二值命题逻辑理论的结论类型和分类

以公式真度为基础,研究了二值命题逻辑系统中有限理论逻辑推出的结论类型和分别基于公式真度以及逻辑等价的分类问题,给出了分类定理以及同一理论结论的相似度的一个下界。     

Automated reasoning with function evaluation for COCOLOG

The Conditional Observer and Controller Logic (COCOLOG) is a logical system for the feedback control of finite input‐state‐output systems wherein the individual first order logical theories have the properties of consistency, completeness and decidability. The efficiency of automatic theorem proving (ATP) is a crucial issue in the implementation of COCOLOG control systems and in this paper we present a so‐called function evaluation (FE) based resolution‐refutation ATP methodology for COCOLOG. FE‐resolution ATP replaces the axioms specifying the dynamics of a finite input‐state‐output machine by a set of defined function relations. The resulting procedure extends to predicates and hence permits the definition of constant and variable FE‐resolution inference. It is shown that FE‐resolution ATP is complete in the sense that a set of clauses which is unsatisfiable in all models with the given interpretation of the functions will yield the empty clause under resolution, paramodulation and FE‐resolution. This revised version was published online in June 2006 with corrections to the Cover Date.     

Nondeterministic operations on finite relational structures

This article builds on a tutorial introduction to universal algebra for language theory (Courcelle, Theoret. Comput. Sci. 163 (1996) 1–54) and extends it in two directions. First, nondeterministic operations are considered, i.e., operations which give a set of results instead of a single one. Most of their properties concerning recognizability and equational definability carry over from the ordinary case with minor modifications. Second, inductive sets of evaluations are studied in greater detail. It seems that they are handled most naturally in the framework presented here. We consider the analogues of top-down and bottom-up tree transducers. Again, most of their closure properties are maintained. We relate them to the logical theory of finite relational structures and hypergraphs. Our central theorem says that every transduction which is definable in counting monadic second-order logic is a bottom-up transduction on term representations. Finally, several examples indicate that one cannot hope for decidable logical theories in the presence of unbounded nondeterminism.     

Two kinds of optimal controls for probabilistic mix-valued logical dynamic networks

This paper addresses two kinds of optimal control problems of probabilistic mix-valued logical control networks by using the semi-tensor product of matrices, and presents a number of new results on the optimal finite-horizon control and the first-passage model based control problems, respectively. Firstly, the probabilistic mix-valued logical control network is expressed in an algebraic form by the semi-tensor product method, based on which the optimal finite-horizon control problem is studied and a new algorithm for choosing a sequence of control actions is established to minimize a given cost functional over finite steps. Secondly, the first-passage model of probabilistic mix-valued logical networks is given and a new algorithm for designing the optimal control scheme is proposed to maximize the corresponding probability criterion. FinMly, an illustrative example is studied to support our new results/algorithms.     

Full-parameter vision navigation based on scene matching for aircrafts

Vision navigation based on scene matching between real-time images and a reference image has many advantages over the commonly used inertial navigation system （INS）, such as no cumulative measurement errors for long-endurance flight. Recent developments in vision navigation are mainly used for partial navigation parameters measurements, such as the position and the relative velocity, which cannot meet the requirements of completely autonomous navigation. We present the concept, principle and method of full-parameter vision navigation （FPVN） based on scene matching. The proposed method can obtain the three-dimensional （3D） position and attitude angles of an aircraft by the scene matching for multiple feature points instead of a single point in existing vision navigations. Thus, FPVN can achieve the geodetic position coordinates and attitude angles of the aircraft and then the velocity vector, attitude angular velocity and acceleration can be derived by the time differentials, which provide a full set of navigation parameters for aircrafts and unmanned aerial vehicles （UAVs）. The method can be combined with the INS and the cumulative errors of the INS can be corrected using the measurements of FPVN rather than satellite navigation systems. The approach provides a completely autonomous and accurate navigation method for long-endurance flight without the help of satellites.     

