Information Gaps as Communication Needs: A New Semantic Foundation for Some Non-Classical Logics

Semantics connected to some information based metaphor are well-known in logic literature: a paradigmatic example is Kripke semantic for Intuitionistic Logic. In this paper we start from the concrete problem of providing suitable logic-algebraic models for the calculus of attribute dependencies in Formal Contexts with information gaps and we obtain an intuitive model based on the notion of passage of information showing that Kleene algebras, semi-simple Nelson algebras, three-valued ukasiewicz algebras and Post algebras of order three are, in a sense, naturally and directly connected to partially defined information systems. In this way wecan provide for these logic-algebraic structures a raison dêetre different from the original motivations concerning, for instance, computability theory.     

Comparative complexity of the representation of languages by probabilistic automata

We analyze the effect of the degree of isolation of a cut point on the number of states P(U, ) of a probabilistic automaton representing the language U. We give an example of a language Uⁿ consisting of words of length n such that there exist numbers < for which P(Uⁿ, )/P(Uⁿ, )0 as n.Translated from Kibernetika, No. 3, pp. 21–25, May–June, 1989.     

Two and three-quarter dimensional meshing facilitators

This paper presents generated enhancements for robust two and three-quarter dimensional meshing, including: (1) automated interval assignment by integer programming for submapped surfaces and volumes, (2) surface submapping, and (3) volume submapping. An introduction to the simplex method, an optimization technique of integer programming, is presented. Simplification of complex geometry is required for the formulation of the integer programming problem. A method of i-j unfolding is defined which explains how irregular geometry can be realigned into a simplified form that is suitable for submap interval assignment solutions. Also presented is the processes by which submapping eliminates the decomposition of surface geometry, through a pseudodecomposition process, producing suitable mapped meshes. The process of submapping involves the creation of interpolated virtual edges, user defined vertex types and i-j-k space traversals. The creation of interpolated virtual edges is the method by which submapping automatically subdivides surface geometry. The interpolated virtual edge is formulated according to an interpolation scheme using the node discretization of curves on the surface. User defined vertex types allow direct user control of surface decomposition and interval assignment by modifying i-j-k space traversals. Volume submapping takes the geometry decomposition to a higher level by using mapped virtual surfaces to eliminate decomposition of complex volumes.     

Fuzzy measurement in the Mishnah and the Talmud

I discuss the attitude of Jewish law sources from the 2nd–:5th centuries to the imprecision of measurement. I review a problem that the Talmud refers to, somewhat obscurely, as impossible reduction. This problem arises when a legal rule specifies an object by referring to a maximized (or minimized) measurement function, e.g., when a rule applies to the largest part of a divided whole, or to the first incidence that occurs, etc. A problem that is often mentioned is whether there might be hypothetical situations involving more than one maximal (or minimal) value of the relevant measurement and, given such situations, what is the pertinent legal rule. Presumption of simultaneous occurrences or equally measured values are also a source of embarrassment to modern legal systems, in situations exemplified in the paper, where law determines a preference based on measured values. I contend that the Talmudic sources discussing the problem of impossible reduction were guided by primitive insights compatible with fuzzy logic presentation of the inevitable uncertainty involved in measurement. I maintain that fuzzy models of data are compatible with a positivistic epistemology, which refuses to assume any precision in the extra-conscious world that may not be captured by observation and measurement. I therefore propose this view as the preferred interpretation of the Talmudic notion of impossible reduction. Attributing a fuzzy world view to the Talmudic authorities is meant not only to increase our understanding of the Talmud but, in so doing, also to demonstrate that fuzzy notions are entrenched in our practical reasoning. If Talmudic sages did indeed conceive the results of measurements in terms of fuzzy numbers, then equality between the results of measurements had to be more complicated than crisp equations. The problem of impossible reduction could lie in fuzzy sets with an empty core or whose membership functions were only partly congruent. Reduction is impossible may thus be reconstructed as there is no core to the intersection of two measures. I describe Dirichlet maps for fuzzy measurements of distance as a rough partition of the universe, where for any region A there may be a non-empty set of - _A (upper approximation minus lower approximation), where the problem of impossible reduction applies. This model may easily be combined with probabilistic extention. The possibility of adopting practical decision standards based on -cuts (and therefore applying interval analysis to fuzzy equations) is discussed in this context. I propose to characterize the uncertainty that was presumably capped by the old sages as U-uncertainty, defined, for a non-empty fuzzy set A on the set of real numbers, whose -cuts are intervals of real numbers, as U(A) = 1/h(A) ₀ ^h(A) log [1+(A)]d, where h(A) is the largest membership value obtained by any element of A and (A) is the measure of the -cut of A defined by the Lebesge integral of its characteristic function.     

