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 Bool.

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): * $x$, * $(x)$, * $\neg a$, * \((\neg(\neg y))\), * \(((x\Rightarrow(y\vee(1\wedge(\neg w))))\wedge 0)\), * \(((a\Leftrightarrow b)\vee(0\Rightarrow y))\).

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

Branches: 1
Chapters: 2
Corollaries: 3 4 5 6
Definitions: 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Examples: 21 22 23
Lemmas: 24 25 26 27 28 29 30 31 32 33 34 35 36 37
Parts: 38
Proofs: 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
Propositions: 57 58
Sections: 59


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References

Bibliography

  1. Hoffmann, Dirk W.: "Grenzen der Mathematik - Eine Reise durch die Kerngebiete der mathematischen Logik", Spektrum Akademischer Verlag, 2011
  2. Mendelson Elliott: "Theory and Problems of Boolean Algebra and Switching Circuits", McGraw-Hill Book Company, 1982