fails to glue on the cover that merges “it” with John (Man(x) against ¬Man(y)) and glues on the one that merges it with the donkey. With shared vocabulary the gluing can also fail because the merged section says more about a local referent than its local section did (the R, S example after Proposition 1). Neither is a compatible family without a global section: the paper defines no overlap condition and exhibits no contextuality in the sense of LIT-016.
- Ambiguity is a choice among covers. “John put the cup on the plate. He broke it” has two covers, each with its unique gluing. The probabilistic section composes F with a distribution functor D_R over a commutative semiring, invokes maximum entropy without using it, and in its worked example (“John gave the bananas to the monkeys. They were ripe. They were cheeky.”) ranks the four candidate covers by summed British News corpus counts of “ripe banana”, “cheeky monkey” and so on (14/48, 24/48, 0, 10/48), choosing bananas-ripe, monkeys-cheeky.
Standing in the record
Filed on 2026-10-09 at the owner’s request, as the paper that first carried
the sheaf-theoretic treatment of contextuality (LIT-016, NOTE-016) into
natural-language semantics. It sits between the record’s contextuality line
(LIT-016, LIT-277, LIT-265; THEORY-012) and its compositional
distributional semantics (LIT-273, LIT-272), and beside Heim’s file change
semantics (LIT-838), DRT’s sister theory. It bears on the sheaf vocabulary
of the manuscript What Survives Translation? (line
pragmatic-transport); NOTE-644 says how.