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Logical reasoning is a mental activity that aims to arrive at a conclusion in a rigorous way. It happens in the form of inferences or arguments by starting from a set of premises and reasoning to a conclusion supported by these premises. The premises and the conclusion are propositions, i.e. true or false claims about what is the case. Together ...
Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to work". [1] Premises and conclusions express propositions or claims that can be true or false. An important ...
A Mastermind player uses abduction to infer the secret colors (top) from summaries (bottom left) of discrepancies in their guesses (bottom right).. Abductive reasoning (also called abduction, [1] abductive inference, [1] or retroduction [2]) is a form of logical inference that seeks the simplest and most likely conclusion from a set of observations.
Examples of sentences that are (or make) true statements: "Socrates is a man." "A triangle has three sides." "Madrid is the capital of Spain." Examples of sentences that are also statements, even though they aren't true: "All toasters are made of solid gold." "Two plus two equals five." Examples of sentences that are not (or do not make ...
Analogy – Cognitive process of transferring information or meaning from a particular subject to another; Axiom system – Mathematical term; concerning axioms used to derive theorems. Axiom – Statement that is taken to be true; Immediate inference – Logical inference from a single statement
A process in logical deduction where quantifiers are removed from logical expressions while preserving equivalence, often used in the theory of real closed fields. elimination rule A rule in logical inference that allows the derivation of simpler formulas from more complex ones, often by removing logical connectives or quantifiers. empty concept
Enderton, for example, observes that "modus ponens can produce shorter formulas from longer ones", [9] and Russell observes that "the process of the inference cannot be reduced to symbols. Its sole record is the occurrence of ⊦q [the consequent] ... an inference is the dropping of a true premise; it is the dissolution of an implication".
In proof by contradiction, also known by the Latin phrase reductio ad absurdum (by reduction to the absurd), it is shown that if some statement is assumed true, a logical contradiction occurs, hence the statement must be false. A famous example involves the proof that is an irrational number: