Exorcising the phantom zone

Patrick Blackburn*, Manuel Martins, María Manzano, Antonia Huertas

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


In this paper we introduce a language of first-order hybrid logic in which function symbols are interpreted by partial functions and prove a number of completeness results. Syntactically, our language builds on the basic propositional hybrid language, has a primitive unary predicate symbol DEN which tests whether a term denotes or not, and permits satisfaction operators to rigidify predicate and function symbols. Semantically, our system is actualist, allows terms to be undefined, and has no truth-value gaps. But should we follow Fitting and Mendelsohn and rule out domain elements not belonging to any world, or should we tolerate them? Here we explore both options. As we shall see, while the choice makes no difference when it comes to validity, it has consequences for richer logics.

Original languageEnglish
Article number104754
JournalInformation and Computation
VolumeIn Press
Publication statusPublished - 2021


  • Denotation
  • First-order hybrid logic
  • Partial function semantics
  • Rigidification

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