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For example, translating the sentence "all skyscrapers are tall" as (() ()) is a logic translation that expresses an English language sentence in the logical system known as first-order logic. The aim of logic translations is usually to make the logical structure of natural language arguments explicit.
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 ...
First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables. Rather than propositions such as "all men are mortal", in first-order logic one can have expressions in the form "for all x , if x is a man, then x is mortal"; where "for all x" is a quantifier, x is a variable, and "...
[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.
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 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.
One definition of a controlled process is an intentionally-initiated sequence of cognitive activities. [6] In other words, when attention is required for a task, we are consciously aware and in control. Controlled processes require us to think about situations, evaluate and make decisions. An example would be reading this article.