# Rule of Inference

(redirected from Rules of inference)

## rule of inference

[′rül əv ′in·frəns]
(computer science)

## Rule of Inference

(transformation rule [in some formal system] or rule of deduction), an admissibility rule that regulates the permissible methods of proceeding from a certain collection of assertions (statements, propositions, or formulas expressing these), called premises, to a certain specific assertion (statement, proposition, or formula), called the conclusion.

Rules of inference in which the form of the premises and conclusion is clearly indicated are termed direct; these include the inference rules of the propositional calculus, which permit one to proceed from an arbitrary conjunction to one of its members or to join an arbitrary proposition to any other proposition by means of the operation of disjunction. If in the premises and conclusion only the types of derivations are indicated from one of which it is permitted to proceed to another, then we have a rule of indirect inference. A typical example of a rule of indirect inference is the deduction theorem, a rule for introducing implications in the natural-deduction propositional and predicate calculi, which permits one to proceed (within certain natural limits) from any derivation A1, A2, …, An-1, Anǀ - B to a derivation of the form A1, A2,…, An–1ǀ–AnB.

Rules of inference that express methods of contensive reasoning were already partially systematized in the bounds of traditional formal logic in the forms of syllogistic modes and were subsequently absorbed, sometimes with changes, into mathematical logic; examples include the rule of modus ponens (syllogism scheme, elimination rule), which permits one to proceed from any implication and its antecedent (premise) to its consequent (conclusion). In addition, rules of inference are divided into primitive (basic, postulated) rules and derived rules (derivable from the primitive rules by means of certain metatheorems).

For the primitive inference rules of formal systems (calculi) that are, like axioms, postulates of a given system, the usual questions of consistency, completeness, and independence arise. Insofar as inference rules in one way or another express the relation of logical necessity, and since there is a close link between this relation and the operation of implication in the majority of logical calculi, the same link exists between the inference rules and theorems of any calculus, in particular between the primitive inference rules and the axioms; for example, the analogues of the inference rules of natural deduction are, respectively, the propositional-calculus axioms A & BA, A &, BB, AAB, and BAB.

### REFERENCES

Słupecki, J., and L. Borkowski. Elementy matematicheskoi logiki i teoriia mnozhestv. Moscow, 1965. (Translated from Polish.)
Serebriannikov, O. F. Evristicheskie printsipy i logicheskie ischisleniia. Moscow, 1970.
Smirnov, V. A. Formal’nyi vyvod i logicheskie ischisleniia. Moscow, 1972.
References in periodicals archive ?
and these sentences express rules of inference that combine knowledge to produce different knowledge.
They are totally ignorant of the tools of comprehending the Quran or hadith, the rules of inference, the objectives of Islamic law and its principles.
Formal rule theories (Braine & O'Brien, 1998; Rips, 1994) postulate that our mind contains a set of formal rules of inference akin to a logical calculus.
Thus, conclusions about the population of which the batch is a part cannot be based on statistical rules of inference.
Examples abound, logical fallacies are elucidated and thoroughly analyzed, and rules of inference are detailed.
In total 18 new relationships were obtained from 20 initially present, where the system applied 7 rules of inference related to the ontology "Relationship" and 6 rules related to "Family".
empirical work that violated basic rules of inference, (11) yet Engstrom
The article offers a partial remedy to this state of affairs by challenging a naturalistically minded argument offered by Stephen Stich and his collaborators against the Goodman account of the justification of rules of inference.
One view is that reasoners rely on abstract rules of inference that operate in virtue of their form (e.
Non-simple propositions and rules of inference can then be established a priori by deductions exemplifying the simple rules of inference from the simple propositions and from non-simple propositions already inferred in this way (for variations on this theme see Boghossian 1996, BonJour 1998 and Peacocke 2005).
He concludes that the problem of scepticism arises from 'a failure to attain a certain equilibrium between rules of inference and the actual inferences we make' (9).

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