The Modality of Finite (Graded Modalities VII)

✍ Scribed by Maurizio Fattorosi-Barnaba; Uliano Paolozzi Balestrini

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 583 KB
• Volume: 45
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19990450406

✦ Synopsis

We prove a completeness theorem for Kr, an extension of K by the operator O r that means "there exists a finite number of accessible worlds such that . . . is true", plus suitable axioms to rule it. This is done by an application of the method of consistency properties for modal systems as in [4] with suitable adaptations. Despite no graded modality is invoked here, we consider this work as pertaining to that area both because Of is a definable operator in the graded infinitary system K& (see [4]), and because this idea was the original source for the development of graded modalities.