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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 ...
Conclusion: It's cloudy. The logical form of this argument is known as modus ponens , [ 39 ] which is a classically valid form. [ 40 ] So, in classical logic, the argument is valid , although it may or may not be sound , depending on the meteorological facts in a given context.
In logic, the logical form of a statement is a precisely-specified semantic version of that statement in a formal system.Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system.
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.
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.
A graphical representation of a partially built propositional tableau. In proof theory, the semantic tableau [1] (/ t æ ˈ b l oʊ, ˈ t æ b l oʊ /; plural: tableaux), also called an analytic tableau, [2] truth tree, [1] or simply tree, [2] is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. [1]