Notre Dame Journal of Formal Logic

Finite and Physical Modalities

Mauro Gattari


The logic Kf of the modalities of finite, devised to capture the notion of 'there exists a finite number of accessible worlds such that . . . is true', was introduced and axiomatized by Fattorosi. In this paper we enrich the logical framework of Kf: we give consistency properties and a tableau system (which yields the decidability) explicitly designed for Kf, and we introduce a shorter and more natural axiomatization. Moreover, we show the strong and suggestive relationship between Kf and the much older logic of the physical modalities of Burks.

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Notre Dame J. Formal Logic, Volume 46, Number 4 (2005), 425-437.

First available in Project Euclid: 12 December 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}
Secondary: 03B25: Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10]

modal logic finite modalities physical modalities tableau system consistency property


Gattari, Mauro. Finite and Physical Modalities. Notre Dame J. Formal Logic 46 (2005), no. 4, 425--437. doi:10.1305/ndjfl/1134397661.

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