## Notre Dame Journal of Formal Logic

### A Variant of Thomason's First-Order Logic CF Based on Situations

#### Abstract

In this paper, we define a first-order logic CFʹ with strong negation and bounded static quantifiers, which is a variant of Thomason's logic CF. For the logic CFʹ, the usual Kripke formal semantics is defined based on situations, and a sound and complete axiomatic system is established based on the axiomatic systems of constructive logics with strong negation and Thomason's completeness proof techniques. With the use of bounded quantifiers, CFʹ allows the domain of quantification to be empty and allows for nondenoting constants. CFʹ is intended as a fragment of a logic for situation theory. Thus the connection between CFʹ and infon logic is discussed.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 39, Number 1 (1998), 74-93.

Dates
First available in Project Euclid: 7 December 2002

https://projecteuclid.org/euclid.ndjfl/1039293021

Digital Object Identifier
doi:10.1305/ndjfl/1039293021

Mathematical Reviews number (MathSciNet)
MR1671742

Zentralblatt MATH identifier
0967.03022

Subjects
Primary: 03B60: Other nonclassical logic
Secondary: 68T27: Logic in artificial intelligence

#### Citation

Wang, Xuegang; Mott, Peter. A Variant of Thomason's First-Order Logic CF Based on Situations. Notre Dame J. Formal Logic 39 (1998), no. 1, 74--93. doi:10.1305/ndjfl/1039293021. https://projecteuclid.org/euclid.ndjfl/1039293021

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