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Formally, the language used for this sequence contains the symbols a-z and A-Z (the variables), ~, *, +, ->, <->, ( and ).

* Every - every variable is a formula.;

* If - if A is a formula, then ~A is a formula.;

* If - if A and B are formulas, then (A*B), (A+B), (A->B) and (A<->B) are all formulas.

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The contradictions of length 6 are ~(a<->a), ~(a->a), (~a*a), (~a<->a), (a*~a) and (a<->~a): 6 formulas, and the tautologies of length 6 are (~a+a) and (a+~a): 2 formulas. So a(6) = 6+2 = 8.

The tautologies of length 6 are (~a+a) and (a+~a).

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allocated for Matthew ScroggsNumber of tautologies and contradictions in propositional calculus of length n.

0, 0, 0, 0, 2, 8, 14, 26, 63, 215, 527

1,5

a(n) is the number of tautologies and contradictions that are n symbols long in propositional calculus with the connectives not (~), and (*), or (+), implies (->) and if and only if (<->).

When measuring the length of a formula all brackets must be included. The connectives -> and <-> are counted as one symbol each (but writing them as such requires non-ASCII characters).

Formally, the language used for this sequence contains the symbols a-z and A-Z (the variables),~,*,+,->,<->,( and ).

The formulas are defined by the following rules:

* Every variable is a formula.

* If A is a formula, then ~A is a formula.

* If A and B are formulas, then (A*B), (A+B), (A->B) and (A<->B) are all formulas.

A formula is a tautology if it is true for any assignment of truth values to the variables.

A formula is a contradiction if it is false for any assignment of truth values to the variables.

This sequence is increasing, as adding a ~ to the start of a tautology or contradiction gives a contradiction or tautology one symbol longer.

M. Scroggs, <a href="http://mscroggs.co.uk/blog/35">Logical Contradictions</a>

M. Scroggs, <a href="http://www.mscroggs.co.uk/blog/tautologies.txt">List of tautologies</a>

M. Scroggs, <a href="http://www.mscroggs.co.uk/blog/contradictions.txt">List of contradictions</a>

The contradictions of length 6 are ~(a<->a), ~(a->a), (~a*a), (~a<->a), (a*~a) and (a<->~a).

The tautologies of length 6 are (~a+a) and (a+~a).

Equals A256120 plus A277275

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Matthew Scroggs, Oct 08 2016

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