Notre Dame Journal of Formal Logic

Finite and Physical Modalities

Mauro Gattari

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 12 December 2005

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1134397661

Digital Object Identifier
doi:10.1305/ndjfl/1134397661

Mathematical Reviews number (MathSciNet)
MR2183053

Zentralblatt MATH identifier
1091.03003

Subjects
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]

Keywords
modal logic finite modalities physical modalities tableau system consistency property

Citation

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


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References

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