Possible Worlds: A Logical Model of Coherence between Identity and Veracity v1

This article presents a general logical-semantic model that allows the evaluation of the global consistency between ontological identities and statements in finite worlds of individuals. Although the model is inspired by the classic problems of truth-teller and liar — such as those found in the so-called “islands of knights and knaves”-, its formal structure allows for a broader application in contexts where it is necessary to analyze the coherence between what an agent is and what it says. The model is based on assigning an ontological identity to each individual (e.g., honest or liar, reliable or faulty sensor) together with a statement that expresses a proposition. Two semantic operators are established: one representing the agent’s identity and another evaluating the truth value of its statement in a possible world. From these assignments, a finite tabular semantics is defined that allows the construction of all possible worlds and the application of a consistency rule that filters those worlds which present coherence between identity and statement. This approach offers a formal and explicit alternative to classical inferential methods, allowing applications in agent logic, diagnosis, model theory and epistemological analysis.