The logical control of an elevator

This paper presents a detailed example of the design of a logical feedback controller for finite state machines. In this approach, the control objectives and associated control actions are formulated as a set of axioms each of the form X implies Y, where X asserts that (i) the current state satisfies a set of conditions and (ii) the control action y will steer the current state towards a given target state; Y asserts that the next control input will take the value y. An automatic theorem prover establishes which of the assertions X is true, and then the corresponding control y is applied. The main advantages of this system are its flexibility (changing the control law is accomplished through changing only the axioms) and the fact that, by the design of the system, control actions will provably achieve the control objectives. The illustrative design problem presented in this paper is that of the logical specification and logical feedback control of an elevator     

Verification of non-monotonic knowledge bases

Non-monotonic Knowledge-Based Systems (KBSs) must undergo quality assurance procedures for the following two reasons: (i) belief revision (if such is provided) cannot always guarantee the structural correctness of the knowledge base, and in certain cases may introduce new semantic errors in the revised theory; (ii) non-monotonic theories may have multiple extensions, and some types of functional errors which do not violate structural properties of a given extension are hard to detect without testing the overall performance of the KBS. This paper presents an extension of the distributed verification method, which is meant to reveal structural and functional anomalies in non-monotonic KBSs. Two classes of anomalies are considered: (i) structural anomalies which manifest themselves within a given extension (such as logical inconsistencies, structural incompleteness, and intractabilities caused by circular rule chains), and (ii) functional anomalies related to the overall performance of the KBS (such as the existence of complementary rules and some types of rule subsumptions). The corresponding verification tests are presented and illustrated on an extended example.     

一种自动的形式化验证技术-模型检测

模型检测是针对有限状态系统行为的逻辑性质的一种自动验证技术,已有许多工业应用.其主要缺陷是空间爆炸问题.本文通过一简单实例介绍其基本思想、检测步骤和相关理论,给出一些处理状态空间爆炸问题的优化技术,并与其它验证方法进行了比较,最后简单介绍了软件模型检测的新进展.     

NKI中的本体、框架和逻辑理论

NKI(国家知识基础设施)是一个大规模知识库,它用框架来表示本体中的概念,用Hom逻辑程序作为自动推理.给出NKI中的本体、框架和逻辑理论的形式表示以及形式表示之间的转换,并证明如果将本体、框架和逻辑理论看作是3个范畴,则这些转换是这3个范畴之间的函子.这个结果保证了在NKI中,基于Horn逻辑程序的推理关于用本体和框架表示的知识库是正确的.     

具有多时间粒度的时态多值依赖及时态模式分解方法研究

一个好的数据库逻辑设计目标是消除数据冗余以及插入、删除和更新异常.对于时态数据库,通过具有多时间粒度的时态函数依赖约束对时态数据库进行规范化已有大量研究.基于时态函数依赖和多值依赖理论提出了多时间粒度约束的时态多值依赖(TMVD)等概念,并给出了时态多值依赖的推理规则,对其有效性、完备性进行了证明.由于包含有限个TMVD的TMVD集通常蕴含着无限个TMVD,给出了TMVD的有限推理规则,对其有效性、完备性进行了证明.最后,基于时态多值依赖集提出了时态第四范式,并给出了时态模式的T4NF的无损分解算法,对算法的可终止性、正确性进行了证明,并对时间复杂度进行了分析.     

Rule-based spreadsheet data transformation from arbitrary to relational tables

The paper discusses issues of rule-based data transformation from arbitrary spreadsheet tables to a canonical (relational) form. We present a novel table object model and rule-based language for table analysis and interpretation. The model is intended to represent a physical (cellular) and logical (semantic) structure of an arbitrary table in the transformation process. The language allows drawing up this process as consecutive steps of table understanding, i. e. recovering implicit semantics. Both are implemented in our tool for spreadsheet data canonicalization. The presented case study demonstrates the use of the tool for developing a task-specific rule-set to convert data from arbitrary tables of the same genre (government statistical websites) to flat file databases. The performance evaluation confirms the applicability of the implemented rule-set in accomplishing the stated objectives of the application.     

Unitary representations of the hyperfinite Heisenberg group and the logical extension methods in physics

In order to provide a general framework for applications of nonstandard analysis to quantum physics, the hyperfinite Heisenberg group, which is a finite Heisenberg group in the nonstandard universe, is formulated and its unitary representations are examined. The ordinary Schrödinger representation of the Heisenberg group is obtained by a suitable standardization of its internal representation. As an application, a nonstandard-analytical proof of noncommutative Parseval's identity based on the orthogonality relations for unitary representations of finite groups is shown. This attempt is placed in a general framework, called the logical extension methods in physics, which aims at the systematic applications of methods of foundations of mathematics to extending physical theories. The program and the achievement of the logical extension methods are explained in some detail.Dedicated to Professor Huzihiro Araki on his sixtieth birthday     

Model checking for action-based logics

A model checker is described that supports proving logical properties of concurrent systems. The logical properties can be described in different action-based logics (variants of Hennessy-Milner logic). The tools is based on the EMC model checker for the logic CTL. It therefore employs a set of translation functions from the considered logics to CTL, as well as a model translation function from labeled transition systems (models of the action-based logics) to Kripke structures (models for CTL). The obtained tool performs model checking in linear time complexity, and its correctness is guaranteed by the proof that the set of translation functions, coupled with the model translation function, preserves satisfiability of logical formulae.     

