A semantics for logical languages that interprets the truth of a formula in a model as the existence of a winning strategy in an associated evaluation game between two players (Verifier and Falsifier); logical connectives and quantifiers are mapped to game rules that govern choices and win conditions.

Principle

Truth is given operationally by the existence of winning strategies: existential quantifiers correspond to Verifier moves that pick witnesses, universals to Falsifier choices, conjunctions to Falsifier selecting a conjunct to challenge, disjunctions to Verifier choosing a disjunct, and negation to role reversal.

Demonstration

Evaluate the formula ∃x∀y R(x,y) on a structure M: the evaluation game has Verifier pick an element a for x; then Falsifier picks b for y; Verifier wins if R(a,b) holds. Existence of a strategy for Verifier that secures a win against all Falsifier replies is equivalent to M ⊨ ∃x∀y R(x,y).

Misapplication

Treating winning strategies as formal proofs of truth without distinguishing between uniform strategies and non-uniform existential witnesses, or applying naive game rules to logics where connectives lack corresponding local move rules (e.g., some probabilistic or graded modalities) without retooling the game.

Consequence

Provides an intuitive, often constructive account of truth that clarifies dependency of choices, enables analysis of informational content and strategies (e.g., independence-friendly logics), and connects semantic notions to algorithmic search problems.

Reversal

Contrast with Tarskian compositional semantics: rather than assigning truth values by structural induction on formulas, game-theoretic semantics reduces truth to the existence of winning strategies — reversing the viewpoint clarifies the operational vs. denotational perspectives.

Boundary

Applies cleanly to logics whose connectives and quantifiers admit local move interpretations; extensions (e.g., fixed-point, probabilistic, or resource-bounded logics) require modified games or enriched strategy concepts to capture the intended semantics.

Semantic Tension

Tension exists with proof-theoretic accounts (truth as provability) and with purely model-theoretic satisfaction, especially regarding uniformity and constructivity of witnesses: GTS emphasizes strategies, while others emphasize valuations or derivations.

Synthesis

Game-theoretic semantics reinterprets truth as the outcome of an information-structured contest: specifying local move rules for syntactic constructs yields games whose winning strategies precisely encode the semantic conditions for formula truth.