12,080
edits
Changes
Directory:Jon Awbrey/Papers/Functional Logic : Quantification Theory (view source)
Revision as of 10:18, 14 December 2008
, 10:18, 14 December 2008→Higher Order Propositions and Logical Operators (''n'' = 2): used bold code font for cactus language
: Each point in <math>X\!</math> may be described by means of a ''singular proposition'', that is, a proposition that describes it uniquely. This form of representation leads to the following enumeration of points:
: Each point in <math>X\!</math> may be described by means of a ''singular proposition'', that is, a proposition that describes it uniquely. This form of representation leads to the following enumeration of points:
:: <math>X = \{\ (\!|u|\!)(\!|v|\!),\ (\!|u|\!) v,\ u (\!|v|\!),\ u v\ \} \cong \mathbb{B}^2.</math>
:: '''<math>X = \{\!</math> <code>(u)(v)</code> , <code>(u)v</code> , <code>u(v)</code> , <code>uv</code> <math>\} \cong \mathbb{B}^2.</math>'''
: Each point in <math>X\!</math> may also be described by means of its ''coordinates'', that is, by the ordered pair of values in <math>\mathbb{B}</math> that the coordinate propositions <math>u\!</math> and <math>v\!</math> take on that point. This form of representation leads to the following enumeration of points:
: Each point in <math>X\!</math> may also be described by means of its ''coordinates'', that is, by the ordered pair of values in <math>\mathbb{B}</math> that the coordinate propositions <math>u\!</math> and <math>v\!</math> take on that point. This form of representation leads to the following enumeration of points: