Sometimes we want to determine what a PC knows, such as whether they have some historical knowledge at hand, or an insight into something that's otherwise inaccessible to the player: "What do I know about the fall of the Magic City?" or "Have I heard about winter hags during my travels in the North?" are appeals to the PC's knowledge.
You can handle such checks as attribute or success checks, and per usual, the choice between the two depends on whether you want a pass-fail result (which could result in them knowing nothing at all) or some gradient of the information about the subject.
Types of Knowledge
Most knowledge related to history falls under the Domain Knowledge skill, whereas knowledge that requires creative interpretation, such as literature and religion, falls under the Lore skill. (While history as a discipline requires a form of interpretation, in this case we're talking about the interpreting of meaning, not the sort of investigative legwork a historian might have to do to make sense of how past events fit together to tell a story about some civilization). Finally, Culture, too, is a Deft skill because it covers a lot of subjects that require intuition and empathy to grasp, such as local politics, fashion, or etiquette.
Lore checks can be run in several interesting ways. For one, the GM doesn't always have to be the sole source of the lore. If the player takes the Consult the Lore action, the answer to the question can be determined by the player. Whether you require them to roll depends on whether there's a chance of meaningful failure with regard to sussing out the information.
Meaningful Failure & Lore
For example, it might be the case that the official lore on the subject of a legendary monster is that the creature is of demonic origin, but a more astute interpretation of the lore (read: a higher roll) reveals that in fact the creature's demonic status is the result of some curse, and its true nature is not evil. Similarly, if your player is spouting lore after a poor roll on a success check, you could interpret their explanation as only partially true or partially misinformed.
Sometimes what a PC might know is beyond the player being able to imagine.
For example, they are playing an Albert Einstein sort of genius with an 8 Smart or an expert rogue that took Trade: Catburglaring as a skill. In both cases, the player can't be expected to come up with the ingenuities that PCs with such extraordinary knowledge might have. It becomes difficult for such players to interrogate the fiction, because it's hard for them to imagine what crazy insight Sherlock Holmes might have upon examining the scene of a murder. Add to this that we don't expect players playing ax-wielding fighters to have personal experience with edged weapons, and yet we let those players make combat rolls to simulate their PCs' experience anyway.
How to Solve for Extraordinary Knowledge
In these situations it's perfectly acceptable to allow the player to be more vague in their approach to surfacing information, especially when it comes to Perception checks. The certifiable genius could say, "I look into my memory palace to recall the exact layout of this place prior to the murder—what do I notice is different?" or "Since my doctoral thesis was on alchemical potions is there anything about the viscosity of this magical liquid that seems off?" In the same vein, the catburglar might know a thing or two about infiltrating a high security complex and say, "So I think back to my years of experience in the trade, is there anything in this map that stands out to me as an obvious weak point to enter this facility?"
All of these inquiries are valid interrogations of the fiction that should allow the GM to trigger a mechanic or outright give the information asked.
Acquiring knowledge by performing research starts with asking the player how they're going about their research. Their approach helps determine the skill and attribute to run with.
- The library sage would probably use the Smart augmented by a skill like Domain Knowledge (Research).
- An investigator roughing up gang members might use Survival, a Mighty skill, to do his research.
- A well-connected merchant might rely on his business contacts to gather intel using a Trade specialty.
- You could even allow for a psychic to use Psionics to consult crystalline codexes containing ancestral memories.
A straight attribute check with a TN or a success check can both work here, with the usual caveats about the status quo. It's always important to recognize that the chance of meaningful failure should precipitate the need for the player to roll at all; it doesn't benefit the narrative for the player to do the research and just turn up with nothing, unless they're simply looking in the wrong place, or there is indeed nothing to be learned and that’s important for the PC to realize.
It's also worthwhile to consider if the research will take several successful rolls over time to complete, similar to how we handle social combat with windows of success. This can be resolved as a montage action, for example.
Riddles & Reasoning
Sometimes you might need to simulate PCs reasoning their way through something the players don't or can't understand. This is similar to the problems with extraordinary knowledge.
For example, a PC might need to solve a riddle that nobody at the table understands, or reconfigure a Rubik's cube-like puzzle in a way that requires complicated math that the table doesn't care to contend with. Not all players like riddles or puzzles, especially when they're modeled after the real world. On top of this, the PCs might be good at puzzles and riddles when their players are not. This can create a disconnect in the fiction that breaks immersion and frustrates players.
One way to solve for this is by allowing the player to decide what the answer to the riddle is, if they succeed in their check. Or, in the case of the Rubik's cube, let them bullshit a solution that suits the fiction, but makes the PC sound smart.
In the case of success checks, you can yield obvious clues that point them in the right direction.
One final note: this doesn't work for mysteries.
While you could construct an adventure that creates clues on the fly and steers the PCs toward a conclusion they invent when they have enough of them with these rules, OSR+ is a simulationist game at heart. Clues should always exist out there in the world, for PCs to surface by interrogating the fiction.
It's their job to figure out what they mean, but it's your job to place them in your scenes so they can be found.