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  • 1 Department of Mathematics Education, Dongguk University, Seoul 100-715, Korea
  • | 2 Department of Mathematics Education (and RINS), Gyeongsang National University, Chinju 660-701, Korea
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Abstract

Based on the Buşneag's model [1,2,3], the notion of pseudo-valuations (valuations) on a pre-logic is introduced, and a pseudo-metric is induced by a pseudo-valuation on pre-logics. Related properties are investigated, and conditions for a real-valued function on a pre-logic to be a pseudo-valuation are discussed. Using the notion of (pseudo) valuation, we show that the binary operation ∗ in pre-logics is uniformly continuous.

  • [1] Buşneag, C. 2007 Valuations on residuated lattices An. Univ. Craiova Ser. Mat. Inform. 34 2128.

  • [2] Buşneag, D. 1996 Hilbert algebras with valuations Math. Japon. 44 285289.

  • [3] Buşneag, D. 2003 On extensions of pseudo-valuations on Hilbert algebras Discrete Math. 263 1124 .

  • [4] Chajda, I. Halas, R. 2002 Algebraic properties of pre-logics Math. Slovaca 52 157175.

Acta Mathematica Hungarica
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  • Impact Factor (2019): 0.588
  • Scimago Journal Rank (2019): 0.489
  • SJR Hirsch-Index (2019): 38
  • SJR Quartile Score (2019): Q2 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.538
  • Scimago Journal Rank (2018): 0.488
  • SJR Hirsch-Index (2018): 36
  • SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)