Is there a hypernym for conjunction and disjunction, in their logical senses? Just using "junction" doesn't seem right to me.
What you are looking for is probably logical connective, also called logical operator. Disjunction and conjunction are examples of binary logical operators.
In logic, a logical connective (also called a logical operator) is a symbol or word used to connect two or more sentences (of either a formal or a natural language) in a grammatically valid way, such that the sense of the compound sentence produced depends only on the original sentences.
P.S. Conventionally and etymologically, the correct term is hyperonym, not
hypernym, since the Greek word for "name" is onoma/onuma, beginning with an o; hence syn-onym and an-onym-ous, not synnym and anymous.
If you are looking for a more general term rather than just being restricted to Mathematical Logic, the terms to use are
Remember Relational Databases (RDBMS)? The term need not pertain to RDBMS, but Relational model syntax exhibits a viable relationship with modern business and legal language usage.
The following are verbs to attain
relationships or anti-
a simultaneous or peer relationship
subordinate or auxiliary relationship
anti-relationship, to prevent a relationship
anti-relationship, to disconnect from a relationship
Consider the following extended definition of relationships:
Inner conjunction, outer conjunction, left-outer conjunction.
To be more specific, the above are for joint-relationships, either to attain a joint or a disjoint.