COUNTERPART SEMANTICS A FOUNDATIONAL STUDY ON QUANTIFIED MODAL LOGICS
Giovanna Corsi, Willard Van Orman · 2002
Counterpart semantics is proposed as the appropriate semantical framework for a foundational investigation of quantified modal logics. It turns out to be a limit case of the categorical semantics of relational universes introduced by Ghilardi and Meloni in 1988. The main result is a deeper understanding of the interplay between substitution, quantification and identity wherever modalities are present. Languages with types and explicit substitutions are the tools used to clarify such an interplay and to disintangle classical problems related to modalities in first-order languages. It is shown that controversial modal principles are neither valid nor provable. Quine's worries are dispelled.