Handling indefinite and maybe information in logical fuzzy relational databases

In this article, fuzzy set theory uses an extension of the classical logical relational database model. A logical fuzzy relational database model was developed with the aim of manipulating imprecise information and adding deduction capabilities to the database system. The essence of this work is the detailed discussion on fuzzy definite, fuzzy indefinite, and fuzzy maybe information and the development of an information theoretical approach of query evaluation on the logical fuzzy relational database. We define redundancies among fuzzy tuples and the operator of their removal. A complete set of fuzzy relational operations in relational algebra and the calculus of linguistically quantified propositions are included also. © 2004 Wiley Periodicals, Inc.     

Reasoning with propositional knowledge based on fuzzy neural logic

In this article, a new kind of reasoning for propositional knowledge, which is based on the fuzzy neural logic initialed by Teh, is introduced. A fundamental theorem is presented showing that any fuzzy neural logic network can be represented by operations: bounded sum, complement, and scalar product. Propositional calculus of fuzzy neural logic is also investigated. Linear programming problems risen from the propositional calculus of fuzzy neural logic show a great advantage in applying fuzzy neural logic to answer imprecise questions in knowledge-based systems. An example is reconsidered here to illustrate the theory. © 1996 John Wiley & Sons, Inc.     

An introduction to fuzzy answer set programming

In this paper we show how the concepts of answer set programming and fuzzy logic can be successfully combined into the single framework of fuzzy answer set programming (FASP). The framework offers the best of both worlds: from the answer set semantics, it inherits the truly declarative non-monotonic reasoning capabilities while, on the other hand, the notions from fuzzy logic in the framework allow it to step away from the sharp principles used in classical logic, e.g., that something is either completely true or completely false. As fuzzy logic gives the user great flexibility regarding the choice for the interpretation of the notions of negation, conjunction, disjunction and implication, the FASP framework is highly configurable and can, e.g., be tailored to any specific area of application. Finally, the presented framework turns out to be a proper extension of classical answer set programming, as we show, in contrast to other proposals in the literature, that there are only minor restrictions one has to demand on the fuzzy operations used, in order to be able to retrieve the classical semantics using FASP.     

Goals and Benchmarks for Automated Map Reasoning

Tarski–Givant’s map calculus is briefly reviewed, and a plan of research is outlined aimed at investigating applications of this ground equational formalism in the theorem-proving field. The main goal is to create synergy between first-order predicate calculus and the map calculus. Techniques for translating isolated sentences, as well as entire theories, from first-order logic into map calculus are designed, or in some cases simply brought nearer through the exercise of specifying properties of a few familiar structures (natural numbers, nested lists, finite sets, lattices). It is also highlighted to what extent a state-of-the-art theorem-prover for first-order logic, namely Otter, can be exploited not only to emulate, but also to reason about, map calculus. Issues regarding “safe" forms of map reasoning are singled out, in sight of possible generalizations to the database area.     

Logical-Probabilistic Calculus: A Tool for Studying the Reliability and Safety of Structurally Complex Systems

The concept of the probabilistic logic is briefly described as an extension of inductive logic. A clear distinction is made between the probabilistic logic and logical-probabilistic calculus—the branch of mathematics that defines the rules of computation and operation with two-valued (true and false) statements. The logical-probabilistic calculus is based on the algebra of logic and rules of substitution of logical arguments in functions of the algebra of logic by their truth probabilities, and logical operations by arithmetical operations.     

Evaluation of queries based on the extended relational calculi

An efficient database search algorithm is presented. Four major enhancements on the preceding works have been made. They are (1) relational calculus is extended to enable processing an arbitrary logical function defined on one or more relations, (2) a set of elementary operations which are similar to but are more efficient in processing compound search conditions than the relational algebra is used, (3) the target list processing is completely separated from the search process, and (4) sequential collation procedure is fully utilized to deal with conditions of a certain type defined on two or more relations. The algorithm is composed of two parts: syntactical transformation of the given extended relational calculus and the search execution. Various optimization issues are integrated into these two parts.     

A Temporal Logic for Supporting Historical Databases

Tackling data with gap-interval time is an important issue faced by the temporal database community. While a number of interval logics have been developed, less work has been reported on gap-interval time. To represent and handle data with time, a clause ‘when’ is generally added into each conventional operator so as to incorporate time dimension in temporal databases, which clause ‘when’ is really a temporal logical sentence. Unfortunately, though several temporal database models have dealt with data with gap-interval time, they still put interval calculus methods on gap-intervals. Certainly, it is inadequate to tackle data with gap-interval time using interval calculus methods in historical databases. Consequently, what temporal expressions are valid in the clause ‘when’ for tackling data with gap-interval time? Further, what temporal operations and relations can be used in the clause ‘when’? To solve these problems, a formal tool for supporting data with gap-interval time must be explored. For this reason, a gap-interval-based logic for historical databases is established in this paper. In particular, we discuss how to determine the temporal relationships after an event explodes. This can be used to describe the temporal forms of tuples splitting in historical databases. Received 2 February 1999 / Revised 9 May 1999 / Accepted in revised form 20 November 1999     

