# statement logic !!!

things you can do with this:

### general things

- parse string -> statement
- parse L (the formal language) string -> statement
- serialize a statement to plaintext, LaTeX, L (the formal language)

### semantic things (statements have meaning I guess)

- evaluate statements
- from a statement generate a LaTeX truth table
- match/replace patterns in statements (e.g. logical laws)
- verify logical-law equivalence of statements (TODO)
- find logical-law equivalence of statements with breadth-first search

### syntactic things (statements are strings of symbols)

- implement formal languages (symbols, axioms schemas, and inference rules):
  <https://en.wikipedia.org/wiki/Post_canonical_system>
- verify derivations in formal languages

### formal languages implemented

- the MIU system (from "Gödel, Escher, Bach")
- L

## requirements

a haskell compiler e.g. GHC

## compile it

```sh
make
```

or look in `Makefile`

## usage

only this has been implemented in the main function:

```sh
echo '((p->q)<->(!q->!p))' | ./logic
```

### output

```
Iff (Implies (Atom "p") (Atom "q")) (Implies (Not (Atom "q")) (Not (Atom "p")))
Tautology
\begin{tabular}{cc||cccccc|c|cccccccc}
$p$ & $q$ & $($ & $($ & $p$ & $\to $ & $q$ & $)$ & $\leftrightarrow $ & $($ & $\neg $ & $q$ & $\to $ & $\neg $ & $p$ & $)$ & $)$ \\
\hline
0 & 0 &  &  & 0 & 1 & 0 &  & \textbf 1 &  & 1 & 0 & 1 & 1 & 0 &  & \\
0 & 1 &  &  & 1 & 0 & 0 &  & \textbf 1 &  & 1 & 0 & 0 & 0 & 1 &  & \\
1 & 0 &  &  & 0 & 1 & 1 &  & \textbf 1 &  & 0 & 1 & 1 & 1 & 0 &  & \\
1 & 1 &  &  & 1 & 1 & 1 &  & \textbf 1 &  & 0 & 1 & 1 & 0 & 1 &  & \\
\end{tabular}
```