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Mathematical Fuzzy Logic and Natural Numbers

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    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.
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