一个带有相似性关系的模糊逻辑

模糊集与模糊逻辑是处理模糊性与不确定性信息的重要数学工具,相似性关系是模糊集的一个基本概念。为了在模糊逻辑中集成相似性关系并考虑其模糊推理,提出了一个带有相似性关系的模糊逻辑,给出了其语法及语义描述,在模糊谓词逻辑情形下,讨论并证明了基于归结与调解方法的模糊推理的有关属性,考虑到许多定理证明器和问题解决系统均是基于否证法,证明了归结与调解方法对模糊谓词演算的反驳完备性定理。     

集合代数是经典命题演算形式系统的语义解释

经典命题演算形式系统(CPC)中的公式只是一些形式符号,其意义是由具体的解释给出的.逻辑代数和集合代数都是布尔代数,都是CPC的解释.集合代数是CPC的集合语义,其中对联结词的解释就是集合运算;对形式公式的解释就是集合函数;对逻辑蕴涵.逻辑等价的解释就是集合包含和集合相等=.标准概率逻辑是在标准概率空间上建立的逻辑体系,命题表示随机事件,随机事件是集合,概率空间中的事件域是集合代数,概率逻辑就是CPC集合语义的实际应用.CPC完全适用于概率命题演算.     

可分析集合、笛卡尔逻辑和命题的可推导性关系

本文在ZFC公理系统的基础上,首先提出可分析集合的概念且可表达为p={x|x∈p}。然后给出受囿变量的定义,引入笛卡尔逻辑以使逻辑的概念像算法的概念一样精确化而成为明确的数学对象,不仅足以适应代数和分析的要求,而且充分满足经典和非经典逻辑的需要,并探讨命题间的可推导性关系,包括:对立、排中、重言、归谬、反对、矛盾、存在、全称、独立、同一和不矛盾。进而,讨论一些逻辑运算和有关的逻辑问题,并进一步阐述可分析集合的几个基本关系和基本运算。     

Toward complex fuzzy logic

Complex fuzzy logic is a postulated logic system that is isomorphic to the complex fuzzy sets recently described in a previous paper. This concept is analogous to the many-valued logics that are isomorphic to type-1 fuzzy sets, commonly known as fuzzy logic. As with fuzzy logics, a complex fuzzy logic would be defined by particular choices of the conjunction, disjunction and complement operators. In this paper, an important assertion from a previous paper, that only the modulus of a complex fuzzy membership should be considered in set theoretic (or logical) operations, is examined. A more general mathematical formulation (the property of rotational invariance) is proposed for this assertion, and the impact of this property on the form of complex fuzzy logic operations is examined. All complex fuzzy logics based on the modulus of a vector are shown to be rotationally invariant. The case of complex fuzzy logics that are not rotationally invariant is examined using the framework of vector logic. A candidate conjunction operator was identified, and the existence of a dual disjunction was proven. Finally, a discussion on the possible applications of complex fuzzy logic focuses on the phenomenon of regularity as a possible fuzzification of stationarity.     

Formalizing the specification and execution of workflows using the event calculus

The event calculus is a logic programming formalism for representing events and their effects especially in database applications. This paper proposes the event calculus as a logic-based methodology for the specification and execution of workflows. It is shown that the control flow graph of a workflow specification can be expressed as a set of logical formulas and the event calculus can be used to specify the role of a workflow manager through a set of rules for the execution dependencies of activities. The proposed framework for a workflow manager maintains a history of events to control the execution of activities. The events are instructions to the workflow manager to coordinate the execution of activities. Based on the already occurred events, the workflow manager triggers new events to schedule new activities in accordance with the control flow graph of the workflow. The net effect is an alternative approach for defining a workflow engine whose operational semantics is naturally integrated with the operational semantics of a deductive database. Within this framework it is possible to model sequential and concurrent activities with or without synchronization. It is also possible to model agent assignment and execution of concurrent workflow instances. The paper, thus, contributes a logical perspective to the task of developing formalization for the workflow management systems.     

Complex fuzzy logic

A novel framework for logical reasoning, termed complex fuzzy logic, is presented in this paper. Complex fuzzy logic is a generalization of traditional fuzzy logic, based on complex fuzzy sets. In complex fuzzy logic, inference rules are constructed and "fired" in a manner that closely parallels traditional fuzzy logic. The novelty of complex fuzzy logic is that the sets used in the reasoning process are complex fuzzy sets, characterized by complex-valued membership functions. The range of these membership functions is extended from the traditional fuzzy range of [0,1] to the unit circle in the complex plane, thus providing a method for describing membership in a set in terms of a complex number. Several mathematical properties of complex fuzzy sets, which serve as a basis for the derivation of complex fuzzy logic, are reviewed in this paper. These properties include basic set theoretic operations on complex fuzzy sets - namely complex fuzzy union and intersection, complex fuzzy relations and their composition, and a novel form of set aggregation - vector aggregation. Complex fuzzy logic is designed to maintain the advantages of traditional fuzzy logic, while benefiting from the properties of complex numbers and complex fuzzy sets. The introduction of complex-valued grades of membership to the realm of fuzzy logic generates a framework with unique mathematical properties, and considerable potential for further research and application.     

