论文标题
不确定的线性逻辑通过概率和模糊逻辑的纤维
Uncertain Linear Logic via Fibring of Probabilistic and Fuzzy Logic
论文作者
论文摘要
从基于计数观测值的命题的简单语义开始，这表明概率和模糊的逻辑对应于两个不同的启发式假设，这些假设是关于目前尚不可用的命题的组合。这两个不同的启发式假设导致了两组不同的公式，用于通过晶格操作传播定量真实价值。结果表明，这两组公式为线性逻辑中的乘法和加性操作员集提供了自然接地。然后，线性逻辑的标准规则是基础语义的后果。线性逻辑作为``资源的逻辑''的概念通过``证据的保护''的原则来体现 - 线性逻辑中削弱和收缩的限制可避免证据的双重计算（超越了通过使用启发式真实价值功能而产生的任何双重计算）。
Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence bases are not currently available. These two different heuristic assumptions lead to two different sets of formulas for propagating quantitative truth values through lattice operations. It is shown that these two sets of formulas provide a natural grounding for the multiplicative and additive operator-sets in linear logic. The standard rules of linear logic then emerge as consequences of the underlying semantics. The concept of linear logic as a ``logic of resources" is manifested here via the principle of ``conservation of evidence" -- the restrictions to weakening and contraction in linear logic serve to avoid double-counting of evidence (beyond any double-counting incurred via use of heuristic truth value functions).
