From 66d013368bd62f567171d11b727c92ed835b7586 Mon Sep 17 00:00:00 2001
From: David VandeBunte <davidvandebunte@gmail.com>
Date: Tue, 20 Feb 2024 10:23:36 -0600
Subject: [PATCH] Modal logic fixups (#363)

* truth-at-w.tex: Add missing w

* truth-in-model.tex: Add missing "in" to "we are interested which"

* schemas.tex: Add missing w
---
 content/normal-modal-logic/syntax-and-semantics/schemas.tex     | 2 +-
 content/normal-modal-logic/syntax-and-semantics/truth-at-w.tex  | 2 +-
 .../normal-modal-logic/syntax-and-semantics/truth-in-model.tex  | 2 +-
 3 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/content/normal-modal-logic/syntax-and-semantics/schemas.tex b/content/normal-modal-logic/syntax-and-semantics/schemas.tex
index baec265f..805dab2f 100644
--- a/content/normal-modal-logic/syntax-and-semantics/schemas.tex
+++ b/content/normal-modal-logic/syntax-and-semantics/schemas.tex
@@ -50,7 +50,7 @@
   W$ be arbitrary. To show that a conditional is true at a world we
   assume the antecedent is true to show that consequent is true as
   well. In this case, let $\mSat{M}{\Box(!A \lif !B)}[w]$ and
-  $\mSat{M}{\Box !A}[w]$. We need to show $\mSat{M}{\Box !B}$. So let
+  $\mSat{M}{\Box !A}[w]$. We need to show $\mSat{M}{\Box !B}[w]$. So let
   $w'$ be arbitrary such that $Rww'$. Then by the first assumption
   $\mSat{M}{!A \lif !B}[w']$ and by the second assumption
   $\mSat{M}{!A}[w']$. It follows that $\mSat{M}{!B}[w']$. Since $w'$
diff --git a/content/normal-modal-logic/syntax-and-semantics/truth-at-w.tex b/content/normal-modal-logic/syntax-and-semantics/truth-at-w.tex
index d1e83916..7f83c91d 100644
--- a/content/normal-modal-logic/syntax-and-semantics/truth-at-w.tex
+++ b/content/normal-modal-logic/syntax-and-semantics/truth-at-w.tex
@@ -80,7 +80,7 @@
 \begin{proof}
   \begin{enumerate}
     \item $\mSat{M}{\lnot\Diamond\lnot !A}[w]$ iff $\mSat/{M}{\Diamond\lnot
-      !A}$ by definition of $\mSat{M}{}[w]$. $\mSat{M}{\Diamond\lnot
+      !A}[w]$ by definition of $\mSat{M}{}[w]$. $\mSat{M}{\Diamond\lnot
       !A}[w]$ iff for some $w'$ with $Rww'$, $\mSat{M}{\lnot
       !A}[w']$. Hence, $\mSat/{M}{\Diamond\lnot !A}[w]$ iff for all
     $w'$ with $Rww'$, $\mSat/{M}{\lnot !A}[w']$. We also have
diff --git a/content/normal-modal-logic/syntax-and-semantics/truth-in-model.tex b/content/normal-modal-logic/syntax-and-semantics/truth-in-model.tex
index fcd3fd07..f93bdc4c 100644
--- a/content/normal-modal-logic/syntax-and-semantics/truth-in-model.tex
+++ b/content/normal-modal-logic/syntax-and-semantics/truth-in-model.tex
@@ -10,7 +10,7 @@
 
 \olsection{Truth in a Model}
 
-Sometimes we are interested which !!{formula}s are true at every world
+Sometimes we are interested in which !!{formula}s are true at every world
 in a given model. Let's introduce a notation for this.
 
 \begin{defn}