VIREX and VRXQuery: interactive approach for visual querying of relational databases to produce XML

VIREX provides an interactive approach for querying and integrating relational databases to produce XML documents and the corresponding schemas. VIREX connects to each database specified by the user; analyzes the catalogue to derive an interactive diagram equivalent to the extended entity-relationship diagram; allows the user to display sample records from the tables in the database; allows the user to rename columns and relations by modifying directly the interactive diagram; facilitates the conversion of the relational database into XML; and derives the XML schema. VIREX works even when the catalogue of the relational database is missing; it extracts the required catalogue information by analyzing the database content. Further, VIREX supports VRXQuery, which is a visual naive-users-oriented query language that allows users to specify queries and define views directly on the interactive diagram as a sequence of mouse clicks with minimum keyboard input. The user is expected to interactively decide on certain factors to be considered in producing the XML result. Such factors include: 1) selecting the relations/attributes to be converted into XML; 2) specifying a predicate to be satisfied by the information to be converted into XML; 3) deciding on the order of nesting between the relations to be converted into XML; 4) ordering for the result. VRXQuery supports selection, projection, nesting/join, union, difference, and order-by. As the result of a query, VIREX displays on the screen the XML schema that satisfies the specified characteristics and generates colored (easy to read) XML document(s). Further, VIREX allows the user to display and review the SQL and XQuery equivalent to each query expressed in VRXQuery.     

An efficient posture recognition method using fuzzy logic

Computer-human interaction plays an important role in virtual reality. Glove-based input devices have many desirable features which make direct interactions between the user and the virtual world possible. However, due to the complexity of the human hand, recognising hand functions precisely and efficiently is not an easy task. Existing algorithms are either imprecise or computationally expensive, making them impractical to integrate with VR applications, which are usually very CPU intensive.In the problem of posture and gesture recognition, both the sample patterns stored in the database and the ones to be recognised may be imprecise. This kind of imprecise knowledge can be best dealt with using fuzzy logic. A fast and simple posture recognition method using fuzzy logic is presented in this paper. Our model consists of three components: the posture database, the classifier and the identifier. The classifier roughly classifies the sample postures before they are put into the posture database. The identifier compares an input posture with the records in the identified class and finds the right match efficiently. Fuzzy logic is applied in both the classification and identification processes to cope with imprecise data. The main goal of this method is to recognise hand functions in an accurate and efficient manner. The accuracy, efficiency and the noise tolerance of the model have been examined through a number of experiments.     

A modular package for efficient I/O operations

We present a package of FORTRAN modules to perform general and efficient I/O operations in external sort, bin sort and related environments. A partition of a user logical record of length IRLU into NREC records of length IRL is carried out when IRLU exceeds the maximum permissible record length for a given computer and file organization. Efficient random direct access to a file requires that IRL be a multiple of the smallest addressable unit on a disk. Overcoming implied DO lists in I/O statements becomes significant in tight memory environments. Corresponding gains in execution times are discussed.     

The order of merging operations for queries in inverted file systems

In inverted file systems, queries can be written as Boolean expressions of inverted attributes. In response to a query, the system accesses address lists associated with the attributes in the query, merges them, and selects those records that satisfy the search logic. In this paper we consider the minimization of the CPU time needed for the merging operation. The time can possibly be reduced by taking address lists that occur in several product terms as a common factor of these products. This means that the union operation must be performed before the intersection operation. We present formulas which can be used to decide whether the above method is advantageous. The time can also be reduced by choosing the order of intersection operations so that it takes into consideration the occurrences of the address lists in the products and the lengths of the address lists. For choosing the order of intersection operations we give a heuristic algorithm that minimizes the total time needed for intersections.     

归结与调解方法的有效性和完备性--基于扩充模糊逻辑

模糊集与模糊逻辑是处理大量存在的不确定性与模糊性信息的重要数学工具,在近似推理等领域有着广泛的应用。该文将王家兵等人提出的真值取在[0,1]区间上的带有相似性关系的模糊逻辑,扩充到很一般的与滋可比的有余完全分配格值逻辑中,将王家兵等人的许多结论进行了推广。首先对带有相似性关系的模糊逻辑的语义描述进行了扩充,然后讨论了在这种模糊推理中归结式与调解式的有效性,最后通过证明一个子句集在扩充模糊逻辑中的不可满足性与它在带有相等关系的二值逻辑中的不可满足性是等价的,得到了基于归结与调解方法对这种广义模糊演算的完备性。     

Linked-list visualization for debugging

Recent extensions to the VIPS debugger are described. In the original version of VIPS, visualization of linked structures was limited to very small lists or to selected portions of larger structures. The newer version of VIPS extends the original work by adding multiple levels of browsers, letting users interactively identify sublists of interest. Animation facilities support the visualization of dynamic list operations simultaneously among the various views. A preliminary evaluation shows that VIPS helps users find bugs about 30% faster using about 25% fewer debugging commands than Dbxtool, and it can display even a large linked list within about one second