A measure of the range of properties, distinctions, or structures that a given logical language or formalism can define or capture on a class of structures; often compared by whether formulas of one language can be translated into another while preserving truth in all structures of interest.

Principle

Expressive power is governed by the available syntactic constructs (quantifiers, quantification over sets/functions, fixed‑point operators, modal operators) and by how these constructs interact with the class of models and built‑in relations; more constructs typically increase what can be defined but may affect other properties.

Demonstration

First‑order logic cannot express graph connectivity, while monadic second‑order logic (MSO) or first‑order logic with transitive closure can; thus MSO or FO+TC has greater expressive power for that property on graphs.

Misapplication

Equating greater expressive power with better practical suitability: more expressive languages can be undecidable or computationally infeasible, so choosing a language requires balancing expressivity with decidability and succinctness.

Consequence

Understanding expressive power guides selection of logics for specification and verification, clarifies which properties can be captured, and underlies results that relate logical fragments to complexity classes (e.g., descriptive complexity correspondences).

Reversal

Expressive weakness: a language too weak to define intended properties, prompting either enrichment of the language or acceptance of inexpressibility and alternative specification methods.

Boundary

Depends on the domain (graphs, orders, arithmetic), whether we fix a signature or allow built‑ins (ordering, arithmetic), and on semantics (finite vs infinite structures); comparisons must specify the class of structures and translation method.

Semantic Tension

Tension between expressive power and algorithmic tractability or conceptual clarity: added expressive constructs can make specifications shorter but harder to analyze, and two languages can be incomparable, each capturing different intuitions.

Synthesis

Expressive power diagnoses what a language can say about structures by linking syntactic resources to semantical definability: it is a practical and theoretical axis for choosing and comparing formalisms, always balanced against decidability, succinctness, and intended models.