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