论文标题
替代词的定理
Theorems of Alternatives for Substructural Logics
论文作者
论文摘要
替代方法的定理可降低子结构逻辑中的有效性，以降低其乘法片段的有效性。值得注意的例子包括Arnon Avron的理论，该理论降低了R-Mingle逻辑RM中综合公式分离的有效性，以使这些公式的线性组合的有效性，以及Gordan定理的实时条件，该定理用于实现的实数，从而使abeligian涉及的综合条件均具有类似的条件。没有添加剂常数的Uninorm逻辑可以接受替代定理。还表明，相对于一类完全有序的残留晶格，可以使用逻辑的替代定理来建立（统一）演绎插值和完整性。
A theorem of alternatives provides a reduction of validity in a substructural logic to validity in its multiplicative fragment. Notable examples include a theorem of Arnon Avron that reduces the validity of a disjunction of multiplicative formulas in the R-mingle logic RM to the validity of a linear combination of these formulas, and Gordan's theorem for solutions of linear systems over the real numbers, that yields an analogous reduction for validity in Abelian logic A. In this paper, general conditions are provided for axiomatic extensions of involutive uninorm logic without additive constants to admit a theorem of alternatives. It is also shown that a theorem of alternatives for a logic can be used to establish (uniform) deductive interpolation and completeness with respect to a class of dense totally ordered residuated lattices.
