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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
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
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
Appeal to consequences, also known as argumentum ad consequentiam (Latin for "argument to the consequence"), is an argument that concludes a hypothesis (typically a belief) to be either true or false based on whether the premise leads to desirable or undesirable consequences. [1]
There are many places to live in California other than San Diego. On the other hand, one can affirm with certainty that "if someone does not live in California" (non-Q), then "this person does not live in San Diego" (non-P). This is the contrapositive of the first statement, and it must be true if and only if the original statement is true.
An erosion gully in Australia caused by rabbits, an unintended consequence of their introduction as game animals. In the social sciences, unintended consequences (sometimes unanticipated consequences or unforeseen consequences, more colloquially called knock-on effects) are outcomes of a purposeful action that are not intended or foreseen.
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.
Material implication does not closely match the usage of conditional sentences in natural language. For example, even though material conditionals with false antecedents are vacuously true, the natural language statement "If 8 is odd, then 3 is prime" is typically judged false. Similarly, any material conditional with a true consequent is ...