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Logical consequence (also entailment or logical 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.
In philosophy and artificial intelligence (especially, knowledge based systems), the ramification problem is concerned with the indirect consequences of an action. It might also be posed as how to represent what happens implicitly due to an action or how to control the secondary and tertiary effects of an action.
Theorems are those logical formulas where is the conclusion of a valid proof, [4] while the equivalent semantic consequence indicates a tautology.. The tautology rule may be expressed as a sequent:
Ramification (mathematics), a geometric term used for 'branching out', in the way that the square root function, for complex numbers, can be seen to have two branches differing in sign. Ramification (botany), the divergence of the stem and limbs of a plant into smaller ones; Ramification group, filtration of the Galois group of a local field ...
The first implication suggests that S is a sufficient condition for N, while the second implication suggests that S is a necessary condition for N. This is expressed as " S is necessary and sufficient for N ", " S if and only if N ", or S ⇔ N {\displaystyle S\Leftrightarrow N} .
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- P {\displaystyle P} or Q {\displaystyle Q} and that either form can replace the other in ...
Compounded Semaglutide vs. Ozempic and Wegovy. What’s the difference between compounded semaglutide and Ozempic and Wegovy?. Well, Ozempic and Wegovy are FDA-approved for type 2 diabetes and ...
Going from a statement to its converse is the fallacy of affirming the consequent.However, if the statement S and its converse are equivalent (i.e., P is true if and only if Q is also true), then affirming the consequent will be valid.