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Logical equivalence. In logic and mathematics, statements and are said to be logically equivalent if they have the same truth value in every model. [1] The logical equivalence of and is sometimes expressed as , , , or , depending on the notation being used. However, these symbols are also used for material equivalence, so proper interpretation ...
Universal generalization / instantiation. Existential generalization / instantiation. In propositional logic, material implication[1][2] is a valid rule of replacement that allows a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not- or and ...
Logical consequence (also entailment) is a fundamental concept in logic which describes the relationship between statements that hold true when one statement logically follows from one or more statements. A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises.
In logic and the philosophy of logic, specifically in deductive reasoning, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions). For example, the rule of inference called modus ponens takes two premises, one in ...
The conditions under which a statement or proposition is considered to be true, playing a central role in the semantic analysis of language. truth function. A function that takes truth values as input and produces a truth value as output, used in logic to model the truth conditions of logical connectives.
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Connectives can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective can be used to join the two atomic formulas and , rendering the complex formula .
One valid argument form is known as modus ponens, not to be mistaken with modus tollens, which is another valid argument form that has a like-sounding name and structure. Modus ponens (sometimes abbreviated as MP) says that if one thing is true, then another will be. It then states that the first is true. The conclusion is that the second thing ...
The propositional calculus[a] is a branch of logic. [1] It is also called (first-order) propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [1] or sometimes zeroth-order logic. [4][5] It deals with propositions [1] (which can be true or false) [6] and relations between propositions, [7] including the ...