Pragmatic Update Operator
The pragmatic update operator (VII.D54) is the endofunctor U_α : Disc → Disc on the category of discourse states, indexed by illocutionary type α ∈ {assert, direct, commit, express, declare}. Speech acts are category operations: each speech act updates the shared context by integrating propositional content according to its illocutionary force, and successive speech acts compose to yield a discourse trajectory.
τ-Definition
The pragmatic update operator (VII.D54) is the endofunctor U_α : Disc → Disc on the category of discourse states, indexed by illocutionary type α ∈ {assert, direct, commit, express, declare}. Speech acts are category operations: each speech act updates the shared context by integrating propositional content according to its illocutionary force, and successive speech acts compose to yield a discourse trajectory.
Categorical invariant. Endofunctor U_α : Disc → Disc indexed by α ∈ {assert, direct, commit, express, declare}, parametrized by content p and context c, satisfying (U1) content integration, (U2) force realization (assertives → common ground; directives → hearer obligation; commissives → speaker obligation), (U3) compositionality U_β ∘ U_α = U_β(U_α(D)).
Primary registry anchor:
VII.D54
τ-Derivation Chain
Phenomenological Correlate
The pragmatic update operator is instantiated whenever a speech act updates a shared discourse context. Examples: an assertion entering the common ground; a request creating an obligation on the hearer; a promise creating an obligation on the speaker; a declaration constituting the act it describes ('I now pronounce you...').
Examples:
- Assertive: 'It is raining' — U_assert(D) adds p to common ground
- Directive: 'Close the door' — U_direct(D) registers an obligation on the hearer
- Commissive: 'I promise to call' — U_commit(D) records a speaker obligation in Reg_C
- Declarative: 'I hereby resign' — U_declare(D) constitutes the act it describes (performative)
Register codomain: Disc (discourse states) — encodes propositional, obligational, and attitudinal components. Updates touch Reg_D (propositional) and Reg_C (commitment) simultaneously
Manuscript reference: manuscript-sources/book-07/part05/ch60.tex
Lean Coverage
Status: Formalized
Module: TauLib.BookVII.Meta.Saturation
Lean kind: structure
Lean symbol: Tau.BookVII.Meta.Saturation.PragmaticUpdateOperator