On Some Alleged Misconceptions about Fuzzy Logic

Entemann (2002) defends fuzzy logic by pointing to what he calls misconceptions concerning fuzzy logic. However, some of these ;misconceptions are in fact truths, and it is Entemann who has the misconceptions. The present article points to mistakes made by Entemann in three different areas. It closes with a discussion of what sort of general considerations it would take to motivate fuzzy logic.     

A decision support tool for the diagnosis of breast cancer based upon Fuzzy ARTMAP

This paper presents research into the application of the fuzzy ARTMAP neural network model to the diagnosis of cancer from fine-needle aspirates of the breast. Trained fuzzy ARTMAP networks are differently pruned so as to maximise accuracy, sensitivity and specificity. The differently pruned networks are then employed in a cascade of networks intended to separate cases into certain and suspicious classes. This mimics the predictive behaviour of a human pathologist. The fuzzy ARTMAP model also provides symbolic rule extraction facilities and the validity of the derived rules for this domain is discussed. Additionally, results are provided showing the effects upon network performance of different input features and different observers. The implications of the findings are discussed.     

Rigid model-based fuzzy control of flexible-joint manipulators

This paper considers the application of fuzzy control to achieve global trajectory tracking and active damping of flexible-joint manipulators. A reasonable approach based on the combined computed torque control using rigid robot model and fuzzy control is suggested for flexible-joint manipulators. Sets of four input variables — one output variable fuzzy control rules for each actuator respectively, are suggested for the perturbation control. The simulation results show that the transient performance and steady-state accuracy are near those of the feedback linearization approach. The simulation results with payload or joint stiffness variation for the single-link case are also shown to demonstrate the robustness of the control law.     

Application of artificial neural network and fuzzy logic in a case-based system for initial process parameter setting of injection molding

Determination of initial process meters for injection molding is a highly skilled job and based on skilled operators know-how and intuitive sense acquired through long-term experience rather than a theoretical and analytical approach. Facing with the global competition, the current trial-and-error practice becomes inadequate. In this paper, application of artificial neural network and fuzzy logic in a case-based system for initial process meter setting of injection molding is described. Artificial neural network was introduced in the case adaptation while fuzzy logic was employed in the case indexing and similarity analysis. A computer-aided system for the determination of initial process meter setting for injection molding based on the proposed techniques was developed and validated in a simulation environment. The preliminary validation tests of the system have indicated that the system can determine a set of initial process meters for injection molding quickly without relying on experienced molding personnel, from which good quality molded parts can be produced.     

A predicate transformer for the progress property ‘to-always’

The temporal property to-always has been proposed for specifying progress properties of concurrent programs. Although the to-always properties are a subset of the leads-to properties for a given program, to-always has more convenient proof rules and in some cases more accurately describes the desired system behavior. In this paper, we give a predicate transformerwta, derive some of its properties, and use it to define to-always. Proof rules for to-always are derived from the properties ofwta. We conclude by briefly describing two application areas, nondeterministic data flow networks and self-stabilizing systems where to-always properties are useful.     

Lattice Image Processing: A Unification of Morphological and Fuzzy Algebraic Systems

