# Category: Mathematics

Things that are related to mathematics.

## Truth

Proposition calculus deals with statements and the relation between statements, where each of them can only be in one of two states; . Therefore, when working with finitely many connected propositions, one can algorithmically determine all possible truth values of all atomic and thus connected propositions.

*Truth* is command-line tool which was written to precisely perform those computations; computing a logical expression’s truth value. Download link: truth.py

A list of all supportet operators can be seen by invoking the tool with a `--help`

flag.

This project was inspired by Albert Menne’s *Einführung in die Logik*^{1}; the operator syntax used is similar to his, translated to be 7-bit-ASCII-compatible.

*Truth* can be used to either verify universally true statements, e.g. *tertium non datur* and a property of the replication, *verum sequitur ex quodlibet*.

-(p&-p) <-> 1 , 1 <- p 1 0010 1 1 1 1 0 1 1001 1 1 1 1 1

Though not only absolute truth, but also complete relational equivalence between two expressions can be shown.

(p->q)|(r>-<s) <-> q|(r|s)&-(r&s)|-p 01 0 1 0 0 0 1 00 000 01 000 110 10 0 0 0 0 0 1 00 000 01 000 001 01 1 1 0 0 0 1 11 000 01 000 110 11 1 1 0 0 0 1 11 000 01 000 101 01 0 1 1 1 0 1 01 110 11 100 110 10 0 1 1 1 0 1 01 110 11 100 101 01 1 1 1 1 0 1 11 110 11 100 110 11 1 1 1 1 0 1 11 110 11 100 101 01 0 1 0 1 1 1 01 011 11 001 110 10 0 1 0 1 1 1 01 011 11 001 101 01 1 1 0 1 1 1 11 011 11 001 110 11 1 1 0 1 1 1 11 011 11 001 101 01 0 1 1 0 1 1 00 111 00 111 110 10 0 0 1 0 1 1 00 111 00 111 001 01 1 1 1 0 1 1 11 111 00 111 110 11 1 1 1 0 1 1 11 111 00 111 101

Complete contravalence can also be shown.

-(p/-p>-<0)|p->q<-r >-< p&-q&r 0 0110 1 0 101 01 0 1 001000 0 1101 1 0 110 01 0 1 111000 0 0110 1 0 101 11 0 1 000100 0 1101 1 0 111 11 0 1 100100 0 0110 1 0 101 01 1 1 001001 0 1101 1 0 010 00 1 1 111011 0 0110 1 0 101 11 1 1 000101 0 1101 1 0 111 11 1 1 100101

^{1}Menne, Albert: *Einführung in die Logik*. Bern: Franke, 1966. (= Dalp-Taschenbücher; 384 D)

## Third Anniversary

Today marks this blog’s third anniversary. To celebrate and take a look back at the year, I have collected a few image highlights.

`17500615947440398742637684298448259300459653195179624088723406481656498345927782897306957959023081425157582777952426879442535942327333206022815634243070984075006080698433225695442819778347008.0`