Logically Possible Worlds and Counterpart Semantics for Modal Logic MARCUS KRACHT AND OLIVER KUTZ Abstract. The paper reviews the technical results from modal logic as well as their philosophical significance. It focuses on possible worlds semantics in general and on the notions of a possible world, of accessibility, and of an object. Contents Introduction 2 Part 1. Worlds without Objects 5 1. Basic Concepts of Modal Propositional Logic 5 2. Translation into Classical Logic 6 3. Ontology and Duality Theory 7 3.1. Logical Consequence 10 3.2. Situations and Possibilities 10 4. Possible Worlds as an Analytic Tool 11 5. Accessibility 13 5.1. Accessibility Relations 13 5.2. Neighbourhoods 14 5.3. Histories 16 Part 2. The World of Objects 17 6. Modal Predicate Logic 17 6.1. The Classical View 19 6.2. Free Logic 20 6.3. Identity, Substitution and Leibniz’ Law 21 6.4. Completion. 24 7. Counterpart Semantics. 25 8. Individual Concepts 32 9. Objects in Counterpart Frames 35 10. Dual Ontologies, or, The Semantical Impact of Haecceitism 39 11. Metaframes 43 Received by the editors May 13, 2005. Key words and phrases. modal logic; counterpart semantics; logical possibility; modal individual; accessibility; possible worlds. 1