How does logical semantics explain the truth of logical statements?

In the context of logic, logical semantics—often referred to as model theory—explains the truth of statements by analyzing the relationship between linguistic expressions and the structures in which they are interpreted.1

Truth Conditions and Interpretations

The foundational approach, developed by Alfred Tarski, defines truth by assigning truth conditions to sentences. An interpretation of a formal language involves mapping constants, predicates, and functions to a specific domain of objects. Once this interpretation is established, the truth-value of a sentence is determined by the standard meanings of logical connectives (e.g., a conjunction is true if and only if both components are true).23

Logical Truth

Logical semantics characterizes a logically true sentence as one that is true under every possible interpretation, often described as being true in every "possible world". This framework allows logicians to define truth independently of the specific nonlogical constants available, providing a systematic way to evaluate the validity of statements within a formal system.13

While Tarski’s method remains central, other approaches like game-theoretic semantics have emerged, where the truth of a sentence is defined by the existence of a winning strategy in a verification game.41