In logic: Scope and basic concepts …new proposition, usually called the conclusion. A rule of inference is said to be truth-preserving if the conclusion derived from the application of the rule is true whenever the premises are true. Inferences based on truth-preserving rules are called deductive, and the study of such inferences is known as deductive… Read More
formal logic
In formal logic: General observations …made that some proposition (the conclusion) follows with strict necessity from some other proposition or propositions (the premises)—i.e., that it would be inconsistent or self-contradictory to assert the premises but deny the conclusion. Read More
In formal logic: Semantic tableaux …to be true while the conclusion is false, this method attempts to interpret (or evaluate) the premises in such a way that they are all simultaneously satisfied and the negation of the conclusion is also satisfied. Success in such an effort would show the argument to be invalid, while failure… Read More
nonmonotonic reasoning
In applied logic: Nonmonotonic reasoning …unexpected way that allows the conclusion to be false, are ruled out. The same idea can also be expressed by saying that the intended models of the premises—the scenarios in which the premises are all true—are the “minimal” or “simplest” ones. Many rules of inference by circumscription have been formulated. Read More
syllogistic
In history of logic: Syllogisms …containing two premises and a conclusion, each of which is a categorical proposition. The subject and predicate of the conclusion each occur in one of the premises, together with a third term (the middle) that is found in both premises but not in the conclusion. A syllogism thus argues that… Read More
In history of logic: Theophrastus of Eresus …adopted a rule that the conclusion of a valid modal syllogism can be no stronger than its weakest premise. (Necessity is stronger than possibility, and an assertoric claim without any modal qualification is intermediate between the two). This rule simplifies modal syllogistic and eliminates several moods that Aristotle had accepted.… Read More
