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2.2 Propositional Logic

Propositional logic is that part of mathematical logic that deals with the composition of formulas. The composition starts with basic formulas that are considered as "black boxes": we are interested in their truth value ("true or false?") but not in what properties they actually describe. Various operations then allow to combine simpler formulas to more complex ones.

Definition 3 (Logical Connective) A (logical)  connective (Junktor) is a syntactic operator that combines formulas to a new formula.

In more detail, the formulas of propositional logic are constructed from the connectives `F', `T', `~', ` /\  ', ` \/ ', ` => ', ` <=> ' as follows:

Proposition 1 (Formulas of Propositional Logic) 

Above propositions provide the basis for a hierarchical construction of formulas.

Example  The syntactic structure of the formula
T /\  F => F
is ambiguous; it may be understood as (T /\  F) => F or as T /\  (F => F).

In the following sections, we will discuss the meanings of these formulas.

  • 2.2.1 Logical Constants
  • 2.2.2 Negations
  • 2.2.3 Conjunctions
  • 2.2.4 Disjunctions
  • 2.2.5 Implications
  • 2.2.6 Equivalences
  • 2.2.7 Summary

  • Author: Wolfgang Schreiner
    Last Modification: October 4, 1999

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