Go up to 2 The Language of Logic
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Formulas and Truth Values
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.
A iff Bto 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").