From 5884f2527442de38bfd9772b9daa12e282294d31 Mon Sep 17 00:00:00 2001
From: JJ
Date: Sun, 5 May 2024 16:55:34 -0700
Subject: meow

---
 linguistics/semantics.md | 34 ++++++++++++++++++++++++++++------
 1 file changed, 28 insertions(+), 6 deletions(-)

(limited to 'linguistics/semantics.md')

diff --git a/linguistics/semantics.md b/linguistics/semantics.md
index 96bbb17..a590de3 100644
--- a/linguistics/semantics.md
+++ b/linguistics/semantics.md
@@ -33,12 +33,34 @@ With basic logic and the lambda calculus under our belt, we may simply get strai
 
 ### Entities and Functions
 
-> I am Alice.
-> Alice is bad.
-> The blue pigeon flew away.
+> *I am Alice.* <br>
+> *Alice is bad.* <br>
+> *The blue pigeon flew away.*
+
+- Noun: $⟨e,t⟩ ↝ λx.Noun(x)$
+- Verb (intransitive): $⟨e,t⟩ ↝ λx.Verb(x)$
+- Verb (transitive): $⟨e,⟨e,t⟩⟩ ↝ λy.λx.Verb(x, y)$
+- Verb (meaningless): $⟨⟨e,t⟩,⟨e,t⟩⟩ ↝ λP.λx.P(x)$
+- Adj: $⟨⟨e,t⟩,⟨e,t⟩⟩ ↝ λNoun.λx.[Adj(x) ∧ Noun(x)]$
+
+- or (clausal): $⟨t,⟨t,t⟩⟩ ↝ λq.λp.[p ∨ q]$
+- and (clausal): $⟨t,⟨t,t⟩⟩ ↝ λq.λp.[p ∧ q]$
+- or (verbal): $⟨⟨e,t⟩,⟨⟨e,t⟩,⟨e,t⟩⟩⟩ ↝ λQ.λP.λx.[P(x) ∨ Q(x)]$
+- and (verbal): $⟨⟨e,t⟩,⟨⟨e,t⟩,⟨e,t⟩⟩⟩ ↝ λQ.λP.λx.[P(x) ∧ Q(x)]$
+- or (quantifiers): $⟨⟨e,⟨e,t⟩⟩,⟨⟨e,⟨e,t⟩⟩,⟨e,⟨e,t⟩⟩⟩⟩ ↝ λQ.λP.λy.λx.[P(x,y) ∨ Q(x,y)]$
+- and (quantifiers): $⟨⟨e,⟨e,t⟩⟩,⟨⟨e,⟨e,t⟩⟩,⟨e,⟨e,t⟩⟩⟩⟩ ↝ λQ.λP.λy.λx.[P(x,y) ∧ Q(x,y)]$
+
+- not: $⟨⟨e,t⟩,⟨e,t⟩⟩ ↝ λP.λx.¬P(x)$
 
 ### Quantification
 
+- every: $⟨⟨e,t⟩,⟨⟨e,t⟩,t⟩⟩ ↝ λQ.λP.∀x.[P(x) → Q(x)]$
+  - everything: $⟨⟨e,t⟩,t⟩ ↝ λP.∀x.P(x)$
+- some: $⟨⟨e,t⟩,⟨⟨e,t⟩,t⟩⟩ ↝ λQ.λP.∃x.[P(x) ∧ Q(x)]$
+  - something: $⟨⟨e,t⟩,t⟩ ↝ λP.∃x.P(x)$
+- no: $⟨⟨e,t⟩,⟨⟨e,t⟩,t⟩⟩ ↝ λQ.λP.∀x.[P(x) → ¬Q(x)] (or λQ.λP.¬∃x.[P(x) ∧ Q(x)])$
+  - nothing: $⟨⟨e,t⟩,t⟩ ↝ λP.¬∃x.P(x)$ (or $λP.∀x.¬P(x))$
+
 ### Reference
 
 ### Numbers and Plurality
@@ -53,9 +75,9 @@ With basic logic and the lambda calculus under our belt, we may simply get strai
 
 ### Command, Request, Obligation
 
-> Alice, run!<br>
-> Alice, please run.<br>
-> Alice should run.
+> *Alice, run!* <br>
+> *Alice, please run.* <br>
+> *Alice should run.*
 
 ### Questions
 ## Resources
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