Re: R.J. Lipton and K.W. Regan • A Negative Comment On Negations
The real reason Rosenblatt’s perceptrons short-shrift XOR and EQ among the sixteen boolean functions on two variables is the adoption of a particular role for neurons in the activity of the brain and a particular model of how neurons serve computation, namely, as threshold activation devices. It is as if we tried to do mathematics using only the inequality instead of using equations. Sure, we can express equations in roundabout ways but why tolerate the resulting inefficiency? As a final observation, for boolean variables is equivalent to so this fits right in with the weakness of implicational inference compared to equational inference rules.
But there are other models for the role neurons play in the activity of the brain and the work they do in computation.
- Logical Graphs
- Minimal Negation Operators
- Logical Graphs • Introduction
- Logical Graphs • Development
- Logic Syllabus • Zeroth Order Logic
- Survey of Animated Logical Graphs
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