Design and analysis of a reconfigurable discrete pin tooling system for molding of three-dimensional free-form objects

This paper presents the design and analysis of a new reconfigurable tooling for the fabrication of three-dimensional (3D) free-form objects. The proposed reconfigurable tooling system comprises a set of matrices of a closely stacked discrete elements (i.e., pins) arranged to form a cavity in which a free-form object can be molded. By reconfiguring the pins, a single tool can be used in the place of multiple tools to produce different parts with the involvement of much lesser time and cost. The structural behavior of a reconfigurable mold tool under process conditions of thermoplastic molding is studied using a finite element method (FEM) based methodology. Various factors that would affect the tool behavior are identified and their effects are analyzed to optimally design a reconfigurable mold tool for a given set of process conditions. A prototype, open reconfigurable mold tool is developed to present the feasibility of the proposed tooling system. Several case studies and sample parts are also presented in this paper.     

A verification framework for spatio-temporal consistency language with CCSL as a specification language

The Spatio-Temporal Consistency Language(STeC)is a high-level modeling language that deals natively with spatio-temporal behaviour,i.e.,behaviour relating to certain locations and time.Such restriction by both locations and time is of first importance for some types of real-time systems.CCSL is a formal specification language based on logical clocks.It is used to describe some crucial safety properties for real-time systems,due to its powerful expressiveness of logical and chronometric time constraints.We consider a novel verification framework combining STeC and CCSL,with the advantages of addressing spatio-temporal consistency of system behaviour and easily expressing some crucial time constraints.We propose a theory combining these two languages and a method verifying CCSL properties in STeC models.We adopt UPPAAL as the model checking tool and give a simple example to illustrate how to carry out verification in our framework.     

<Emphasis FontCategory="SansSerif">VeriSiMPL</Emphasis> 2: An open-source software for the verification of max-plus-linear systems

This work presents a technique to generate finite abstractions of autonomous Max-Plus-Linear (MPL) systems, a class of discrete-event systems employed to characterize the dynamics of the timing related to the synchronization of successive events. Abstractions of MPL systems are derived as finite-state transition systems. A transition system is obtained first by partitioning the state space of the MPL system into finitely many regions and then by associating a unique state of the transition system to each partitioning region. Relations among the states of the transition system are then set up based on the underlying dynamical transitions between the corresponding partitioning regions of the MPL state space. In order to establish formal equivalences, the obtained finite abstractions are proven either to simulate or to bisimulate the original MPL system. The approach enables the study of general properties of the original MPL system formalized as logical specifications, by verifying them over the finite abstraction via model checking. The article presents a new, extended and improved implementation of a software tool (available online) for the discussed formal abstraction of MPL systems, and is tested on a numerical benchmark against a previous version.     

REASONING WITH BACKGROUND KNOWLEDGE–A THREE-LEVEL THEORY

We address the problem of reasoning in cases when knowledge bases containing background knowledge are understood not as sets of formulas (rules and facts) but as collections of partially ordered theories. In our system, the usual, two-part logical structures, consisting of a metalevel and an object level, are augmented by a third level–a referential level. The referential level is a partially ordered collection of theories; it encodes background knowledge. As usual, current situations are described on the object level, and the metalevel is a place for rules that can eliminate some of the models permitted by the object level and the referential level. As a logic of reasoning the system generalizes the standard model of a rational agent: deducing actions and deriving new information about the world from a logical theory–its knowledge base. It is a natural logical system in which priorities on the possible readings of predicates, not special rules of inference, are the main source of nonmonotonicity. We introduce a theory forming operator PT(x) to exploit the priorities, and we investigate its basic logical properties. Then we show how such a system can be augmented by metarules. Although this paper concentrates on basic logical properties of the new theory, this formalism has already been applied to model a number of natural language phenomena such as the notion of text coherence, Gricean maxims, vagueness, and a few others. The paper also briefly compares it with the model of background knowledge of CYC, as proposed by Lenat and Guha.     

数据库设计工具集DBTOOLS的设计

本文介绍的数据库设计工具集DBTOOLS包括扩充的E—R模型设计工具EERD、从E—R模型到关系模型转换工具ERTR、从DFD、DD到关系模型转换工具DDTR,DBTOOLS以自动转换和人工干预相结合的方式工作,提供对关系数据库概念结构设计和逻辑结构设计的支持,DBTOOLS的设计中强调语义信息的描述和运用,以及对数据库应用系统增量开发的支持。