premise


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premise

Logic a statement that is assumed to be true for the purpose of an argument from which a conclusion is drawn

Premise

 

in the broad sense, that on the basis of which an inference or conclusion is drawn. Premises may be facts or judgments of facts, principles, axioms, postulates, or any events or propositions that are raw data from which some information that is new to us can be extracted directly or through reasoning. In this sense we may speak equally of premises of induction and premises of deduction.

In the narrow sense, premises proper in formally deductive logical constructs are propositions to which is applied some rule of inference or formulas symbolizing the propositions and comprising statements of the rules of inference in the investigator’s language. The concept of logical corollary is symmetrical to the concept of premise. These concepts are generally relative: a proposition may be a premise in one application of a rule of inference and a corollary in another. In logical formalisms of the axiomatic type, the premises of the first steps of deduction are stated in advance in the form of axioms and thus play the role of absolute premises, or prerequisites: the deductive procedure must necessarily begin with them. In natural calculi, in which reasoning follows the principle of assumptions that was known even in antiquity, there are no absolute premises.

Whatever their character, premises are a necessary condition for logical argumentation or proof. Here the question of the nonextraneous character of premises turns out to be essential. A premise that is extraneous to a given argument may always be replaced by the contradictory premise without damage to the argument. A law of logic that may be called the law of the extraneous premise corresponds to the rule

(A & BC) & (AC)) ⊃ (A & ┐ BC)

The fundamental task of logic is to investigate the corollaries of given premises and to find nonextraneous premises corresponding to given consequences. Within the limits of the formalism of the algebra of propositions, these problems have an exhaustive solution.

M. M. NOVOSELOV

References in periodicals archive ?
However, there are several challenges at the customer premises that must be overcome for derived voice services to be widely deployed to residential customers.
While virtually any type of property can be appraised under each of these four fundamental premises, the results under each for the same property may be dramatically different.
He said that SAFMA then submitted an application to the authority for allowing it to use the premises as a library, but the authority, during tendency of the application, sealed the SAFMA premises without giving any notice.
Following the hearing, Supt Mark Wiggins told the ECHO: Merseyside Police recovered a substantial quantity of amphetamine and a firearm from the premises and it is clear that members of the criminal fraternity were using the premises to meet.
The police had held meetings with the premises licence holder to address problems at the premises.
Some power company transmission lines and transformers, for example, may actually be located on the insured premises. If that type of supply equipment fails, causes a service interruption, and causes a loss, then the exclusion is triggered even though the failed equipment is located on the insured premises.
A total of 800 new exchanges are expected to benefit from the advanced copper broadband, including 400 exchanges in rural areas that will serve more than 900,000 premises.
Tower contended that the claim falls within an exclusion in the policy for claims arising out of a premises at which the insured does not reside.
Occupying business premises by way of an occupational lease will enable you to occupy premises for an agreed period without significant capital expenditure.
How can such prospective tenants give landlords the comfort level they need that they will be able to regain possession of the demised premises promptly in the event that the tenant defaults?
The Licensing Act establishes a single scheme for licensing premises are used for the supply of alcohol, to provide regulated entertainment or to provide late night refreshment.