Monadic Gödel logics

01.06.2010 - 31.12.2012
Forschungsförderungsprojekt
ödel logics are one of the most important examples of many-valued logics. They are both intermediate logics (logics between classical and intuitionistic logic) and prominent examples for fuzzy logics. The concept of fuzzy properties has been propagated by Lotfi Zadeh to represent inferences involving vague information, it is now the basis of various applications. Although this project addresses mathematical problems it is intended to incorporate the results into the most important expert system for medical diagnosis at the Vienna General Hospital. Fuzzy logics in general allow sentences to be assigned not only 1 for ¿true¿ and 0 for ¿false¿, but also any number between 0 and 1 to represent relative falsity or truth. In Gödel logics, the meaning of these truth values only depends on their order. Kurt Gödel (1906¿1978), one of the most famous logicians of modern age, described this group of logics to prove that infinitely many logics between intuitionistic and classic logic exist. This project deals in particular with the characterization of the monadic fragments of Gödel logics. These fragments are formed by restricting the predicate symbols to unary ones and constitute the most important fragment in the language of predicate logic. We aim to determine the decidability of the validity and of the satisfiability of sentences in this fragment and in the related one-variable and two-variable fragments. We also want to investigate the closely linked problem whether the validity of sentences in the monadic fragment of Łukasiewicz logic is decidable. This is the most important among the open mathematical problems in the field of fuzzy logic.

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Grant funds

  • FWF - Österr. Wissenschaftsfonds (National) Austrian Science Fund (FWF)

Forschungsschwerpunkte

  • Computational Intelligence: 100%

Publikationen