Linguistic Applications of First Order Intuitionistic Linear Logic

In this paper we will discuss the first order multiplicative intuitionistic fragment of linear logic, MILL1, and its applications to linguistics. We give an embedding translation from formulas in the Lambek Calculus to formulas in MILL1 and show this translation is sound and complete. We then exploit the extra power of the first order fragment to give an account of a number of linguistic phenomena which have no satisfactory treatment in the Lambek Calculus. This revised version was published online in August 2006 with corrections to the Cover Date.     

相对化One-Way函数的存在性

One-Way函数在计算复杂性和密码技术中均有重要的应用.将Grollmann和Selman的结果推广到相对化和非一致复杂类的情形,证明了复杂类UP/poly,UP,P/poly等之间的包含关系与强相对化one-way函数、弱相对化one-way函数存在问题的等价性.     

On the completeness of the Lambek Calculus with respect to relativized Relational Semantics

Recently M. Szabolcs [12] has shown that many substructural logics including Lambek CalculusL are complete with respect to relativized Relational Semantics. The current paper proves that it is sufficient forL to consider a relativization to the relation x dividesy in some fixed semigroupG.Research partially supported by the Russian Fund for Fundamental Research Grant 93-012-590.     

Relativized collapsing between BPP and PH under stringent oracle access

We propose a new model of stringent oracle access defined for a general complexity class. For example, when comparing the power of two machine models relative to some oracle set X, we restrict that machines of both types ask queries from the same segment of the set X. In particular, for investigating polynomial-time (or polynomial-size) computability, we propose polynomial stringency, bounding query length to any fixed polynomial of input length. Under such stringent oracle access, we show an oracle G such that BPP^G = PH^G.