Uncertain Linear Logic via Fibring of Probabilistic and Fuzzy Logic
  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).
