Taucon

Mostly made to generate a list of all possible TAUtologies and CONtradictions up to a limit.

The program only considers expressions where every operand is a variable. So expressions like T, T -> F, T <-> T are valid, but not counted.

Operators considered are ∨, ∧, ->, <-> and ~. There are only two precedence levels, one for binary operators and one for unary operators, all order of evaluation is expressed using parenthesis

The following table presents the results, the function f represents the whole program, it's shown as f(i, j) where i = number of operators, j = number of variables. The columns are:

inconst column represents the number of logically contingent expressions (ie. the number of expressions that are not a tautology or contradiction)
const column represents the number of tautologies and contradictions (contradictions + tautologies)
con column represents the number of contradictions
tau column represents the numbe of tautologies

	inconst	const	con	tau
`f(0, 0)`	0	0	0	0
`f(0, 1)`	1	0	0	0
`f(0, 2)`	0	0	0	0
`f(0, 3)`	0	0	0	0
`f(0, 4)`	0	0	0	0
`f(1, 0)`	0	0	0	0
`f(1, 1)`	3	2	0	2
`f(1, 2)`	8	0	0	0
`f(1, 3)`	0	0	0	0
`f(1, 4)`	0	0	0	0
`f(2, 0)`	0	0	0	0
`f(2, 1)`	23	22	6	16
`f(2, 2)`	190	26	0	26
`f(2, 3)`	192	0	0	0
`f(2, 4)`	0	0	0	0
`f(3, 0)`	0	0	0	0
`f(3, 1)`	263	242	48	194
`f(3, 2)`	4374	1114	78	1036
`f(3, 3)`	11724	756	0	756
`f(3, 4)`	7680	0	0	0
`f(4, 0)`	0	0	0	0
`f(4, 1)`	3199	3146	710	2436
`f(4, 2)`	108566	33274	3740	29534
`f(4, 3)`	557970	63150	2244	60906
`f(4, 4)`	880776	33144	0	33144

TODO: allow determination of equivalency between two propositions with different numbers of variables.

padeir0/taucon

Taucon