0310053 - ÚI 2009 RIV NL eng J - Journal Article
Hájek, Petr
Mathematical Fuzzy Logic and Natural Numbers.
[Matematická fuzzy logika a přirozená čísla.]
Fundamenta Informaticae. Roč. 81, č. 1-3 (2007), s. 155-163. ISSN 0169-2968. E-ISSN 1875-8681
R&D Projects: GA AV ČR IAA100300503
Institutional research plan: CEZ:AV0Z10300504
Keywords : fuzzy logic * arithmetic * essential undecidability
Subject RIV: BA - General Mathematics
Impact factor: 0.693, year: 2007

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 for all. Essential undecidability of this fuzzy arithmetic is proved by a careful analysis of the classical proof of essential undecidability of arithmetic.

Je formulována slabá varianta Robinsonovy aritmetiky Q s ne nutně totálními operacemi; tato teorie se vyšetruje v rámci základní matematické predikátové logiky BL. Je podán důkaz podstatné nerozhodnutelnosti této fuzzy aritmetiky.
Permanent Link: http://hdl.handle.net/11104/0162032