Categorical Logic

It is highly recommended that all users read the below thoroughly before starting.

"Relational frame training"(through a certain paid online program) is the only consistently validated training protocol for enhancing one's fluid intelligence. Studies have shown up to 2 standard deviations of improvement in IQ through several weeks/months of training in young children and high school students. Additionally, it has been shown that information is more often than not processed/interpreted through existing cognitive schemas, or abstract models that have been formed over repetition and exposure to new schemas. The idea is that through exposure to many new, perhaps unusual, logical constructs formed by this program, users are able to familiarize themselves with increasingly complex schemas, and perhaps this will help them process real life phenomena of similar complexity/schematic structure.

Inspired from the aforementioned commercially available online program, which uses the relations same/opposite and more/less,

Categorical Logic uses relations such as "All X is some Y", "No X is the intersection of Y and Z", and "Some X is Y if All Z is Q or Some Q is the union of T and R". Interestingly, this system can be used as a plausible base for expressing relations of types same/opposite and more/less, and perhaps many other types of relations, simply by reframing/purposefully naming each set.

Categorical Logic allows users to choose:

the maximum number of "sets"(X/Y/Z/etc) referred to in a problem,

the maximum number of relations per statement(ex: Some X is Y if All Z is Q or Some Q is R; this has 3 relations presented, the first being true if the determined combination of the next two results in true),

the number of questions per problem(problem = a collection of statements),

and whether or not each new statement is shown sequentially(one at a time) in order to ensure that the user is only accessing statements that came before the current one through memory.

A statement can only be true if it is deductible through inference. A statement is false if a collection of statements does not ensure its truth.

As of now, the maximum number of sets the program can process and compute with is 7 or 8. At 7 or 8, the program may take between 5-15 seconds to generate a new problem. The minimum is 3. Below 3, the program may not work, due to some relations being of the format: "all A is the union of B and C". It is recommended to stay at each level number of sets for more training trials per increase in number of sets, due to a disproportionate increase in the total number of possible networks of relations, and thus different cognitive schemas, per 1 increase in that parameter.

The combinations of sets are treated, logically speaking, exactly like individual sets. "Some A is all B" means some elements existing in A also exist in B. "Some A is the union of B and C" means some elements existing in A also exist in the set which is the union of B and C. An element does not need to be in both B and C in order for it to be in the union of B and C

Statements that relate the truth/falsehood of relations through the "if" conditional are to be interpreted from left to right. ex: "some A is some B if all C is some D if some B is some C"; this means that "some A is some B" is true, if "all C is some D" is true/will be true, and ""all C is some D" is true/will be true if "some B is some C" is true. Otherwise, the first relation, "some A is some B", is determined as false. Remember, a statement is true only if the statements that came before it ensure its truth. Regarding the program and how it works, the first relations of any statement are the only relations which may or may not "construct" the given "situation".

There may be some logic errors. If one is found, please take a screenshot and send it to itrn7rec@gmail.com so that it can be fixed.