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In the extreme case where the list of antecedent formulas of a sequent is empty, the consequent is unconditional. This differs from the simple unconditional assertion because the number of consequents is arbitrary, not necessarily a single consequent. Thus for example, ' ⊢ B 1, B 2 ' means that either B 1, or B 2, or both must be true.
A condition subsequent is a philosophical and legal term referring to a defined event which terminates a proposition or a contractual obligation. [ 1 ] [ 2 ] In contrast to a condition precedent , a condition subsequent brings the event (or obligation) to an end, rather than being necessary for to the event or obligation to occur.
In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal fallacy (or an invalid form of argument) that is committed when, in the context of an indicative conditional statement, it is stated that because the consequent is true, therefore the ...
Logical consequence (also entailment or implication) 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 consequent is the second half of a hypothetical proposition. In the standard form of such a proposition, it is the part that follows "then". In an implication, if P implies Q, then P is called the antecedent and Q is called the consequent. [1] In some contexts, the consequent is called the apodosis. [2] Examples:
Contrast consequent and subsequent. ocean The vast, contiguous body of salt water covering more than 70% of the Earth's surface area and surrounding the continental landmasses; or any portion of this larger body of water that is divided and distinguished from the other portions, each of which is called an ocean, by the presence of the ...
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements.For example, in the conditional statement: "If P then Q", Q is necessary for P, because the truth of Q is guaranteed by the truth of P.
Venn diagram of (true part in red) In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or biimplication or bientailment, is the logical connective used to conjoin two statements and to form the statement "if and only if" (often abbreviated as "iff " [1]), where is known as the antecedent, and the consequent.