Mathematical Fuzzy Logic and Natural Numbers

Issue title: Topics in Logic, Philosophy and Foundations of Mathematics and Computer Science. In Recognition of Professor Andrzej Grzegorczyk

Article type: Research Article

Authors: Hájek, Petr

Affiliations: Institute of Computer Science, Academy of Sciences of the Czech Republic, 182 07 Prague, Czech Republic. E-mail: [email protected]

Abstract: A weak variant of Robinson's arithmetic Q where the binary operations of addition and multiplication are replaced by ternary relations (not necessarily defining total crisp functions) is formulated and investigated over the mathematical fuzzy logic BL∀. Essential undecidability of this fuzzy arithmetic is proved by a careful analysis of the classical proof of essential undecidability of arithmetic.

Journal: Fundamenta Informaticae, vol. 81, no. 1-3, pp. 155-163, 2007