Repairing the interpolation theorem in quantified modal logic

✍ Scribed by Carlos Areces; Patrick Blackburn; Maarten Marx

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 244 KB
• Volume: 124
• Category: Article
• ISSN: 0168-0072
• DOI: 10.1016/s0168-0072(03)00059-9

✦ Synopsis

Quantiÿed hybrid logic is quantiÿed modal logic extended with apparatus for naming states and asserting that a formula is true at a named state. While interpolation and Beth's deÿnability theorem fail in a number of well-known quantiÿed modal logics (for example in quantiÿed modal K, T, D, S4, S4.3 and S5 with constant domains), their counterparts in quantiÿed hybrid logic have these properties. These are special cases of the main result of the paper: the quantiÿed hybrid logic of any class of frames deÿnable in the bounded fragment of ÿrst-order logic has the interpolation property, irrespective of whether varying, constant, expanding, or contracting domains are assumed.