This paper explores some aspects of the algebraic theory of mathematical morphology from the viewpoints of minimax algebra and translation-invariant systems and extends them to a more general algebraic structure that includes generalized Minkowski operators and lattice fuzzy image operators. This algebraic structure is based on signal spaces that combine the sup-inf lattice structure with a scalar semi-ring arithmetic that possesses generalized additions and -multiplications. A unified analysis is developed for: (i) representations of translation-invariant operators compatible with these generalized algebraic structures as nonlinear sup- convolutions, and (ii) kernel representations of increasing translation-invariant operators as suprema of erosion-like nonlinear convolutions by kernel elements. The theoretical results of this paper develop foundations for unifying large classes of nonlinear translation-invariant image and signal processing systems of the max or min type. The envisioned applications lie in the broad intersection of mathematical morphology, minimax signal algebra and fuzzy logic.Petros Maragos received the Diploma degree in electrical engineering from the National Technical University of Athens in 1980, and the M.Sc.E.E. and Ph.D. degrees from Georgia Tech, Atlanta, USA, in 1982 and 1985.In 1985 he joined the faculty of the Division of Applied Sciences at Harvard University, Cambridge, Massachusetts, where heworked for 8 years as professor of electrical engineering, affiliated with the interdisciplinary Harvard Robotics Lab. He has also been a consultant to several industry research groups including Xeroxs research on document image analysis. In 1993, he joined the faculty of the School of Electrical and Computer Engineering at Georgia Tech. During parts of 1996-98 he was on academic leave working as a senior researcher at the Institute for Language and Speech Processing in Athens. In 1998, he joined the faculty of the National Technical University of Athens where he is currently working as professor of electrical and computer engineering. His current research and teaching interests include the general areas of signal processing, systems theory, pattern recognition, and their applications to image processing and computer vision, and computer speech processing and recognition.He has served as associate editor for the IEEE Trans. on Acoustics, Speech, and Signal Processing, editorial board member for the Journal of Visual Communications and Image Representation, and guest editor for the IEEE Trans. on Image Processing; general chairman for the 1992 SPIE Conference on Visual Communications and Image Processing, and co-chairman for the 1996 International Symposium on Mathematical Morphology; member of two IEEE DSP committees; and president of the International Society for Mathematical Morphology.Dr. Maragos research work has received several awards, including: a 1987 US National Science Foundation Presidential Young Investigator Award; the 1988 IEEE Signal Processing Societys Paper Award for the paper Morphological Filters; the 1994 IEEE Signal Processing Societys Senior Award and the 1995 IEEE Baker Award for the paper Energy Separation in Signal Modulations with Application to Speech Analysis; and the 1996 Pattern Recognition Societys Honorable Mention Award for the paper Min-Max Classifiers. In 1995, he was elected Fellow of IEEE for his contributions to the theory and applications of nonlinear signal processing systems.     

Neuro-fuzzy approach for development of new neuron model

The training time of ANN depends on size of ANN (i.e. number of hidden layers and number of neurons in each layer), size of training data, their normalization range and type of mapping of training patterns (like X–Y, X–Y, X–Y and X–Y), error functions and learning algorithms. The efforts have been done in past to reduce training time of ANN by selection of an optimal network and modification in learning algorithms. In this paper, an attempt has been made to develop a new neuron model using neuro-fuzzy approach to overcome the problems of ANN incorporating the features of fuzzy systems at a neuron level. Fuzzifying the neuron structure, which incorporates the features of simple neuron as well as high order neuron, has used this synergetic approach.     

Women's voice: The case of nursing information systems

This paper looks at the cultural transformation of nursing. It argues that introducing computers in a female occupation is not simply a case of imposing male technology on female care-oriented practices and values. In order to understand current changes of nursing practice, three points of view have to be simultaneously kept in focus: 1) the differences between women's interests and ambitions; 2) the readings of a technology that have already been established through previous examples of design and use (in hospitals up to date primarily for the purpose of establishing discipline and management control); and 3) the social practices that dominate a field of work (in the case of health work the already technology-driven cure aspect).     

An Algebraic Approach to Propositional Fuzzy Logic

We investigate the variety corresponding to a logic (introduced in Esteva and Godo, 1998, and called there), which is the combination of ukasiewicz Logic and Product Logic, and in which Gödel Logic is interpretable. We present an alternative (and slightly simpler) axiomatization of such variety. We also investigate the variety, called the variety of algebras, corresponding to the logic obtained from by the adding of a constant and of a defining axiom for one half. We also connect algebras with structures, called f-semifields, arising from the theory of lattice-ordered rings, and prove that every algebra can be regarded as a structure whose domain is the interval [0, 1] of an f-semifield , and whose operations are the truncations of the operations of to [0, 1]. We prove that such a structure is uniquely determined by up to isomorphism, and we establish an equivalence between the category of algebras and that of f-semifields.     

On the Characteristics of Growing Cell Structures (GCS) Neural Network

In this paper, a self-developing neural network model, namely the Growing Cell Structures (GCS) is characterized. In GCS each node (or cell) is associated with a local resource counter (t). We show that GCS has the conservation property by which the summation of all resource counters always equals , thereby s is the increment added to (t) of the wining node after each input presentation and (0 < < 1.0) is the forgetting (i.e., decay) factor applied to (t) of non-wining nodes. The conservation property provides an insight into how GCS can maximize information entropy. The property is also employed to unveil the chain-reaction effect and race-condition which can greatly influence the performance of GCS. We show that GCS can perform better in terms of equi-probable criterion if the resource counters are decayed by a smaller .     

