Premiseswith

Premiseswith is a coined term used in some discussions of logic and argumentation to describe a relation between a set of premises and an additional condition or context. It is not an established standard in formal logic, but appears in analyses that treat premises as being qualified by extra requirements, often expressed informally as "premises with X" or as a binding of premises to a constraint.

Etymology: The term is a portmanteau of premises and with, indicating a conjunction of a base set of premises with a condition.

Definitions and use: In theoretical work, premiseswith may denote a pairing of a premises set with a side condition; in diagrams, it might label a node representing the premises plus context. In natural language processing and knowledge representation, it can be used to annotate datasets where arguments are accompanied by contextual constraints.

Notation and examples: In formal notation, one might see something like P, Q with R to indicate that P and Q are premises under condition R. In practice, the definition of the operator is left to the author, so explicit specification is required for clarity.

Relation to related terms: It is distinct from the ordinary concept of a premise, and from the notion of a condition or constraint; it is closer to a labeling convention or an operator for representing context.

See also: Premise; Condition; Constraint; Argument diagram; Knowledge representation.