Editing Three-valued logic (section)

== Representation of values ==
As with bivalent logic, truth values in ternary logic may be represented numerically using various representations of the [[ternary numeral system]].  A few of the more common examples are:
* in [[balanced ternary]], each digit has one of 3 values: −1, 0, or +1; these values may also be simplified to −, 0, +, respectively;<ref>{{cite book
 | last = Knuth
 | first = Donald E.
 | author-link = Donald Knuth
 | title = The Art of Computer Programming Vol. 2
 | publisher = Addison-Wesley Publishing Company
 | year = 1981
 | location = Reading, Mass.
 | pages = 190
}}</ref>
* in the [[redundant binary representation]], each digit can have a value of −1, 0, 0/1 (the value 0/1 has two different representations);
* in the [[ternary numeral system]], each [[numerical digit|digit]] is a ''[[trit (computing)|trit]]'' (trinary digit) having a value of: 0, 1, or 2;
* in the [[skew binary number system]], only the least-significant non-zero digit can have a value of 2, and the remaining digits have a value of 0 or 1;
* 1 for ''true'', 2 for ''false'', and 0 for ''unknown'', ''unknowable''/''[[undecidable problem|undecidable]]'', ''irrelevant'', or ''both'';<ref>{{Cite journal |author-first=Brian |author-last=Hayes |author-link=Brian Hayes (scientist) |title=Third base |journal=[[American Scientist]] |publisher=[[Sigma Xi]], the Scientific Research Society |date=November–December 2001 |volume=89 |issue=6 |pages=490–494 |doi=10.1511/2001.40.3268 |url=http://bit-player.org/wp-content/extras/bph-publications/AmSci-2001-11-Hayes-ternary.pdf |access-date=2020-04-12 |url-status=live |archive-url=https://web.archive.org/web/20191030114823/http://bit-player.org/wp-content/extras/bph-publications/AmSci-2001-11-Hayes-ternary.pdf |archive-date=2019-10-30}}</ref>
* 0 for ''false'', 1 for ''true'', and a third non-integer "maybe" symbol such as ?, #, {{sfrac|1|2}},<ref>{{cite book|url=https://books.google.com/books?id=ud3sEeVdTIwC&pg=PT1113|title=The Penguin Dictionary of Mathematics. Fourth Edition.|last=Nelson|first=David|publisher=Penguin Books|year=2008|isbn=9780141920870|location=London, England|at=Entry for 'three-valued logic'}}</ref> or xy.

Inside a [[ternary computer]], ternary values are represented by [[ternary signal]]s.

This article mainly illustrates a system of ternary [[propositional logic]] using the truth values {false, unknown, true}, and extends conventional Boolean [[connectives]] to a trivalent context.