Glue Semantics

Origin. Dalrymple, Lamping, Saul (1993). LFG interface. Linear logic for meaning assembly. Resource-sensitive composition. Foundation of LFG semantics.

Models. Syntax provides resources. Linear logic assembles meaning. Meaning constructors. Multiple attachments. Flexible composition.

Formalism.

Meaning constructors: f : G. f: meaning (λ-term). G: glue formula (linear logic). Resource contribution.

Glue logic: Linear logic fragment. ⊸: linear implication (consume-produce). ⊗: tensor (both required). Resource-sensitive.

Assembly: Collect meaning constructors from words. Prove goal type from resources. Proof = meaning derivation. Multiple proofs = ambiguity.

Example: "John sleeps." John: j : g_john sleeps: λx.sleep(x) : g_subj ⊸ g_sentence Prove: g_sentence. Result: sleep(j).

Modifiers: Contribute resource and consume modified. Adjective: λPλx.P(x) ∧ red(x) : (g ⊸ g) ⊸ (g ⊸ g). Flexible attachment. Scope through resource handling.

Quantifier scope: Multiple derivations. Each proof = one reading. Underspecification natural. No scope mechanism needed.

LFG interface: F-structure provides resources. σ-projection: f-structure to semantics. Glue assembles. Modular architecture.

Symbols.

Symbol	Unicode	Meaning
⊸	U+22B8	linear implication
⊗	U+2297	tensor
f : G	—	meaning constructor
g	—	semantic resource

Metatheory. Linear logic assembly. Resource composition. Proof-based. Flexible attachment.

Applies to. LFG semantics. Compositional semantics. Scope. Modification.

Limitations. LFG-specific originally. Proof complexity. Ambiguity explosion. Technical setup.