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In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
A logical argument, seen as an ordered set of sentences, has a logical form that derives from the form of its constituent sentences; the logical form of an argument is sometimes called argument form. [6] Some authors only define logical form with respect to whole arguments, as the schemata or inferential structure of the argument. [7]
A formal system (also called a logical calculus, or a logical system) consists of a formal language together with a deductive apparatus (also called a deductive system). The deductive apparatus may consist of a set of transformation rules (also called inference rules) or a set of axioms, or have both. A formal system is used to derive one ...
Propositional logic only considers logical relations between full propositions. First-order logic also takes the internal parts of propositions into account, like predicates and quantifiers. Extended logics accept the basic intuitions behind classical logic and apply it to other fields, such as metaphysics, ethics, and epistemology. Deviant ...
Thus first-order logical consequence is semidecidable: it is possible to make an effective enumeration of all pairs of sentences (φ,ψ) such that ψ is a logical consequence of φ. Unlike propositional logic , first-order logic is undecidable (although semidecidable), provided that the language has at least one predicate of arity at least 2 ...
The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...
A form of logical expression where all quantifiers are moved to the front, standardizing the structure of first-order logical statements. primitive recursion A form of recursion where a function is defined in terms of itself, using simpler cases, with a base case to stop the recursion. primitive recursive function
This writing mode frequently uses the tools of descriptive writing (see below), but also exposition. Narration is an especially useful tool for sequencing or putting details and information into some kind of logical order, traditionally chronological. Working with narration helps us see clear sequences separate from other modes.