Does martial weapon training include uncommon weapons?

Question

At 1st level, a ranger gets training in martial weapons. Does that include the weapons in the uncommon martial group? Can any level 1 ranger be trained in using a dogslicer, for example, or is the only way to receive that training through a feat like goblin weapon familiarity?

Answer 1

Yes, it does

As described under the Uncommon trait:

Something of uncommon rarity requires special training or comes from a particular culture or part of the world. Some character choices give access to uncommon options, and the GM can choose to allow access for anyone.

You need some ability, trait, background, feat or heritage that grants you access to Uncommon weapons, but once you obtained it, it is still a martial weapon and uses your normal proficiencies. The GM may always give you access to that item based on your character origins (see Item Selection). For instance, a dog slicer may be available if you say that your human character was born in a goblin tribe, but if you are attacked by a group of goblins, you should be able to grab one of the weapons and still easily wield it in combat.

At your discretion, you can grant the player character uncommon or rare items that fit their backstory and concept, keeping in mind how many items of those rarities you have introduced into your game.

However, note that some Uncommon weapons are also Advanced, as such, you need a different kind of proficiency to be able to wield them. With the exception of the Dwarven War Axe, all Advanced weapons are also uncommon, which can lead to mistakes. But as you noted, there are uncommon martial (Dog Slicer) and uncommon simple (Katar) weapons that use simple and martial weapon proficiency.

Answer 2

Yes it does.

If we look at Rarity we see:

Uncommon items are available only to those who have special training, grew up in a certain culture, or come from a particular part of the world.

Furthermore, if we look at the Uncommon trait, it says:

Something of uncommon rarity requires special training or comes from a particular culture or part of the world. Some character choices give access to uncommon options, and the GM can choose to allow access for anyone.

These show that all Rarity does, is restrict access to something. If you were to loot a dogslicer after fighting a goblin, you would be able to use it, but otherwise you would be unable to obtain one unless you had something granting you access.

This can be seen in the Monastic Weaponry feat:

You have trained with the traditional weaponry of your monastery or school. You gain access to uncommon weapons that have the monk trait and become trained in simple and martial monk weapons. When your proficiency rank for unarmed attacks increases to expert or master, your proficiency rank for these weapons increases to expert or master as well.

You can use melee monk weapons with any of your monk feats or monk abilities that normally require unarmed attacks, though not if the feat or ability requires you to use a single specific type of attack, such as Crane Stance.

Note that it only grants you training in simple and martial weapon, not Uncommon Simple and martial weapons. This means that uncommon weapons are considered to be weapons of that category (simple, martial, or advanced).