logic

Generally, by logic, people mean first order logic, a formal set of rules for building mathematical statements out of symbols like (negation^{👁 Mathworld
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) and (implication^{👁 Mathworld
👁 Planetmath}
) along with quantifiers^{👁 Mathworld
👁 Planetmath}
like (for every) and (there exists).

More generally, a logic is any set of rules for forming sentences^{👁 Mathworld
👁 Planetmath}
(the logic’s syntax) together with rules for assigning truth values to them (the logic’s semantics). Normally it includes a (possibly empty) set of types (also called sorts), which represent the different kinds of objects that the theory discusses (typical examples might be sets, numbers, or sets of numbers). In addition^{👁 Planetmath
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it specifies particular quantifiers, connectives^{👁 Mathworld
👁 Planetmath}
, and variables. Particular theories in the logic can then add relations^{👁 Mathworld
👁 Planetmath}
and functions to fully specify a logical language.

Title	logic
Canonical name	Logic
Date of creation	2013-03-22 13:00:09
Last modified on	2013-03-22 13:00:09
Owner	Henry (455)
Last modified by	Henry (455)
Numerical id	9
Author	Henry (455)
Entry type	Definition
Classification	msc 03B15
Classification	msc 03B10
Related topic	FuzzySubset
Defines	syntax
Defines	semantics
Defines	type
Defines	sort