South African prosecutors say Oscar Pistorius' sentence of five years in prison for shooting dead his girlfriend is nowhere near enough punishment.

They want the double-amputee track star to be convicted of a more serious charge and to face a longer prison term.

On Tuesday, a court in Pretoria began hearing arguments for and against an appeal of the original verdict in which Pistorius was found guilty of culpable homicide, or negligent killing, in the death of Reeva Steenkamp.

Pistorius didn't attend the hearing, which continues Wednesday.

'Shockingly light'

In appeal documents filed previously, the prosecution called Pistorius' sentence "shockingly light" and inappropriate. They had originally sought conviction on a charge of murder.

Prosecutors are arguing that Judge Thokozile Masipa misinterpreted a complex South African standard defining a technical form of intent that proved to be a central aspect of the case, according to CNN Legal Analyst Kelly Phelps.

As a result, prosecutors argue, he should not have been convicted on the culpable homicide charge chosen by the judge.

In explaining her sentence, Masipa concluded that Pistorius did not intend to kill Steenkamp.

But critics of the verdict have argued that Masipa didn't correctly apply the intent standard, which is broader in South African law than what it typically means in casual conversation, Phelps says.

Harsher or lighter sentence?

In their appeal of the sentence, prosecutors will have to prove the five years given by Masipa is inappropriate in light of sentencing guidelines and similar cases, according to Phelps. Prosecutor Gerrie Nel called for a minimum sentence of 10 years.

If Judge Masipa sides with the prosecution on Tuesday, the case will go to the Supreme Court of Appeals in Bloemfontein, which will then hear the appeal itself, opening the door to the possibility of a harsher sentence. If she sides with the defense, and the verdict is not overturned, it could lead to a more lenient sentence, according to Phelps.

Under South African law, Pistorius has to serve at least one-sixth of his sentence -- 10 months, as things stand -- before asking to be placed under correctional supervision. Correctional supervision usually means house arrest.

Pistorius, 28, made history when he became the first double-amputee to compete in the able-bodied Olympics in 2012. He was born without the fibulae in his legs, which were amputated below the knee when he was 11 months old.