Exercise · ZW-AXIOMATIC-SYSTEM-009 · ★★☆ Intermediate
Which of these statements about a formal system is correct?
Choose one option.
Show answer
- C. Its theorems are the formulas derivable from the axioms using the rules
Explanation
Theorems are exactly the formulas obtained from the axioms through the rules. Changing the rules changes what can be derived, and the other options confuse formal proof with obviousness or opinion.
Review the concept: Axiomatic system
An axiomatic system is a triple \(\mathcal{S}=(\mathcal{L},\mathcal{A},\mathcal{R})\) made of a formal language, axioms and rules of inference.
\[\mathcal{S}=(\mathcal{L},\mathcal{A},\mathcal{R})\]
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