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Mathematical logic, also called 'logistic', 'symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the nineteenth century with the aid of an artificial notation and a rigorously deductive method. [4]
In logic, a set of symbols is commonly used to express logical representation. ... for example “⌜G⌝” denotes the Gödel number of G. (Typographical note ...
Formal logic is also known as symbolic logic and is widely used in mathematical logic. It uses a formal approach to study reasoning: it replaces concrete expressions with abstract symbols to examine the logical form of arguments independent of their concrete content. In this sense, it is topic-neutral since it is only concerned with the ...
The propositional calculus[a] is a branch of logic. [1] It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [1] or sometimes zeroth-order logic. [4][5] It deals with propositions [1] (which can be true or false) [6] and relations between propositions, [7] including the construction of ...
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Connectives can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective can be used to join the two atomic formulas and , rendering the complex formula .
In propositional logic, modus ponens (/ ˈmoʊdəsˈpoʊnɛnz /; MP), also known as modus ponendo ponens (from Latin 'method of putting by placing'), [ 1 ]implication elimination, or affirming the antecedent, [ 2 ] is a deductive argument form and rule of inference. [ 3 ] It can be summarized as " P implies Q.P is true.
Logical conjunction. In logic, mathematics and linguistics, and ( ) is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as [1] or or (prefix) or or [2] in which is the most modern and widely used. The and of a set of operands is true if and only if all of its ...
Wherever logic is applied, especially in mathematical discussions, it has the same meaning as above: it is an abbreviation for if and only if, indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon (although, as noted above, if is more often used than iff in statements of definition).