Translate a text into a set of inference rules

Question

I'm working on a question from one of my past college test. I have to translate a text into a set of formal rules of inference. The text is:

"Ugo is a LP student that also writes software in Snowball. Anyone who writes software in Snowball finds a good paid job. So we can say that some LP student can find a good paid job."

Since there are quantifiers I assume it's a first-order logic problem, so I defined the individual constants and the predicates:

$C=\{ugo\}$

$P=\{LPS, SD, GPW\}$

Where:

1. LPS mean LP student
2. SD mean Snowball developer
3. GPW mean good paid worker

My try with the rules:

[maybe modus pones] $$ \frac{(\forall x)(SD(x)\rightarrow GPW(x)), SD(ugo)}{GPW(ugo)} $$ [dont know if its a real rule] $$ \frac{LPS(ugo), GPW(ugo) }{(\exists x)(LPS(x), GPW(x))} $$

Answer 1

"I have to translate a text into a set of formal rules of inference". Eh? Really?? You can't translate propositions into rules of inference - they are different kinds of thing entirely. Propositions are true or false; rules of inference truth-preserving or otherwise.

The informal inference

Ugo is a LP student that also writes software in Snowball. Anyone who writes software in Snowball finds a good paid job. So we can say that some LP student can find a good paid job

can be regimented

$$(Lu \land Su),\ \ \forall x(Sx \rightarrow Gx)\ \therefore\ \exists x(Lx \land Gx)$$

using obvious letters for the predicates and '$u$' as a constant denoting Ugo to translate the three propositions involved. The obvious proof showing that the conclusion does indeed follow from the two premisses would go

$$ \quad\quad\quad\quad\quad\quad\quad(Lu \land Su) \quad\quad\quad \forall x(Sx \rightarrow Gx)\\ \quad\quad\quad\quad\quad\quad\_\_\_\_\_\_\quad\quad\quad\_\_\_\_\_\_\_\_\_\_\\ (Lu \land Su)\quad\quad\quad Su \quad\quad\quad\quad (Su \to Gu)\\ \_\_\_\_\_\_\_\_\quad\quad\quad\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\ Lu \quad\quad\quad\quad\quad\quad\quad\quad\quad Gu\quad\quad\quad\\ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\ (Lu \land Gu)\\ \_\_\_\_\_\_\\ \exists x(Lx \land Gx)$$

where the rules used are And-Elimination (twice), Universal Elimination [a.k.a. U. Instantiation], and Modus Ponens, and then And-Introduction, and Existential Introduction. [Or a rearrangement of that proof, if you use e.g. a Fitch-style system.]