Higher-Order and Modal Logic as a Framework for Explanation-Based Generalization

Certain tasks, such as formal program development and theorem proving, fundamentally rely upon the manipulation of higher-order objects such as functions and predicates. Computing tools intended to assist in performing these tasks are at present inadequate in both the amount of knowledge they contain (i.e., the level of support they provide) and in their ability to learn (i.e., their capacity to enhance that support over time). The application of a relevant machine learning technique—explanation-based generalization (EBG)—has thus far been limited to first-order problem representations. We extend EBG to generalize higher-order values, thereby enabling its application to higher-order problem encodings.Logic programming provides a uniform framework in which all aspects of explanation-based generalization and learning may be defined and carried out. First-order Horn logics (e.g., Prolog) are not, however, well suited to higher-order applications. Instead, we employ Prolog, a higher-order logic programming language, as our basic framework for realizing higher-order EBG. In order to capture the distinction between domain theory and training instance upon which EBG relies, we extend Prolog with the necessity operator of modal logic. We develop a meta-interpreter realizing EBG for the extended language, Prolog, and provide examples of higher-order EBG.     

A Universal Method of Scientific Inquiry

A paradigm of scientific discovery is defined within a first-order logical framework. Within this paradigm, the concept of successful scientific inquiry is formalized and investigated. Among other results, it is shown that a simple method of scientific inquiry is universal in the sense that it leads to success on every problem for which success is in principle possible.     

Modal logic as metalogic

The goal of this paper is to show how modal logic may be conceived as recording the derived rules of a logical system in the system itself. This conception of modal logic was propounded by Dana Scott in the early seventies. Here, similar ideas are pursued in a context less classical than Scott's.First a family of propositional logical systems is considered, which is obtained by gradually adding structural rules to a variant of the nonassociative Lambek calculus. In this family one finds systems that correspond to the associative Lambek calculus, linear logic, relevant logics, BCK logic and intuitionistic logic. Above these basic systems, sequent systems parallel to the basic systems are constructed, which formalize various notions of derived rules for the basic systems. The deduction theorem is provable for the basic systems if, and only if, they are at least as strong as systems corresponding to linear logic, or BCK logic, depending on the language, and their deductive metalogic is not stronger than they are.However, though we do not always have the deduction theorem, we may always obtain a modal analogue of the deduction theorem for conservative modal extensions of the basic systems. Modal postulates which are necessary and sufficient for that are postulates of S4 plus modal postulates which mimic structural rules. For example, the modal postulates which Girard has recently considered in linear logic are necessary and sufficient for the modal analogue of the deduction theorem.All this may lead towards results about functional completeness in categories. When functional completeness, which is analogous to the deduction theorem, fails, we may perhaps envisage a modal analogue of functional completeness in a modal category, of which our original category is a full subcategory.     

The quantifier structure of sentences that characterize nondeterministic time complexity

For every nondeterministic Turing machineM of time complexityT(n), there is a second-order sentence of a very restricted form, whose set of finite models encodes the set of strings recognized byM. Specifically, has a relational symbol which is interpreted as addition restricted to finite segments of the natural numbers, and a prefix consisting of existentially quantified unary second-order variables followed by a universal-existential first-order part. Here, every input stringx is encoded by a model of sizeT(|x|). Using a closely related encoding of strings as models where the size of the model is the length of the string, a consequence is that ifT(n)=n ^d, then there is a sentence with a similar prefix but whose second-order variables ared-ary and whose finite models encode the strings accepted byM. Potential applications to low-level complexity are discussed.     

燃煤锅炉供热系统的模糊控制

介绍燃煤锅炉供热系统的自动化节能模糊控制方案,燃煤锅炉供热系统是一个大惯性的滞后系统,传统的单纯PID控制效果不理想,而基于工人熟练的经验和专家知识的模糊控制能够达到比较好的效果。系统中对控制参考量水温和炉膛负压这两个输入量模糊化处理,由控制规则推出输出模糊子集,再应用模糊推理合成规则得出PID的系数,PID控制器根据输出量来控制鼓风机、引风机、炉排电机和水泵的变频器。     

铁矿石境外投资风险评估的模糊神经网络模型

论文将模糊理论与神经网络结合,对铁矿石境外投资所涉及的风险因素分别从资产影响、威胁频度两方面进行分析,建立了铁矿石境外投资的风险层次化结构,并构造了各因素所对应评判集的隶属度矩阵;综合运用模糊推理算法与神经网络仿真技术,对铁矿石境外投资的风险进行评估,进而判定铁矿石境外投资风险等级。最后,通过计算铁矿石境外投资的市场风险说明了算法的应用,并将结果与模糊综合评估得到的风险值进行比较,检测了模型的有效性。     

改进FCM在交互式图像分割中的应用

为解决由于自然纹理的干扰而导致的分割图像边缘模糊问题,对模糊C均值聚类算法进行改进并应用于交互式图像分割中。用户通过输入种子点来获得目标和背景的主要特征,并将输入的种子点作为聚类中心点;提出全局空间相似性度量标准并引入Gabor能量滤波器来计算图像中各点到聚类中心的距离;算法首次引入边缘密度概念定义权重因子,根据图像特点,自适应地计算图像中任意一点的纹理特征和颜色特征在特征空间中所占比例,使得到的特征更加准确地描述图像的本质属性。对具有自然纹理背景的图像进行仿真实验,应用两种性能指标来比较本文所提算法与随机游走算法的分割精度。实验结果表明,本文算法分割精度高于模糊聚类和随机游走算法。     

神经网络PID在PLC系统控制中的应用研究

针对传统的PID算法由于难以给出精确的数学模型,使得系统参数设定困难,同时系统控制效果上存在一定的缺陷,造成系统安全性和可靠性降低,系统控制质量不高。为了解决传统的PID算法所带来的问题,提出了基于模糊神经网络的PID算法,将PID算法、模糊控制算法以及神经网络算法相结合,形成了一种智能控制算法。将算法应用在PLC控制系统中,实验表明算法有效的实现了PID参数的自整定,并且提高了控制质量,具有一定的实际应用推广价值。     

一种谱分解降维的模糊有监督局部保持投影策略

提出一种谱分解降维的模糊有监督局部保持投影策略。首先针对监督局部保持投影SLPP存在过学习和不能较好地保持图像空间的差异信息等问题,通过最小化局部离散度和最大化差异离散度准则提取投影方向,找到一种线性鉴别分析的等价形式。其次,通过采用模糊k近邻(FKNN)方法得到相应的样本分布隶属度信息,同时考虑到离群样本对整个分类结果的不利影响,提出一种模糊化方法,根据样本的隶属度对样本分布矩阵重定义所做的贡献,将每个样本的隶属度融入到SLPP特征抽取的过程中,从而得到完整有效的模糊样本特征向量集,有效解决了小样本问题的特征抽取问题。第三,提出一种谱分解的矩阵分析方法,在SLPP投影准则下,对散布矩阵实现降维。在ORL和NUST603人脸库上的实验结果验证了该方法的有效性。