How does possible-world semantics extend the interpretation of language beyond actual objects?

Possible-world semantics extends the interpretation of language beyond actual objects by treating meanings as functions that correlate linguistic expressions with their truth conditions across a range of alternative scenarios.12

In this framework, the meaning of a sentence is understood as knowing the circumstances—or the specific possible worlds—in which that sentence would be true. This approach shifts the focus from merely identifying the extension of a term (the actual objects it denotes) to its intension, which encompasses its behavior across a wider domain of possibilities.123

Key aspects of this interpretation include:

• Modal Propositions: A proposition is considered necessarily true if it holds in all possible worlds, and possibly true if it holds in at least one.4
• Intensional Logic: Terms are assigned interpretations within a domain of "possible" objects, allowing for a general theory of meanings such as propositions and individual concepts.12
• Truth-Conditions: By conceiving of possible worlds as alternatives to the actual course of events, logicians can define the meaning of linguistic expressions based on how they map to truth-values across these varied contexts.1