Search results
Results from the WOW.Com Content Network
Logical connectives can be used to link zero or more statements, so one can speak about n-ary logical connectives. The boolean constants True and False can be thought of as zero-ary operators. Negation is a unary connective, and so on.
a set of operator symbols, called connectives, [18] [1] [50] logical connectives, [1] logical operators, [1] truth-functional connectives, [1] truth-functors, [37] or propositional connectives. [ 2 ] A well-formed formula is any atomic formula, or any formula that can be built up from atomic formulas by means of operator symbols according to ...
The scope of a logical connective occurring within a formula is the smallest well-formed formula that contains the connective in question. [2] [6] [8] The connective with the largest scope in a formula is called its dominant connective, [9] [10] main connective, [6] [8] [7] main operator, [2] major connective, [4] or principal connective; [4] a connective within the scope of another connective ...
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 ...
In mathematics, the associative property [1] is a property of some binary operations that means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs.
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
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 ∧ {\displaystyle \wedge } [ 1 ] or & {\displaystyle \&} or K {\displaystyle K} (prefix) or × {\displaystyle \times } or ⋅ {\displaystyle \cdot } [ 2 ] in ...
Sentences without any logical connectives or quantifiers in them are known as atomic sentences; by analogy to atomic formula. Sentences are then built up out of atomic sentences by applying connectives and quantifiers. A set of sentences is called a theory; thus, individual sentences may be called theorems.