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Topic · Computational Theory and Mathematics

Advanced Algebra and Logic

Advanced Algebra and Logic is a research topic within Computational Theory and Mathematics. Science Explorer counts 33k research works in it since 1950. 10.0% of them reached the world's top 10% most cited for their field and year.

This cluster of papers explores the intersection of fuzzy logic, residuated lattices, t-norms, MV-algebras, quantum logic, and automata theory. It delves into mathematical fuzzy logic, modal logics, and algebraic semantics within the context of probability theory.

  • Fuzzy Logic
  • Residuated Lattices
  • t-norms
  • MV-algebras
  • Quantum Logic
  • Automata Theory
  • Mathematical Fuzzy Logic
  • Modal Logics
  • Algebraic Semantics
  • Probability Theory
Research works
33k
fractional, since 1950
In the world top 10%
3.3k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
-1%
the tick is no change
Largest producer
China
20% of the 10 largest, 2022-now
Advanced Algebra and Logic

Which countries lead Advanced Algebra and Logic research?

By volume, China and the United States publish the most (410 and 375 works in 2022-now).

By volume, 2022-now

  1. 1 China 410 works
  2. 2 United States 375 works
  3. 3 India 294 works
  4. 4 Germany 156 works
  5. 5 Italy 150 works
  6. 6 Russia 145 works
  7. 7 Türkiye 140 works
  8. 8 France 134 works
  9. 9 Iran 128 works
  10. 10 Iraq 118 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 20.0%United States: 18.3%India: 14.3%Germany: 7.6%6 others listed: 39.8%20%largest
China410 · 20.0%United States375 · 18.3%India294 · 14.3%Germany156 · 7.6%6 others listed815 · 39.8%

Shares of the rows listed above, not of the whole node.

Which institutions lead Advanced Algebra and Logic research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Advanced Algebra and Logic research, followed by Russian Academy of Sciences and University of Baghdad.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 58 works
  2. 2 Russian Academy of SciencesRussia 41 works
  3. 3 University of BaghdadIraq 25 works
  4. 4 Czech Academy of SciencesCzechia 24 works
  5. 5 University of OstravaCzechia 24 works
  6. 6 Lomonosov Moscow State UniversityRussia 23 works
  7. 7 TU WienAustria 20 works
  8. 8 Slovak Academy of SciencesSlovakia 16 works
  9. 9 Consejo Nacional de Investigaciones Científicas y TécnicasArgentina 16 works
  10. 10 University of AmsterdamNetherlands 15 works

Who are the leading researchers in Advanced Algebra and Logic?

The most-cited researchers publishing on Advanced Algebra and Logic include David H. Haussler, Noam Chomsky and Francisco Herrera.

  1. 1 David H. Haussler United States 209k citations
  2. 2 Noam Chomsky United States 141k citations
  3. 3 Francisco Herrera Spain 141k citations
  4. 4 Lotfi A. Zadeh United States 141k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Advanced Algebra and Logic?

The most cited paper in Advanced Algebra and Logic is "Dynamical Theory of Crystal Lattices" (Max Born, Kun Huang, Melvin D. Lax, 1955), with 10,595 citations. Next come "Fuzzy sets as a basis for a theory of possibility" (8,108) and "Fuzzy logic in control systems: fuzzy logic controller. I" (5,627).

Most cited papers
#PaperReleasedCitations
1 Dynamical Theory of Crystal Lattices Max Born, Kun Huang, Melvin D. Lax · American Journal of Physics Oct 1955 10,595
2 Fuzzy sets as a basis for a theory of possibility Lotfi A. Zadeh · Fuzzy Sets and Systems 1978 8,108
3 Fuzzy logic in control systems: fuzzy logic controller. I C.C. Lee · IEEE Transactions on Systems Man and Cybernetics 1990 5,627
4 Fuzzy logic = computing with words Lotfi A. Zadeh · IEEE Transactions on Fuzzy Systems May 1996 3,246
5 ROUGH FUZZY SETS AND FUZZY ROUGH SETS* Didier Dubois, Henri M. Prade · International Journal of General Systems Jun 1990 3,003
All 97 most cited papers, with filters and sorting

Where is Advanced Algebra and Logic research done?

The largest centres of Advanced Algebra and Logic research in 2022-now are Moscow (Russia), Beijing (China), Xi'an (China) and Paris (France). Among places with at least 20 works in it, it is an unusually large share of all research in Ostrava.

Largest cities, 2022-now

  1. 1 MoscowRussia 74 works
  2. 2 BeijingChina 71 works
  3. 3 Xi'anChina 60 works
  4. 4 ParisFrance 50 works
  5. 5 TehranIran 46 works
  6. 6 PragueCzechia 41 works
  7. 7 BaghdadIraq 36 works
  8. 8 ViennaAustria 30 works
  9. 9 TokyoJapan 29 works
  10. 10 ChengduChina 29 works

Where it is the local speciality

  1. OstravaCZ · 24.6 works30×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Advanced Algebra and Logic than the world average.

See Advanced Algebra and Logic on the map

Where is the best place to study Advanced Algebra and Logic?

Among universities, judged by research, Jordan University of Science and Technology, Amasya Üniversitesi and Ruhr University Bochum score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%60%mean 20%fractional works in this field (log) →share of work in the world top 10% →Jordan University of…Amasya ÜniversitesiRuhr University BochumUniversity of Ostrava
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Jordan University of Science and TechnologyJordan 74.147.8%18.1×10 +66.2%
2Amasya ÜniversitesiTürkiye 65.733.3%41.1×12 +673.5%
3Ruhr University BochumGermany 62.626.6%10.7×14 +23.4%
4University of OstravaCzechia 56.66.2%101.7×24 -19.7%
5University of AmsterdamNetherlands 56.115.3%7.8×15 -6.9%
6University of TübingenGermany 54.423.7%8.7×12 +299.8%
7Universidad de CádizSpain 53.017.5%18.5×12 +68.2%
8TU WienAustria 51.22.8%20.5×20 -9.5%
9University of BaghdadIraq 50.44.2%10.8×25 +5.8%
10Karadeniz Technical UniversityTürkiye 49.622.6%16.2×10 +3.1%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Advanced Algebra and Logic, country by country

Is Advanced Algebra and Logic research growing?

Output in 2022-2025 was 1% lower than in 2018-2021, peaking in 2011.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Advanced Algebra and Logic as a percentage of every work published that year, 0.016% in 2024.

still counting0.050%0.10%0.15%Advanced Algebra and Logic0.015% in 202519801990200020102020

Fractional works of Advanced Algebra and Logic over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Advanced Algebra and Logic10.1% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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