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Axiomatizing distance logics. (English) Zbl 1185.03034
Summary: In [H. Sturm et al., Lect. Notes Comput. Sci. 1919, 37–56 (2000; Zbl 0998.68157); O. Kutz et al., ACM Trans. Comput. Log. 4, No. 2, 260–294 (2003)] we introduced a family of ‘modal’ languages intended for talking about distances. These languages are interpreted in ‘distance spaces’ which satisfy some (or all) of the standard axioms of metric spaces. Among other things, we singled out decidable logics of distance spaces and proved expressive completeness results relating classical and modal languages. The aim of this paper is to axiomatize the modal fragments of the semantically defined distance logics of [Kutz et al., loc. cit.] and give a new proof of their decidability.

MSC:
03B45 Modal logic (including the logic of norms)
03B25 Decidability of theories and sets of sentences
54E35 Metric spaces, metrizability
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References:
[1] CHAGROV A., Num. 35 Oxford Logic Guides (1997)
[2] GARGOV G., Mathematical Logic and its Applications. Proceedings of the Summer School and Conference dedicated to the 80th Anniversary of Kurt Gödel, Druzhba, 1986 pp 253–
[3] DOI: 10.1007/978-1-4613-0609-2_22 · doi:10.1007/978-1-4613-0609-2_22
[4] DOI: 10.1093/logcom/2.1.5 · Zbl 0774.03003 · doi:10.1093/logcom/2.1.5
[5] KUTZ O., Proceedings of the 8th Conference on Principles of Knowledge Representation and Reasoning (KR 2002) pp 215–
[6] DOI: 10.1145/635499.635504 · Zbl 1365.68407 · doi:10.1145/635499.635504
[7] DOI: 10.2307/2275293 · Zbl 0788.03019 · doi:10.2307/2275293
[8] DOI: 10.1007/3-540-40006-0_4 · doi:10.1007/3-540-40006-0_4
[9] WOLTER F., Proc. of the 7th Conf. on Principles of Knowledge Representation and Reasoning (KR 2000), USA pp 3– (2000)
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