vault backup: 2023-09-19 12:50:29

Notes/MFES/T - Aula 2 - 18 Setembro 2023.md

@@ -58,7 +58,7 @@ A formula $F$ is:
 
 - $F \models G$ iff for every assignment $A$, if $A \models F$ then $A \models G$. We say $G$ is a **consequence** of $F$.
 - $F \equiv G$ iff $F \models G$ and $G \models F$. We say $F$ and $G$ are **equivalent**.
-- Let $\Gamma = {F_1, F_2, F_3,...}$ be a set of formulas.
+- Let $\Gamma = { F_1, F_2, F_3,... }$ be a set of formulas.
 	- $A \models \Gamma$ iff $A \models F_i$ for each formula $F_i$ in $\Gamma$. We say $A$ models $\Gamma$.
 	- $\Gamma \models G$ iff $A \models \Gamma$ implies $A \models G$ for every assignment $A$. We say $G$ is a **consequence** of $\Gamma$.
 
@@ -67,8 +67,18 @@ A formula $F$ is:
    >  - $\Gamma \models G$ and $\Gamma$ finite iff $\models \land \Gamma \implies G$.
    >  
 
+ - Let $\Gamma = { F_1, F_2, F_3,... }$ be a set of formulas.
+	 - $\Gamma$ is *consistent* or *satisfiable* iff there is an assignment that models $\Gamma$.
+	 - We say that $\Gamma$ is inconsistent or unsatisfiable iff there is not consistent and denote this by $\Gamma \models \bot$.
 
-### 1.3 Basic Equivalences 
+   > [!tip]+ Proposition
+   >  - {$F, \neg F$} \$models \bot$
+   >  - If $\Gamma \models \bot$ and $\Gamma \subseteq \Gamma '$, then $\Gamma ' \models \bot$
+   >  - $\Gamma \models F$ iff $\Gamma, \neg F \models \bot$
+
+- Formula
+   
+### 1.2.1 Basic Equivalences 
 1. $\neg \neg A \equiv A$
 2. $A \lor A \equiv A$
 3. $A \land A \equiv A$
@@ -89,3 +99,5 @@ A formula $F$ is:
 18. $A \iff B \equiv (A \implies B) \land (B \implies A)$
 
 
+
+