Module lambda

Expand description

Lambda calculus transformations for Montague-style compositional semantics.

This module provides functions for manipulating logical expressions using lambda abstraction and application. It supports:

Quantifier raising via type-lifting (proper names → generalized quantifiers)
Beta reduction for applying lambda abstractions
Scope enumeration to generate all possible quantifier scopings
Intensional contexts for opaque verbs (believes, seeks, wants)
Event semantics transformation (Davidson-style)

§Key Functions

Function	Purpose
`lift_proper_name`	Lifts a proper name to a generalized quantifier
`lift_quantifier`	Creates a quantifier lambda term
`beta_reduce`	Performs beta reduction on applications
`enumerate_scopings`	Generates all scope permutations respecting islands
`enumerate_intensional_readings`	Generates de re / de dicto readings
`to_event_semantics`	Converts predicate to neo-Davidsonian event form

Quantifiers are assigned an island_id during parsing. The scoping algorithm only permutes quantifiers within the same island. This prevents:

Opaque verbs create intensional contexts where substitution of co-referential terms may change truth value. The module provides:

make_intensional: Wraps an expression in an intensional operator
substitute_respecting_opacity: Blocks substitution inside intensional contexts

apply_adverb: Adds an adverbial modifier to an event.
beta_reduce: Performs beta reduction on lambda applications.
enumerate_intensional_readings
enumerate_scopings: Generates all possible quantifier scopings for an expression.
is_opaque_verb: Checks if a verb creates an opaque (intensional) context.
lift_proper_name
lift_quantifier
make_intensional: Wraps an expression in an intensional operator.
substitute_respecting_opacity: Substitutes a variable with a replacement, respecting opacity boundaries.
to_event_semantics: Converts a predicate to Neo-Davidsonian event semantics.