But they differ from classical logic by the fundamental fact that they do not restrict the number of truth values to only two: they allow for a larger set \(W\) of truth degrees.
Nevertheless, this exponential growth of the number of truth values turns out to be unproblematic, because the logic of the generalized so-called Belnap trilattices in the truth vocabulary as well as in the falsity vocabulary always is first-degree entailment.
Truth tables of much greater complexity, those with a number of truth-functions, can be constructed by means of a computer.
One may mention many-valued, or multivalued, logics, which admit a finite number of truth-values; fuzzy logic, with an imprecise membership relationship (though, paradoxically, a precise equality relation); and quantum logic, where conjunction may be only partially defined and implication may not be defined at all.
Since there are only two truth values and each wff contains only a finite number of variables, there are only a finite number of truth-value assignments to the variables to be considered (if there are n distinct variables in the wff, there are 2n such assignments); these can easily be systematically tabulated.
"In Russia unfortunately there are usually a number of truths, or levels of truth.
Once you bring football into the equation, an amazing number of truths cease to be self-evident.
Using this criterion, one could then establish a number of truths: that God exists, that he is not a deceiver, that he guarantees the veracity of clear and distinct ideas, and that an external world exists that can be known through mathematical physics.
The most popular approach is to use an infinite number of truth-values represented by the real numbers between 0 (for full falsehood) and 1 (for full truth).
Many of these attempts have focused on modifying or extending the underlying strong three-valued logic, e.g. modifying the semantics of the conditional (Field, 2003, 2008) or allowing an unbounded number of truth-values (Cook, 2007; Schlenker, 2010).
Ideas are infinite in the sense that they are 'inexhaustible.' One can discover in the idea of extension, for example, 'infinite numbers of intelligible triangles, tetragons, pentagons, and other such figures,' as well as an infinite number of truths that can be demonstrated of them (ibid).
