Truth value assignment

As a truth value assignment is referred to in the propositional logic , a function that the statements of a formal propositional language truth values assigns. The truth value assignment is thus the propositional special case of an evaluation function ( denotation function ).

There are two possible approaches to defining a truth value assignment:

1. The truth value assignment is only defined using the atomic statements of the language. The truth values ​​of complex statements can then all be calculated from the truth values ​​of the linked atomic statements (see truth value function ).
2. The truth value assignment is defined over all statements of the language. Since the truth values ​​of complex statements can nonetheless be calculated from those of the atomic ones, in this case appropriate adjustments to the definition of a truth value function must be made for the values ​​of complex statements. For the conjunction (AND connection) ∧ this would be e.g. B. that for every truth value assignment F and for any statements A, B: F (A ∧ B) = F (A) F (B). ${\displaystyle \cdot }$

The distinction between 1. and 2. is only a technical detail.