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The procedural interpretation of logic programs, which uses backward reasoning to reduce goals to subgoals, is a special case of the use of a problem-solving strategy to control the use of a declarative, logical representation of knowledge to obtain the behaviour of an algorithm. More generally, different problem-solving strategies can be ...
A set of sentences is called a theory; thus, individual sentences may be called theorems. To properly evaluate the truth (or falsehood) of a sentence, one must make reference to an interpretation of the theory. For first-order theories, interpretations are commonly called structures. Given a structure or interpretation, a sentence will have a ...
In logic programming, programs consist of sentences expressed in logical form, and computation uses those sentences to solve problems, which are also expressed in logical form. In a pure functional language , such as Haskell , all functions are without side effects , and state changes are only represented as functions that transform the state ...
[23] [3] An inference is the mental process of reasoning that starts from the premises and arrives at the conclusion. [18] [24] But the terms "argument" and "inference" are often used interchangeably in logic. The purpose of arguments is to convince a person that something is the case by providing reasons for this belief.
A relationship between two structures in logic and mathematics where they satisfy the same first-order sentences. elimination of quantifiers A process in logical deduction where quantifiers are removed from logical expressions while preserving equivalence, often used in the theory of real closed fields. elimination rule
Jean Piaget identifies several mental operations of the concrete operational stage of cognitive development: [3] Mental operations according to Jean Piaget. Seriation—the ability to sort objects in an order according to size, shape, or any other characteristic. For example, if given different-shaded objects they may make a color gradient.
The corresponding first-order theory is the set of sentences that are actually true of the real numbers. There are several different such theories, with different expressive power, depending on the primitive operations that are allowed to be used in the expression.
Propositional logic, as currently studied in universities, is a specification of a standard of logical consequence in which only the meanings of propositional connectives are considered in evaluating the conditions for the truth of a sentence, or whether a sentence logically follows from some other sentence or group of sentences.