Is there a hypernym for conjunction and disjunction, in their logical senses? Just using "junction" doesn't seem right to me.
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What you are looking for is probably logical connective, also called logical operator. Disjunction and conjunction are examples of binary logical operators.
P.S. Conventionally and etymologically, the correct term is hyperonym, not
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
Consider the following extended definition of relationships:
To be more specific, the above are for joint-relationships, either to attain a joint or a disjoint.