Title: The Functional Interpretation of Modal Necessity
Abstract: Since the early days of Kripke-style possible-worlds semantics for modalities, there has been a significant amount of research into the development of mechanisms for handling and characterising modal logics by means of ‘naming’ possible worlds, either directly by introducing identifiers, or indirectly by some other means (such as, e.g., using formulas to identify the possible world). To list a few, we have [Gabbay, forthcomingl’s ‘labelling’ formulas with names for worlds in the framework of Labelled Deductive Systems; [Fitch, 1966b]’s tree-proof deduction procedures for modal logics; [Thomason and Stalnaker, 1968]’s device of predicate abstraction introduced to handle Skolemisation across worlds and characterise non-rigid designators; [Fitting, 1972, 1975]’s ε-calculus based axiom systems for modal logics, as well as his tableaux systems for modal logics with predicate abstraction [Fitting, 1981, 1989]; the irreflexivity rule of [Gabbay and Hodkison, 1990]’s axiomatic systems of temporal logic; the explicit reference to possible worlds in the deterministic modal logics of [Farinas del Cerro and Herzig, 1990]; [Ohlbach, 1991]’s semantics-based translation methods for modal logics and its functional representation of possible worlds structures. In first-order predicate logics the individuals over which one quantifies are naturally assumed to have names. The main connectives of modal logics are such that they quantify over (higher-order) objects which are not usually given names, in some cases for methodological reasons.
Publication Year: 1997
Publication Date: 1997-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 14
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