A measurable shortfall between the set of properties a logic or specification language can define and the set of properties required by an application, specification, or verification task.

Principle

Expressivity is evaluated relative to target properties; the gap is the difference between required definability and available definability under the chosen syntax, semantics, and resource constraints (e.g., decidability, complexity).

Demonstration

A temporal logic used to specify safety properties may lack the ability to quantify over data values needed for a particular application; the missing data-quantification constructs constitute an expressivity gap for that application.

Misapplication

Treating implementation difficulty or tool immaturity as an expressivity gap — for instance blaming the language for slow solvers rather than for lacking definitional constructs — confuses expressive limits with practical engineering gaps.

Consequence

Identifying an expressivity gap directs whether to extend the language, embed domain-specific predicates, adopt complementary logics, or accept runtime checks where static specification cannot reach.

Reversal

Expressive Sufficiency: the condition where the language's definitional power meets the application's property set and so there is no material gap to bridge.

Boundary

The gap depends on the chosen notions of expressivity (syntactic definability, semantic definability, and resource-aware definability); narrowing it often trades off decidability or tractability for expressive reach.

Semantic Tension

Competes with notions of succinctness and decidability — a language can be expressive but unwieldy; the expressivity gap concerns existence of definitions, while succinctness and complexity measure practicality.

Synthesis

An Expressivity Gap pinpoints the unmet definitional needs of a task relative to a language's capabilities and motivates concrete remedies (language extension, hybrid approaches, or acceptance of approximation) while being mindful of trade-offs.