The growth of configurations

The transition ruleF of a cellular automaton may sometimes be regarded as a rule of growth of a crystal from a seed. A study is made of the iterates,F,F ² .For certain one-dimensional growth rules, the limiting shapes of the crystals are computed, and an asymptotic formula for the size of the crystal as a function of time is obtained.     

New,Faster Algorithms for Supervised Competitive Learning: Counterpropagation and Adaptive-Resonance Functionality

Hecht-Nielsen's counterpropagation networks often learn to associate input and output patterns more quickly than backpropagation networks. But simple competitive learning cannot separate closely spaced input patterns without adaptive-resonance-like (ART) functionality which prevents neighboring patterns from stealing each other's templates. We demonstrate pseudo-ART functionality with a new, simple, and very fast algorithm which requires no pattern normalization at all. Competition can be based on either Euclidean or L1-norm matching. In the latter case, the new algorithm emulates fuzzy ART. We apply the pseudo-ART scheme to several new types of counterpropagation networks, including one based on competition among combined input/output patterns, and discuss application with and without noise.     

Relevant logic programming

In this paper we present a fragment of (positive) relevant logic which can be computed by a straightforward extension to SLD resolution while allowing full nesting of implications. These two requirements lead quite naturally to a fragment in which the major feature is an ambiguous user-level conjunction which is interpreted intensionally in query positions and extensionally in assertion positions. These restrictions allow a simple and efficient extension to SLD resolution (and more particularly, the PROLOG evaluation scheme) with quite minor loss in expressive power.     

Semantic analysis in XTRA,an English — Chinese machine translation system

This paper concerns the resolution of lexical ambiguity in a machine translation environment. We describe the integration of principles of selection restrictions. Preference Semantics, and intelligent relaxation of constraints in handling lexical ambiguity. The approach differs from many previous MT systems in that it is more powerful than brute force systems, while more realistic than systems that assume a large degree of coded encyclopedia information for full understanding.     

Query answering via cooperative data inference

This paper proposes the use of accessible information (data/knowledge) to infer inaccessible data in a distributed database system. Inference rules are extracted from databases by means of knowledge discovery techniques. These rules can derive inaccessible data due to a site failure or network partition in a distributed system. Such query answering requires combining incomplete and partial information from multiple sources. The derived answer may be exact or approximate. Our inference process involves two phases to reason with reconstructed information. One phase involves using local rules to infer inaccessible data. A second phase involves merging information from different sites. We shall call such reasoning processes cooperative data inference. Since the derived answer may be incomplete, new algebraic tools are developed for supporting operations on incomplete information. A weak criterion called toleration is introduced for evaluating the inferred results. The conditions that assure the correctness of combining partial results, known as sound inference paths, are developed. A solution is presented for terminating an iterative reasoning process on derived data from multiple knowledge sources. The proposed approach has been implemented on a cooperative distributed database testbed, CoBase, at UCLA. The experimental results validate the feasibility of this proposed concept and can significantly improve the availability of distributed knowledge base/database systems.List of notation Mapping - --< Logical implication - = Symbolic equality - ==< Inference path - Satisfaction - Toleration - Undefined (does not exist) - Variable-null (may or may not exist) - ^* Subtuple relationship - ^* s-membership - s-containment - Open subtuple - Open s-membership - Open s-containment - _P Open base - P Program - I Interpretation - DIP Data inference program - t Tuples - R Relations - Ø Empty interpretation - Open s-union - Open s-interpretation - Set of mapping from the set of objects to the set of closed objects - W Set of attributes - _W Set of sound inference paths on the set of attributes W - Set of relational schemas in a DB that satisfy MVD - ⁺ Range closure of W wrt      

A geometric view of parametric linear programming

We present a new definition of optimality intervals for the parametric right-hand side linear programming (parametric RHS LP) Problem () = min{c ^t x¦Ax =b + ¯b,x 0}. We then show that an optimality interval consists either of a breakpoint or the open interval between two consecutive breakpoints of the continuous piecewise linear convex function (). As a consequence, the optimality intervals form a partition of the closed interval {; ¦()¦ < }. Based on these optimality intervals, we also introduce an algorithm for solving the parametric RHS LP problem which requires an LP solver as a subroutine. If a polynomial-time LP solver is used to implement this subroutine, we obtain a substantial improvement on the complexity of those parametric RHS LP instances which exhibit degeneracy. When the number of breakpoints of () is polynomial in terms of the size of the parametric problem, we show that the latter can be solved in polynomial time.This research was partially funded by the United States Navy-Office of Naval Research under Contract N00014-87-K-0202. Its financial support is gratefully acknowledged.