Who to define the meta-function using induction prinicple?

Question

I'm a beginner in Automated Theorem Proving, and I want to proof using the induction principle from the syntactic definition of propositional formulae, define the meta-function $V[\phi]$ which gives set of propositional variables of the propositional formula $\phi$.

Other problem for solving is: Using the induction principle from the syntactic definition of propositional formulae, dene the meta-function $L[\phi]$ which gives the length of the propositional formula $\phi$.

See also the post : length-of-a-formula-in-propositional-logic. — Mauro ALLEGRANZA, Jun 06 '18 at 18:18

score 0 · Accepted Answer · answered Jun 06 '18 at 14:51

0

Induction definition of $V[ϕ] = \text { the set of propositional variables of the formula } ϕ$.

(i) If $ϕ$ is atomic, i.e. $ϕ := p_i$ for some propositional variable $p_i$, then : $V[ϕ] = \{ p_i \}$.

(ii) For $ϕ = \lnot \psi$, we have : $V[ϕ] = V[\psi]$.

(iii) For $ϕ = \chi \cdot \psi$, where $\cdot = \{ \to, \leftrightarrow, \land, \lor \}$, we have : $V[ϕ] = V[\chi] \cup V[\psi]$.

answered Jun 06 '18 at 14:51

Mauro ALLEGRANZA

94,169

Thank you very much, for L it's the same or? – Laurentiu Jun 06 '18 at 16:17
@Laurentiu - and lenght is defined as ... ? – Mauro ALLEGRANZA Jun 06 '18 at 17:06

Who to define the meta-function using induction prinicple?

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