Proper Semantics for Substructural Logics, from a Stalker Theoretic Point of View
Proper Semantics for Substructural Logics, from a Stalker Theoretic Point of View
复制标题
从潜行者理论的角度来看，子结构逻辑的正确语义
DOI：
10.1007/s11225-008-9106-9
复制
发表时间：
2008
期刊：
影响因子：
0.7
通讯作者：
Sato Kentaro
中科院分区：
文献类型：
--
作者：
Sato Kentaro
我们研究了与同余关系相关的剩余结构中的滤子(我们称之为滤子)，并基于这些滤子的素性的概念发展了一般子结构逻辑的语义理论。我们首先将Stone的层表示定理推广到一般的子结构逻辑，然后定义-滤子的素性是定义表示层的空间的“点”(或跟踪器)。对于某些子结构逻辑，在各种众所周知的语义下，素数FL-滤子将被证明与真值集一致。我们还研究了需要哪些结构规则来解释素滤子方面的每个连接词，其方式与Klipke或Routley-Meyer语义学中的方式相同。我们可以认为，在这个意义上，每个连接词所需要的一套结构规则反映了赋予连接词意义的难度。一个令人惊讶的发现是，线性逻辑的连接词⅋是按照这个意义上的难度线性排序的。
We study filters in residuated structures that are associated with congruence relations (which we call-filters), and develop a semantical theory for general substructural logics based on the notion of primeness for those filters. We first generalize Stone’s sheaf representation theorem to general substructural logics and then define the primeness of-filters as being “points” (or stalkers) of the space, the spectrum, on which the representing sheaf is defined. Prime FL-filters will turn out to coincide with truth sets under various well known semantics for certain substructural logics. We also investigate which structural rules are needed to interpret each connective in terms of prime-filters in the same way as in Kripke or Routley-Meyer semantics. We may consider that the set of the structural rules that each connective needs in this sense reflects the difficulty of giving the meaning of the connective. A surprising discovery is that connectives, ⅋ of linear logic are linearly ordered in terms of the difficulty in this sense.
FL 子结构逻辑的代数化、参数化局部演绎定理和插值
DOI：
--
发表时间：
2006
期刊：
Studia Logica 83
影响因子：
--
作者：
N.Galatos;H.Ono
通讯作者：
H.Ono