Sentence examples for exclusive disjunction from inspiring English sources
noun
A disjunction which is true if only one, but not both, of its disjuncts is true.
that disjunctive updates should not be identified with the exclusive disjunction.
Classically, an exclusive disjunction is true if and only if one of the disjuncts is true.
This "quantifier exclusive-or" is certainly not the only option (contra McCawley [1993], 128 130) available to someone who seeks a semantic account of exclusive disjunction in natural language, and who wants merely to account for lists with more than two "exclusive disjuncts" in a way that avoids the "odd counting" feature of formulae composed exclusively of 0110 disjunctions.
For clarity, exclusive disjunction (either x or y, but not both), symbolized x ⊻ y, must be distinguished from inclusive disjunction (either x or y, or both x and y), symbolized x ∨ y.
For disjunctive premises (employing ∨, which signifies "either... or"), the terms modus tollendo ponens and modus ponendo tollens are used for arguments of the forms A ∨ B; ∼A, therefore B, and A ∨ B; A, therefore ∼B (valid only for exclusive disjunction: "Either A or B but not both").
(¬(p↔ q) is the exclusive disjunction of p and q).
In practical terms, the simulation images were constructed by repositioning the 3D digital image in 6 degrees of freedom, and the matching fitness was by counting the voxels that did not correspond between the constructed images and a flat panel X-ray detector derived X-ray scans (i.e., exclusive disjunctions).
The set of punctured cumomers is, therefore, the logical conjunction-exclusive disjunction expansion of the set of isotopomers with respect to s; or, in coding theory parlance, the Reed Muller spectral domain [13, 14] of the set of isotopomers with respect to s.
The side condition is that the two occurrences of aye are to be filled by occurrences of the same well-formed English declarative sentence, that the discontinuous expression 'Either … or … '; expresses classical non-exclusive disjunction, and that the six-word sentence-prefix 'it is not the case that'; expresses classical negation.
To make matters explicit, the earlier discussed truth-function ∨ is called inclusive, or non-exclusive or 1110 disjunction.
Stoic disjunction is exclusive and non-truth-functional.
