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A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises ...
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
For instance, Hume's principle, and Basic Law V. accessibility relation In modal logic, a relation that describes which worlds are accessible from other worlds in the semantics of possible world models. actual world In modal logic, the world that is considered to be the real world, as opposed to possible worlds which are considered in modal ...
Deductive reasoning is the psychological process of drawing deductive inferences.An inference is a set of premises together with a conclusion. This psychological process starts from the premises and reasons to a conclusion based on and supported by these premises.
The most reliable forms of logic are modus ponens, modus tollens, and chain arguments because if the premises of the argument are true, then the conclusion necessarily follows. [5] Two invalid argument forms are affirming the consequent and denying the antecedent. Affirming the consequent All dogs are animals. Coco is an animal.
The entailment relation in full CLL is undecidable. [8] When considering fragments of CLL, the decision problem has varying complexity: Multiplicative linear logic (MLL): only the multiplicative connectives. MLL entailment is NP-complete, even restricting to Horn clauses in the purely implicative fragment, [9] or to atom-free formulas. [10]
In natural language, an instance of the paradox of entailment arises: It is raining. And It is not raining. Therefore George Washington is made of rakes. This arises from the principle of explosion, a law of classical logic stating that inconsistent premises always make an argument valid; that is, inconsistent premises imply any conclusion at all.
In deductive reasoning, a sound argument is an argument that is valid and all of its premises are true (and as a consequence its conclusion is true as well). An argument is valid if, assuming its premises are true, the conclusion must be true. An example of a sound argument is the following well-known syllogism: (premises) All men are mortal.