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The accounts discussed above all yield monotonic consequence relations, i.e. ones such that if is a consequence of , then is a consequence of any superset of . It is also possible to specify non-monotonic consequence relations to capture the idea that, e.g., 'Tweety can fly' is a logical consequence of
Although the consequence in first conditional sentences is usually expressed using the will (or shall) future (usually the simple future, though future progressive, future perfect and future perfect progressive are used as appropriate), other variations are also possible – it may take the form of an imperative, it may use another modal verb ...
:= means "from now on, is defined to be another name for ." This is a statement in the metalanguage, not the object language. This is a statement in the metalanguage, not the object language. The notation a ≡ b {\displaystyle a\equiv b} may occasionally be seen in physics, meaning the same as a := b {\displaystyle a:=b} .
In logical argument and mathematical proof, the therefore sign, ∴, is generally used before a logical consequence, such as the conclusion of a syllogism. The symbol consists of three dots placed in an upright triangle and is read therefore. While it is not generally used in formal writing, it is used in mathematics and shorthand.
A conditional sentence is a sentence in a natural language that expresses that one thing is contingent on another, e.g., "If it rains, the picnic will be cancelled." They are so called because the impact of the sentence’s main clause is conditional on a subordinate clause.
The double turnstile is a binary relation. It has several different meanings in different contexts: To show semantic consequence, with a set of sentences on the left and a single sentence on the right, to denote that if every sentence on the left is true, the sentence on the right must be true, e.g. .
Writing a closed letter 'O' means that you are a private person and an introvert. If the dot on your 'i' lands high above the letter, you are considered to be imaginative.
Logical consequence, also known as a consequence relation, or entailment Consequent , in logic, the second half of a hypothetical proposition or consequences Consequentialism , a theory in philosophy in which the morality of an act is determined by its effects