Topic
Proof theory
6 concepts and 62 practice problems on proof theory, part of Logic.
6concepts
62exercises
≈ 3 hof study approx.
Concepts
- Axiomatic system 11 exercisesAn axiomatic system is a triple S=(L,A,R) made of a formal language, axioms and rules of inference.
- Rule of inference 10 exercisesA rule of inference authorizes the formal step from the premises φ_1,…,φ_n to the conclusion ψ.
- Modus ponens 11 exercisesLet P and Q be propositions. Modus ponens allows concluding Q from P⇒ Q and P.
- Formal proof 10 exercisesA formal proof of φ_n is a sequence φ_1,…,φ_n in which each term is an axiom, an admitted hypothesis, or the result of a rule app…
- Consistency 10 exercisesA system S is consistent if there is no formula φ such that S proves both φ and ¬φ.
- Logical completeness 10 exercisesA calculus S is complete if every formula φ that is valid under its semantics is provable in S.