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Definition: Syntax of PL0 - Propositions as Boolean Terms

The variables and functions defined in signature of propositional logic $PL0$ are called Boolean, named after the English mathematician George Boole.

First, we agree that the formal language \(L\subseteq \Sigma^* \) of $PL0$ is defined over an alphabet \(\Sigma\) containing the following letters:

We will now specify the syntax of $PL0$:

Examples

This syntax enables us to construct propositions (Boolean terms):

Please note that we did not yet define any meaning (semantics) of propositions. We will catch up on this now.

| | | | | created: 2015-06-07 09:39:47 | modified: 2020-05-04 18:49:39 | by: bookofproofs | references: [656], [711]

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Bibliography (further reading)

[656] Hoffmann, Dirk W.: “Grenzen der Mathematik – Eine Reise durch die Kerngebiete der mathematischen Logik”, Spektrum Akademischer Verlag, 2011

[711] Mendelson Elliott: “Theory and Problems of Boolean Algebra and Switching Circuits”, McGraw-Hill Book Company, 1982