Semi-Parses and Standard Operators

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A parse, as noted in the previous section, is the variable representing a truth function’s output, given a specific condition value of that function’s domain. That is, a truth function has the same value as it’s parse, , when . Unfortunately, we don’t always have the luxury of defining the value of every member of a function’s domain. If I were to define a domain, , such that every member of was also a member of , , and had only unique variables, then assigning a specific value to would not define enough information to isolate one parse of . In stead, I would be left with truth function with a domain, , including only those variables that are in and not in . Such a function would be called a semi-parse with respect to , and would be written:

Standard Operator Functions
Among the many strange and complex truth functions that are possible
when the concept is generalized there are several very boring functions that
only ever return the value of one operand. These standard operator functions will return zero when their specific operand is zero and one when that operand is one. A standard operator is denoted , where is the number of operands in the truth function and is the specific operand represented by the standard operator; naturally, . In general the standard operator is defined as:

Common Standard Operators

Two Operand Standard Operators

Three Operand Standard Operators

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