logic/readme.md

statement logic !!!

things that are in here:

statement things

Logic/Statement/Parse.hs

• parse string -> statement
• serialize a statement -> plaintext, LaTeX

Logic/Language/Impl/L.hs

• serialize a statement -> L (the formal language)
• parse L (the formal language) string -> statement

semantic statement things

Logic/Statement/Eval.hs

• assign truth values and evaluate statements
• determine tautology, contradiction, or contingent

Logic/Statement/Serialize.hs

• generate a LaTeX truth table from a statement

Logic/Statements/Laws.hs

• 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 (slow)

syntactic things

Logic/Language.hs

• implement formal languages (symbols, axioms schemas, and inference rules) with a clunky api, see also https://en.wikipedia.org/wiki/Post_canonical_system

Logic/Language/Derivation.hs

• verify derivations in formal languages

formal languages

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

general things

Logic/Parse.hs

• generic sequence parser

Logic/Graph.hs

• generic breadth-first search

requirements

a haskell compiler e.g. GHC

compile it

make

or look in Makefile

usage

only this has been implemented in the main function:

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}