A relational structure (W,R) consisting of a nonempty set W of possible worlds and a binary accessibility relation R ⊆ W×W used to interpret modal or temporal operators independently of any valuation of propositional atoms.

Principle

Modal truth is evaluated relative to worlds and their relations: the accessibility relation encodes the modal or temporal constraints that determine how truth propagates between worlds (e.g., necessity requires truth at all accessible worlds).

Demonstration

A frame for a system of temporal 'next' modality can be a directed graph where nodes are program states and edges model the 'next' transition; properties of R (e.g., reflexivity, transitivity) correspond to modal axioms such as T or S4.

Misapplication

Confusing a frame with a full Kripke model by assuming it includes truth assignments; treating frame properties as semantic truths about the domain rather than constraints that characterize classes of frames for which certain formulas are valid.

Consequence

Frames classify and separate modal logics by structural constraints on R; frame conditions provide a way to derive correspondence and completeness results linking axioms to relational properties.

Reversal

A Kripke model is the reversal in that it extends a frame by adding a valuation that assigns truth to propositional variables at each world; talking only about valuations without a relation loses modal structure.

Boundary

Applies to the relational semantics of modal, temporal and intuitionistic variants where worlds and accessibility are meaningful; frames do not specify valuations, probabilities, intensional interpretations or algebraic equivalents unless explicitly augmented.

Semantic Tension

Competes with algebraic or neighborhood semantics: frames emphasize relational, world-based structure, while alternative semantics encode modality via algebraic operations or sets of neighborhoods; the metaphorical reading of 'possible worlds' also competes with purely technical relational views.

Synthesis

A Kripke frame is the abstract relational substrate (W,R) that captures how modalities relate worlds; by isolating structure from valuation it lets one study the effect of accessibility constraints on validity and correspondences across modal systems.