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Rules of inference are syntactical transform rules which one can use to infer a conclusion from a premise to create an argument. A set of rules can be used to infer any valid conclusion if it is complete, while never inferring an invalid conclusion, if it is sound.
For example, the rule of inference called modus ponens takes two premises, one in the form "If p then q" and another in the form "p", and returns the conclusion "q". The rule is valid with respect to the semantics of classical logic (as well as the semantics of many other non-classical logics ), in the sense that if the premises are true (under ...
Deductively valid arguments follow a rule of inference. [38] A rule of inference is a scheme of drawing conclusions that depends only on the logical form of the premises and the conclusion but not on their specific content. [39] [40] The most-discussed rule of inference is the modus ponens. It has the following form: p; if p then q; therefore q.
Download as PDF; Printable version; In other projects Wikidata item; Appearance. ... Pages in category "Rules of inference" The following 43 pages are in this ...
The premises are shown above a line, called the inference line, [11] [12] separated by a comma, which indicates combination of premises. [13] The conclusion is written below the inference line. [11] The inference line represents syntactic consequence, [11] sometimes called deductive consequence, [14] which is also symbolized with ⊢.
Typical Hilbert-style systems have a small number of rules of inference, along with several infinite schemas of logical axioms. It is common to have only modus ponens and universal generalization as rules of inference. Natural deduction systems resemble Hilbert-style systems in that a deduction is a finite list of formulas.
In addition to deductive inference and defeasible inference, there is also probabilistic inference. [ 12 ] : 65–69 A probabilistic version of the generalization, "birds can fly", might be: "There is a 75% chance that a bird will be found to be able to fly" or "if something is a bird it probably can fly".
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science.Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language.