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New semantics for modal predicate logics

In Benedikt Löwe, Thoralf Räsch & Wolfgang Malzkorn (eds.), Foundations of the Formal Sciences II. Kluwer Academic Publishers. pp. 151--162 (2003)

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  1. First-order belief and paraconsistency.Srećko Kovač - 2009 - Logic and Logical Philosophy 18 (2):127-143.
    A first-order logic of belief with identity is proposed, primarily to give an account of possible de re contradictory beliefs, which sometimes occur as consequences of de dicto non-contradictory beliefs. A model has two separate, though interconnected domains: the domain of objects and the domain of appearances. The satisfaction of atomic formulas is defined by a particular S-accessibility relation between worlds. Identity is non-classical, and is conceived as an equivalence relation having the classical identity relation as a subset. A tableau (...)
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  • Intensional Logic — Beyond First Order.Melvin Fitting - unknown
    Classical first-order logic can be extended in two different ways to serve as a foundation for mathematics: introduce higher orders, type theory, or introduce sets. As it happens, both approaches have natural analogs for quantified modal logics, both approaches date from the 1960’s, one is not very well-known, and the other is well-known as something else. I will present the basic semantic ideas of both higher order intensional logic, and intensional set theory. Before doing so, I’ll quickly sketch some necessary (...)
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  • First-order intensional logic.Melvin Fitting - 2004 - Annals of Pure and Applied Logic 127 (1-3):171-193.
    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 (...)
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