   Go up to 2 The Language of LogicGo forward to 2.2 Propositional Logic ## 2.1 Preliminaries

The fundamental entities of logic are introduced in the following definition. Formulas and Truth Values

Definition 1 (Truth Value, Formula) A  truth value (Wahrheitswert) or  Boolean value (Boolescher Wert) is one of the values true or false.

A (logical)  formula (logische Formel) or  proposition (Aussage) is a syntactic phrase whose meaning is a truth value.

This definition introduces two layers of a formula: its  syntax (Syntax), i.e., the concrete external representation, and its  semantics (Semantik), i.e., the underlying meaning.

Operational Interpretation  In the Logic Evaluator, every formula is an instance of a Java class that implements the following interface:

```public interface Formula
{
boolean eval() throws EvalException;
}
```

For every `Formula` f, the evaluation of `f.eval()` returns the boolean value denoted by f (or throws an exception if some error has occurred).

For stating relationships between formulas, we will use the following notion.

Definition 2 (Equivalence of Formulas) Let A and B be formulas. We write
A  iff B
to indicate that A has the same meaning as B in any context; we read this as "A is  equivalent to B" ("A ist äquivalent zu B") or as "A if and only if B" ("A genau dann wenn B").

Author: Wolfgang Schreiner
Last Modification: October 4, 1999   