There are many ways to model a character's capabilities in a role-playing game including class and attributes (the classic model), attributes and skills, class and attributes and skills, attributes only, skills only, and class only. Some games add feats, stunts, and/or specializations. For Omnia, I chose the "class only" category (alternatively known as "profession only," "occupation only," "vocation only," etc.) Characters are defined by their Abilities, which may be vocations or avocations. I settled on this method because I discovered that I had the most fun creating characters when I listed what their careers and hobbies were, rather than trying to figure out where they stood in an arbitrary scale of general attributes or specific skills. I can rank how good a character is at a particular job far more easily than I can assess a character's overall intelligence, strength, or coordination. Besides, overall ratings are wildly inaccurate by nature. A weightlifter, a gymnast, and a boxer may all be strong, but they are strong in ways that do not necessarily crossover to each other's area of expertise. A dancer, a gemcutter, and an archer may all be coordinated, but with radically different sets of motor skills. A physicist, a linguist, and a military strategist may all be highly intelligent with no knowledge whatsoever in each other's chosen field. I just don't see the point or appeal in ranking general attributes when the question in the game is, "Which character is the deadlier duelist?" or "Which character is the stealthier ninja?" or "Which character is the more talented singer?" The general attributes are irrelevant. What matters is how good characters are at what they do, because the character who may not be too smart at most things might be a genius at safecracking and calculating odds. The character who might not have massive upper body strength might be a champion marathon runner. The character who can't walk without tripping might be the most accurate knifethrower on the Mississippi River. Some people might enjoy assigning attribute ratings to Phyllis Diller, but I would rather rank her as a Comedienne, Concert Pianist, Writer, and Artist.
The next question I can imagine being asked is, "What about attribute checks? How do characters do things in general without attributes?" The simple answer is this: The characters can do what the characters can do. Most of the time, checks are a waste of time. Yes, your character can climb the hill. Yes, your character can bandage a wound. Yes, your character can search the closet for a secret door. Yes, your character can use all five senses in most situations. If your character wants to act as a ship's navigator, they can do it if they have the Ability of "Navigator." If your character wants to forge horseshoes for the party's horses, they can do it if they have the Ability of "Blacksmith." A check is only necessary if there is a reasonable risk of failure due to the circumstances. I am far more interested in describing the characters' environment and letting them do what they ought to be able to do rather than forcing them to make boring attribute or skill checks just to experience and interact with their surroundings.