Contravalence
Contra is in the classical logic and mathematics the name for the connection of two statements by the two connective , of either  or , exclusive or as well Kontravalentor is.
Synonymous with contravalence, the terms exclusive disjunction (also complete or antivalent disjunction ), bisubtraction , exclusive or, antivalence, contradictory opposition , contrajunction or alternation are used. In switching algebra one speaks of the exclusiveor gate (XOR gate), in propositional logic it is called XOR operation.
Definition and characteristics
Defines the contra is the truth function of their Junktors: A contra is only true if both different by it related statements truth values have, that is, if either the one or the other is true, but if not both true or both false at the same time are. The Latin expression for this exclusive or as "either  or" is "aut  aut".
A truth table (matrix) gives the aut function as a truth value function of contravalence as follows:
A.  B.  

true  true  not correct 
true  not correct  true 
not correct  true  true 
not correct  not correct  not correct 
The contravalence is associative and commutative . It is also selfinverse and distributive with respect to logical AND , but not with respect to OR :
 It always applies ,
 however, is only if is wrong.
 It is selfinverse because: .
Differentiation and similarities
The difference to the nonexclusive or (in the narrower sense the disjunction) consists in the “tightened information” that “it is certain from the start that one of the two alternatives must be true”, that is, not only at least but also at most one of the two Facts exist.
Equivalences of contravalence, i.e. formulas with other connectors that have the same truth value sequence, are:
 Negation of the biconditional (negation of equivalence )
 or
 or
 .
Importance and practical application
The importance of contravalence is rather small in modern logic, "since it allows relatively few connections to be formulated". In switching algebra, however, it is of great importance as an XOR link. The property that the double application of the XOR operation corresponds to the identity, i.e. This means that it is selfinverse, is used in cryptography  where it enables the same function to be used for encryption and decryption  as well as in the RAID system.
Notation and pronunciation
Symbols of the contravalentor include:
 ⌴ half a square open at the top.
 XOR
 ">  <"
 "> <"
The way of speaking for the junction also varies:
 "A versus B"
 "A or (but) B"
 "Either A, or B"
 "A, except that B"
 "A, except that B"
 "A, unless B"
 "A if and only if not B"
Colloquially, the contravalentor is paraphrased as "either  or". But this expression can also have other colloquial meanings that do not correspond to contravalence; For example, “Either Emil or I will pick you up” can also be understood as true if both of them pick up the conversation partner.
See also

Propositional logic
 Equivalence ( XNOR gate )
 Negation ( nongate )
 Subjunction ( implication )
 Conjunction ( AND gate )
 Disjunction ( OR gate )
Individual evidence

↑ See Lorenz: Disjunction. In: Jürgen Mittelstraß (Hrsg.): Encyclopedia Philosophy and Philosophy of Science. 2nd edition 2005.
In a different meaning also the truth value function that interprets this junctor  ↑ z. B. Lorenz: Disjunction. In: Mittelstraß (Hrsg.): Encyclopedia Philosophy and Philosophy of Science, 2nd edition 2005
 ↑ z. B: Paul Lorenzen : Logic, 4th ed. (1970), p. 48 (to avoid the word "disjunction")
 ↑ z. B. Menne: Logic, 6th edition (2001), p. 39
 ↑ Strobach: Introduction to Logic (2005), p. 22: sometimes, but not well according to the Latin meaning
 ↑ ^{a } ^{b } ^{c} Essler / Martínez: Grundzüge der Logik I, 4th ed. (1991), p. 51
 ↑ Schülerduden, Philosophie, 2nd ed. (2002), Disjunction
 ↑ Hilbert / Ackermann: Grundzüge, 6th edition (1972), p. 6; Reichenbach: Fundamentals of symbolic logic (1999), p. 33
 ↑ Essler / Martínez: Grundzüge der Logic I, 4th ed. (1991), p. 98 fn. 33
 ↑ Lorenzen: Logic. 4th ed. (1970), p. 39.
 ↑ Menne: Logic, 6th edition (2001), p. 39
 ↑ Essler / Martínez: Grundzüge der Logic I, 4th ed. (1991), p. 51
 ↑ Detel: Basic Course Philosophy I: Logic (2007), p. 71
 ^ ^{A } ^{b } ^{c} Wilhelm K. Essler: Introduction to Logic (= Kröner's pocket edition . Volume 381). 2nd, expanded edition. Kröner, Stuttgart 1969, DNB 456577998 , p. 96.
 ↑ Spies: Introduction to Logic (2004), p. 13.
 ↑ Rosenkranz: Introduction to Logic (2006), p. 81.