Lukasiewicz逻辑系统中的广义重言式理论
Theory of Generalized Tautology in Lukasiewicz Logic System
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摘要: 将逻辑系统-W,W,Wk中的广义重言式理论进行推广并应用到Lukasiewicz逻辑系统中,主要结果是:得 到了逻辑公式集F(S)在该系统中关于﹁同余的分划;证明了在该逻辑系统中对每个无理数α而言,不存在可达α- 重言式,且对每个实数α而言,不存在可达α+-重言式;给出了广义重言式、广义矛盾式各类之间的关系定理。Abstract: Theory of generalized tautology in logic system-W, WandWkis generalized and applied to Lukasiewicz logic system. The main resultsare asfollows: congruence about onset of logic formulasF(S)hasbeenobtained in thesystem; it is proved that in this system, for any irrational numberα, there does not exist accessibleα-tautology; and for any real numberα, there does not exist accessibleα+-tautology; and the relation theorems have been given between categories of generalized contradictions and between categories of generalized tautologies respectively.
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Key words:
- fuzzy logic /
- valuation /
- semantics /
- Lukasiewicz logic system /
- generalized tautology /
- generalized contradiction /
- partition
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