[ΛΟΓΟΣ] De Logica Propositionali

[Gaius Florius Lupus]

[Publius Sextius Laevus]

Salvete Lupe, et Omnes Logici Rationabilesque

How would the if-then-else if-else:
if (p) then
q=V
else if (r) then
s=V
else
t=V
end if

be expressed?

(p=>q) and ((not p and r)=>s) and ((not p and not r)=>t)

noting that q=V does not necessarily mean p=V.

Valete
Laevus

[Gaius Florius Lupus]

Salve Laeve,

You are using modern programming language, which is indeed also a form of deductive logic, mostly based on propositional logic, but still with a different syntax. In propositional logic there is no ELSE, ENDIF is indicated by brackets, and we deal strictly with propositions, not terms.

In your case "q=V", "s=V" and "t=V" are the propositions, q,s,t and V are terms.
We would have to redefine them as propositions the following way and replacing the lower case letters with upper case letters to indicate terms and vice versa:
q ≡ Q=V
s ≡ S= V
t ≡ T= V
Terms are now upper case letters and propositions lower case letters.

Then we can write it as following:
[p ⇒ q] ∧ [¬p ⇒ ((r ⇒ s) ∧ (¬r ⇒ t))]

Vale!