PRELIS 是LISREL的一部分。它主要用于在构建结构模型之前,对数据进行前期处理和初
步分析。PRELIS 的主要用途包括:
o 将其它格式的数据文件(SAS, SPSS, Excel, Stat 等等)读入并存储为PRELIS 数据文
件。
o 将 PRELIS(*.psf)数据输出为其他软件可读的相应格式。
o 对 PRELIS 数据进行处理。(定义变量类型,处理缺失值,数据筛选,生成子数据集
等)。
o 回归模型分析及初步的因子分析等。
o 计算矩阵(协方差矩阵,多项相关系数以及渐近协方差矩阵等)。
o 可以用图表直观地表现数据的状况。
在这里,我们用不同类型的变量为例介绍如何应用PRELIS 来实现上述功能。本章中的
所有数据都存在LISREL 安装文件夹中的TUTORIAL 子文件夹里。
Possible world semantics underlies many of the applications of modal logic in
computer science and philosophy. The standard theory arises from interpreting the
semantic denitions in the ordinary meta-theory of informal classical mathematics.
If, however, the same semantic denitions are interpreted in an intuitionistic metatheory
then the induced modal logics no longer satisfy certain intuitionistically
invalid principles. This thesis investigates the intuitionistic modal logics that arise
in this way.
Natural deduction systems for various intuitionistic modal logics are presented.
From one point of view, these systems are self-justifying in that a possible world
interpretation of the modalities can be read o directly from the inference rules. A
technical justication is given by the faithfulness of translations into intuitionistic
rst-order logic. It is also established that, in many cases, the natural deduction
systems induce well-known intuitionisticmodal logics, previously given by Hilbertstyle
axiomatizations.
The main benet of the natural deduction systems over axiomatizations is their
susceptibility to proof-theoretic techniques. Strong normalization (and con
uence)
results are proved for all of the systems. Normalization is then used to establish
the completeness of cut-free sequent calculi for all of the systems, and decidability
for some of the systems.
Lastly, techniques developed throughout the thesis are used to establish that
those intuitionistic modal logics proved decidable also satisfy the nite model
property. For the logics considered, decidability and the nite model property
presented open problems
A topos is a categorical model of constructive set theory. In particular, the eective topos is the
categorical 'universe' of recursive mathematics. Among its objects are the modest sets, which
form a set-theoretic model for polymorphism. More precisely, there is a bration of modest sets
which satises suitable categorical completeness properties, that make it a model for various
polymorphic type theories.
These lecture notes provide a reasonably thorough introduction to this body of material,
aimed at theoretical computer scientists rather than topos theorists. Chapter 2 is an outline of
the theory of brations, and sketches how they can be used to model various typed -calculi.
Chapter 3 is an exposition of some basic topos theory, and explains why a topos can be regarded
as a model of set theory. Chapter 4 discusses the classical PER model for polymorphism, and
shows how it 'lives inside' a particular topos|the eective topos|as the category of modest
sets. An appendix contains a full presentation of the internal language of a topos, and a map of
the eective topos.
Chapters 2 and 3 provide a sampler of categorical type theory and categorical logic, and
should be of more general interest than Chapter 4. They can be read more or less independently
of each other; a connection is made at the end of Chapter 3.
The main prerequisite for reading these notes is some basic category theory: limits and colimits,
functors and natural transformations, adjoints, cartesian closed categories. No knowledge
of indexed categories or categorical logic is needed. Some familiarity with 'ordinary' logic and
typed -calculus is assumed.