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From: Mild Shock <janburse@fastmail.fm>
Newsgroups: comp.lang.prolog
Subject: neural networks cover rule based in zero order logic (Was: Higher
 Order Logic Programming and Autograd)
Date: Sat, 15 Mar 2025 16:13:51 +0100
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A storm of symbolic differentiation libraries
was posted. But what can these Prolog code
fossils do?

Does one of these libraries support Python symbolic
Pieceweise ? For example one can define rectified
linear unit (ReLU) with it:

                 /   x      x  >= 0
     ReLU(x) := <
                 \   0      otherwise

With the above one can already translate a
propositional logic program, that uses negation
as failure, into a neural network:

NOT     \+ p             1 - x
AND     p1, ..., pn      ReLU(x1 + ... + xn - (n-1))
OR      p1; ...; pn      1 - ReLU(-x1 - .. - xn + 1)

For clauses just use Clark Completion, it makes
the defined predicate a new neuron, dependent on
other predicate neurons,

through a network of intermediate neurons. Because
of the constant shift in AND and OR, the neurons
will have a bias b.

So rule based in zero order logic is a subset
of neural network.

Python symbolic Pieceweise
https://how-to-data.org/how-to-write-a-piecewise-defined-function-in-python-using-sympy/

rectified linear unit (ReLU)
https://en.wikipedia.org/wiki/Rectifier_(neural_networks)

Clark Completion
https://www.cs.utexas.edu/~vl/teaching/lbai/completion.pdf