Contradictory Proposition

A Contradictory Proposition is a logic proposition/logic sentence that is (must necessarily be) false (a contradictory statement).

• AKA: Unsatisfiable Sentence.
• Context:
  • It can be detected by a Satisfiability Task.
  • …
• Example(s):
  • [math]\displaystyle{ x ∧ ¬x }[/math].
  • [math]\displaystyle{ (x → y) ∧ x ∧ ¬y }[/math].
  • …
• Counter-Example(s):
  • a Tautological Logic Sentence, such as [math]\displaystyle{ x \lor \lnot x }[/math].
  • a Satisfiable Logic Sentence.
• See: Contradictory Binary Logic Sentence.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/contradiction Retrieved:2015-5-8.
  • In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other. Illustrating a general tendency in applied logic, Aristotle's law of noncontradiction states that "One cannot say of something that it is and that it is not in the same respect and at the same time."

    By extension, outside of classical logic, one can speak of contradictions between actions when one presumes that their motives contradict each other.

2009

• http://www.logic-classroom.info/glossary.htm
  • contradiction refers to the opposition between two propositions which cannot both be false together and cannot both be true together.

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