Natural deduction for modal logic with a backtracking operator

• Autores: Jonathan Payne
• Localización: Journal of Philosophical Logic, ISSN-e 1573-0433, Vol. 44, Nº. 3, 2015, págs. 237-258
• Idioma: inglés
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• Resumen

  • 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)