caa a22 4500 605539065 CHVBK 20210128100905.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10992-014-9316-8 doi (NATIONALLICENCE)springer-10.1007/s10992-014-9316-8 Payne Jonathan Institute of Philosophy, University of London, Senate House, Malet Street, WC1E 7HU, London, UK aut Natural Deduction for Modal Logic with a Backtracking Operator [Elektronische Daten] [Jonathan Payne] Harold Hodes in [1] introduces an extension of first-order modal logic featuring a backtracking operator, and provides a possible worlds semantics, according to which the operator is a kind of device for ‘world travel'; he does not provide a proof theory. In this paper, I provide a natural deduction system for modal logic featuring this operator, and argue that the system can be motivated in terms of a reading of the backtracking operator whereby it serves to indicate modal scope. I prove soundness and completeness theorems with respect to Hodes' semantics, as well as semantics with fewer restrictions on the accessibility relation (Hodes restricts his attentionto S5). The Author(s), 2014 Modal logic nationallicence Backtracking nationallicence Natural deduction nationallicence Journal of Philosophical Logic Springer Netherlands 44/3(2015-06-01), 237-258 0022-3611 44:3<237 2015 44 10992 https://doi.org/10.1007/s10992-014-9316-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10992-014-9316-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Payne Jonathan Institute of Philosophy, University of London, Senate House, Malet Street, WC1E 7HU, London, UK aut NATIONALLICENCE 773 0- Journal of Philosophical Logic Springer Netherlands 44/3(2015-06-01), 237-258 0022-3611 44:3<237 2015 44 10992