Questions on use and formulation of logical operations, including both functions for programming and for mathematical operations.

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Logic programming with Mathematica

My question is: Wikipedia says that there is logic programming paradigm support in Mathematica (like In Prolog). Could anyone provide me with an example of using this paradigm in Mathematica?
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Using quantifiers with free indices as declarative conditions in equation solving

This is a toy example: Is there a way to rewrite Reduce[{Norm@{c[1], c[2], c[3]} == 1, 0 <= c[1] < c[2] < c[3]}, {c[1], c[2], c[3]}] ...
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Reference request for logic programming in Mathematica

I'm learning Mathematica(v8) to use it to program formal logic. Can anyone recommend a logic-specific tutorial text? A reference list of logic-related functions would also be very appreciated!
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Unknown number of variables in a logical statement

Resolve[ ForAll[{i, y[i]}, Implies[i >= 0 && i < 3 && Implies[i < 3, y[i] > 0], Sum[y[i], {i, 0, 2}]>0]]] returns ...