ﻻ يوجد ملخص باللغة العربية
Danos and Regnier (1989) introduced the par-switching condition for the multiplicative proof-structures and simplified the sequentialization theorem of Girard (1987) by the use of par-switching. Danos and Regner (1989) also generalized the par-switching to a switching for $n$-ary connectives (an $n$-ary switching, in short) and showed that the expansion property which means that any excluded-middle formula has a correct proof-net in the sense of their $n$-ary switching. They added a remark that the sequentialization theorem does not hold with their switching. Their definition of switching for $n$-ary connectives is a natural generalization of the original switching for the binary connectives. However, there are many other possible definitions of switching for $n$-ary connectives. We give an alternative and natural definition of $n$-ary switching, and we remark that the proof of sequentialization theorem by Olivier Laurent with the par-switching works for our $n$-ary switching; hence that the sequentialization theorem holds for our $n$-ary switching. On the other hand, we remark that the expansion property does not hold with our switching anymore. We point out that no definition of $n$-ary switching satisfies both the sequentialization theorem and the expansion property at the same time except for the purely tensor-based (or purely par-based) connectives.
The purpose of this note is to discuss some of the questions raised by Dunn, J. Michael; Moss, Lawrence S.; Wang, Zhenghan in Editors introduction: the third life of quantum logic: quantum logic inspired by quantum computing.
Linear logical frameworks with subexponentials have been used for the specification of among other systems, proof systems, concurrent programming languages and linear authorization logics. In these frameworks, subexponentials can be configured to all
We continue the study of computable embeddings for pairs of structures, i.e. for classes containing precisely two non-isomorphic structures. Surprisingly, even for some pairs of simple linear orders, computable embeddings induce a non-trivial degree
We use the geometric axioms point of view to give an effective listing of the complete types of the theory $DCF_{0}$ of differentially closed fields of characteristic $0$. This gives another account of observations made in earlier papers.
We use the framework of reverse mathematics to address the question of, given a mathematical problem, whether or not it is easier to find an infinite partial solution than it is to find a complete solution. Following Flood, we say that a Ramsey-type