Inquiry and Analogy • Measure for Measure
Let us define two families of measures,
by means of the following equations:
Table 14 shows the value of each on each of the 16 boolean functions In terms of the implication ordering on the 16 functions, says that is above or identical to in the implication lattice, that is, in the implication ordering.
Table 15 shows the value of each on each of the 16 boolean functions In terms of the implication ordering on the 16 functions, says that is below or identical to in the implication lattice, that is, in the implication ordering.
Applied to a given proposition the qualifiers and tell whether is above or below respectively, in the implication ordering. By way of example, let us trace the effects of several such measures, namely, those which occupy the limiting positions in the Tables.
Expressed in terms of the propositional forms they value positively, is a totally indiscriminate measure, accepting all propositions whereas and are measures valuing the constant propositions and respectively, above all others.
Finally, in conformity with the use of fiber notation to indicate sets of models, it is natural to use notations like the following to denote sets of propositions satisfying the umpires in question.
- Logic Syllabus
- Boolean Function
- Boolean-Valued Function
- Logical Conjunction
- Minimal Negation Operator
- Introduction to Inquiry Driven Systems
- Functional Logic • Part 1 • Part 2 • Part 3
- Cactus Language • Part 1 • Part 2 • Part 3 • References • Document History
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