David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Annals of Pure and Applied Logic 127 (1-3):171-193 (2004)
First-order modal logic is very much under current development, with many different semantics proposed. The use of rigid objects goes back to Saul Kripke. More recently, several semantics based on counterparts have been examined, in a development that goes back to David Lewis. There is yet another line of research, using intensional objects, that traces back to Richard Montague. I have been involved with this line of development for some time. In the present paper, I briefly sketch several of the approaches to first-order modal logic. Then I present one that I call FOIL in the Montague tradition that, I believe, is both expressive and natural. I briefly discuss in what sense it can be made to encompass the other approaches. Finally, I provide tableau rules to go with the FOIL semantics
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References found in this work BETA
Melvin Fitting (1972). Tableau Methods of Proof for Modal Logics. Notre Dame Journal of Formal Logic 13 (2):237-247.
Silvio Ghilardi (1991). Incompleteness Results in Kripke Semantics. Journal of Symbolic Logic 56 (2):517-538.
Silvio Ghilardi (1992). Quantified Extensions of Canonical Propositional Intermediate Logics. Studia Logica 51 (2):195 - 214.
David Lewis (1971). Counterparts of Persons and Their Bodies. Journal of Philosophy 68 (7):203-211.
Citations of this work BETA
Melvin Fitting (2012). Prefixed Tableaus and Nested Sequents. Annals of Pure and Applied Logic 163 (3):291 - 313.
Mirosław Szatkowski (2011). Partly Free Semantics for Some Anderson-Like Ontological Proofs. Journal of Logic, Language and Information 20 (4):475-512.
Nuel Belnap & Thomas Müller (2013). BH-CIFOL: Case-Intensional First Order Logic. Journal of Philosophical Logic (2-3):1-32.
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