From Infinite to Finite by Identifying Variables in Many-Valued Logic
Arto K. Salomaa · Journal of automata, languages and combinatorics · 2018
The paper investigates compositions of many-valued truth-functions. There are specific $n$-valued truth-functions $f$, customarily referred to as Sheffer functions such that any $n$-valued truth-function of an arbitrary number of variables can be expressed as a composition of $f$. Moreover, there are infinitely many bases for the set of all $n$-valued truth-functions. However, the number of bases is finite if attention is restricted to bases where no variable identification is possible. Moreover, an upper bound for this number in terms of $n$ is effectively computable.