Hypersequent and the Proof Theory of Intuitionistic Fuzzy Logic

@inproceedings{Baaz2000HypersequentAT,
  title={Hypersequent and the Proof Theory of Intuitionistic Fuzzy Logic},
  author={Matthias Baaz and Richard Zach},
  booktitle={CSL},
  year={2000}
}
Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Goedel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Goedel logics by Avron. It is shown that the system is sound… CONTINUE READING
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References

Publications referenced by this paper.
SHOWING 1-10 OF 14 REFERENCES

Hypersequents

A. Avron
  • logical consequence and intermediate logics for concurrency. Ann. Math. Artificial Intelligence, 4:225–248
  • 1991
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

Logic with Truth Values in a Linearly Ordered Heyting Algebra

  • J. Symb. Log.
  • 1969
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

Zum intuitionistischen Aussagenkalkül

K. Gödel
  • Anz. Akad. Wiss. Wien, 69:65– 66
  • 1932
VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

Proof Theory

G. Takeuti
  • North-Holland, Amsterdam, 2nd ed.
  • 1987
VIEW 12 EXCERPTS
HIGHLY INFLUENTIAL

Metamathematics of Fuzzy Logic

  • Trends in Logic
  • 1998
VIEW 2 EXCERPTS