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Notes/MFES/T - Aula 2 - 18 Setembro 2023.md
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@ -67,16 +67,16 @@ A formula $F$ is:
> - $\Gamma \models G$ and $\Gamma$ finite iff $\models \land \Gamma \implies G$. > - $\Gamma \models G$ 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 $\Gamma$. - $\Gamma$ 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 $\Gamma \models \bot$. - We say that $\Gamma$ is inconsistent or unsatisfiable iff there is not consistent and denote this by $\Gamma \models \bot$.
> [!tip]+ Proposition > [!tip]+ Proposition
> - {$F, \neg F$} \$models \bot$ > - {$F, \neg F$} $\models \bot$
> - If $\Gamma \models \bot$ and $\Gamma \subseteq \Gamma '$, then $\Gamma ' \models \bot$ > - If $\Gamma \models \bot$ and $\Gamma \subseteq \Gamma '$, then $\Gamma ' \models \bot$
> - $\Gamma \models F$ iff $\Gamma, \neg F \models \bot$ > - $\Gamma \models F$ iff $\Gamma, \neg F \models \bot$
- Formula - Formula $G$ is a subformula of formula F if it occurs syntactically within F
- Formula G is a strict subformula of F if G is a subformula of $F$ and $G \neg \equals F$
### 1.2.1 Basic Equivalences ### 1.2.1 Basic Equivalences
1. $\neg \neg A \equiv A$ 1. $\neg \neg A \equiv A$