Categorization of Predicates

I am developing a database that attempts to processes a new predicate introduced into the db in a manner similar to it's category. Has someone already categorized predicates before? I want to categorize predicates that combine two things (ie thing1 predicate thing2) from a very general and logically processable point of view. Are the below categorizations correct?

BIDIRECTIONAL PREDICATES:
t1 and t2 can be exchanged and the proposition remains true. For example:

John agreesWith Bob.
Bob agreesWith John.

Mary isNextTo John.
John isNextTo Mary.

UNIDIRECTIONAL PREDICATES:
Exchanging t1 and t2 results in a false proposition. For example:

John ate the apple. Its negation, The apple ate John, is false. Mary cut the wood. Its negation, The wood cut Mary, is false.

HIERARCHAL/TRANSITIVE PREDICATES:
If we have: t1 predicate t2.
And we have: t2 predicate t3.
Then: t1 predicate t3, is also true.
For example:

John isA Person. Person isA Thing. John isA Thing. Bread isPartOf sandwich. Sandwich isPartOf lunch. Bread isPartOf lunch.

TIA

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