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Propositional Logic

Propositional logic is a logical calculus dealing with prime propositions – simple statements that express a single complete thought, which is either true or false, but never both. For instance,

  • Socrates was a human.
  • $2+3=5$
  • It is raining.

Propositional logic also studies the rules, how the truth of such prime propositions changes, if they are combined to more complex propositions using connectives. The most important connectives are:

  • “… and …”, denoted by the sign “$\wedge$”,
  • “… or …”, denoted by the sign “$\vee$”,
  • “not …”, denoted by the sign “$\neg$”,
  • “either … or …”, denoted by the sign “$\oplus$”,
  • “if … then …”, denoted by the sign “$\Rightarrow$”,
  • “… if and only if …”, denoted by the sign “$\Leftrightarrow$”.

It will turn out later that propositional logic and its connectives are embedded into more complex classical logical calculi and, as such, they are particularly important for mathematics and have many important applications in computer sciences and electronics.

We will now apply the basic concepts of logic to formally construct propositional logic.

| | | | Contributors: bookofproofs

1.Definition: Signature of Propositional Logic - PL0

2.Definition: Syntax of PL0 - Propositions as Boolean Terms

3.Definition: Interpretation of Propositions - the Law of Excluded Middle

4.Definition: Semantics of PL0

5.Equivalent Transformations in Propositional Logic

6.Contradictory Propositions in Propositional Logic

7.Normal Forms in $PL0$

8.Definition: Boolean Algebra

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