Higraphs: an overview of theory and application

This paper presents an overview of the established concepts of David Harel' s higraphs, to increase their visibility. Higraphs are a union of extended graph and extended set theory which allows the understandable definition of complex semantics, having a powerful intuitive cognitive nature. Viewing 'the big picture' is cited as an example of this understandability. A number of other applications of higraphs are given. Some novel applications are suggested, including the use of higraphs in analyzing business processes, graphical user interface specification, graph domain specification and executable graphs, A proposition is made that process graphs and data-entity state-transition higraphs are duals. Finally, a case is made for 'informal' higraphs in group communications

Set processing in a network environment

A combination of a local network, a mass storage system, and an autonomous set processor serving as a data/storage management machine is described. Its characteristics include: content-accessible data bases usable from all connected devices; efficient storage/access of large data bases; simple and direct programming with data manipulation and storage management handled by the set processor; simple data base design and entry from source representation to set processor representation with no predefinition necessary; capability available for user sort/order specification; significant reduction in tape/disk pack storage and mounts; flexible environment that allows upgrading hardware/software configuration without causing major interruptions in service; minimal traffic on data communications network; and improved central memory usage on large processors

Universics - a Common Formalization Framework for Brain Informatics and Semantic Web

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Simplification of rules extracted from neural networks

Artificial neural networks (ANNs) have been proven to be successful general machine learning techniques for, amongst others, pattern recognition and classification. Realworld problems in agriculture (soybean, tea), medicine (cancer, cardiology, mammograms) and finance (credit rating, stock market) are successfully solved using ANNs. ANNs model biological neural systems. A biological neural system consists of neurons interconnected through neural synapses. These neurons serve as information processing units. Synapses carrt information to the neurons, which then processes or responds to the data by sending a signal to the next level of neurons. Information is strengthened or lessened according to the sign ..and magnitude of the weight associated with the connection. An ANN consists of cell-like entities called units (also called artificial neurons) and weighted connections between these units referred to as links. ANNs can be viewed as a directed graph with weighted connections. An unit belongs to one of three groups: input, hidden or output. Input units receive the initial training patterns, which consist of input attributes and the associated target attributes, from the environment. Hidden units do not interact with the environment whereas output units presents the results to the environment. Hidden and output units compute an output ai which is a function f of the sum of its input weights w; multiplied by the output x; of the units j in the preceding layer, together with a bias term fh that acts as a threshold for the unit. The output ai for unit i with n input units is calculated as ai = f("f:,'J= 1 x;w; - 8i ). Training of the ANN is done by adapting the weight values for each unit via a gradient search. Given a set of input-target pairs, the ANN learns the functional relationship between the input and the target. A serious drawback of the neural network approach is the difficulty to determine why a particular conclusion was reached. This is due to the inherit 'black box' nature of the neural network approach. Neural networks rely on 'raw' training data to learn the relationships between the initial inputs and target outputs. Knowledge is encoded in a set of numeric weights and biases. Although this data driven aspect of neural network allows easy adjustments when change of environment or events occur, it is difficult to interpret numeric weights, making it difficult for humans to understand. Concepts represent by symbolic learning algorithms are intuitive and therefore easily understood by humans [Wnek 1994). One approach to understanding the representations formed by neural networks is to extract such symbolic rules from networks. Over the last few years, a number of rule extraction methods have been reported (Craven 1993, Fu 1994). There are some general assumptions that these algorithms adhere to. The first assumption that most rule extraction algorithms make, is that non-input units are either maximally active (activation near 1) or inactive (activation near 0). This Boolean valued activation is approximated by using the standard logistic activation function /(z) = 1/( 1 + e-•z ) and setting s 5.0. The use of the above function parameters guarantees that non-input units always have non-negative activations in the range [0,1). The second underlying premise of rule extraction is that each hidden and output unit implements a symbolic rule. The concept associated with each unit is the consequent of the rule, and certain subsets of the input units represent the antecedent of the rule. Rule extraction algorithms search for those combinations of input values to a particular hidden or output unit that results in it having an optimal (near-one) activation. Here, rule extraction methods exploit a very basic principle of biological neural networks. That is, if the sum of its weighted inputs exceeds a certain threshold, then the biological neuron fires [Fu 1994). This condition is satisfied when the sum of the weighted inputs exceeds the bias, where (E'Jiz,=::l w; > 9i)• It has been shown that most concepts described by humans usally can be expressed as production rules in disjunctive normal form (DNF) notation. Rules expressed in this notation are therefore highly comprehensible and intuitive. In addition, the number of production rules may be reduced and the structure thereof simplified by using propositional logic. A method that extracts production rules in DNF is presented [Viktor 1995). The basic idea of the method is the use of equivalence classes. Similarly weighted links are grouped into a cluster, the assumption being that individual weights do not have unique importance. Clustering considerably reduces the combinatorics of the method as opposed to previously reported approaches. Since the rules are in a logically manipulatable form, significant simplifications in the structure thereof can be obtained, yielding a highly reduced and comprehensible set of rules. Experimental results have shown that the accuracy of the extracted rules compare favourably with the CN2 [Clark 1989] and C4.5 [Quinlan 1993] symbolic rule extraction methods. The extracted rules are highly comprehensible and similar to those extracted by traditional symfiolic methods

Extending a set-theoretic implementation of Montague Semantics to accommodate n-ary transitive verbs.

Natural-language querying of databases remains an important and challenging area. Many approaches have been proposed over many years yet none of them has provided a comprehensive fully-compositional denotational semantics for a large sub-set of natural language, even for querying first-order non-intentional, non-modal, relational databases. One approach, which has made significant progress, is that which is based on Montague Semantics. Various researchers have helped to develop this approach and have demonstrated its viability. However, none have yet shown how to accommodate transitive verbs of arity greater than two. Our thesis is that existing approaches to the implementation of Montague Semantics in modern functional programming languages can be extended to solve this problem. This thesis is proven through the development of a compositional semantics for n-ary transitive verbs (n ≥ 2) and implementation in the Miranda programming environment. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2005 .R69. Source: Masters Abstracts International, Volume: 44-03, page: 1413. Thesis (M.Sc.)--University of Windsor (Canada), 2005

Fault Diagnosis of Car Engine by Using a Novel GA-Based Extension Recognition Method

Due to the passenger’s security, the recognized hidden faults in car engines are the most important work for a maintenance engineer, so they can regulate the engines to be safe and improve the reliability of automobile systems. In this paper, we will present a novel fault recognition method based on the genetic algorithm (GA) and the extension theory and also apply this method to the fault recognition of a practical car engine. The proposed recognition method has been tested on the Nissan Cefiro 2.0 engine and has also been compared to other traditional classification methods. Experimental results are of great effect regarding the hidden fault recognition of car engines, and the proposed method can also be applied to other industrial apparatus

Nominalism In Mathematics - Modality And Naturalism

I defend modal nominalism in philosophy of mathematics - under which quantification over mathematical ontology is replaced with various modal assertions - against two sources of resistance: that modal nominalists face difficulties justifying the modal assertions that figure in their theories, and that modal nominalism is incompatible with mathematical naturalism. Shapiro argues that modal nominalists invoke primitive modal concepts and that they are thereby unable to justify the various modal assertions that figure in their theories. The platonist, meanwhile, can appeal to the set-theoretic reduction of modality, and so can justify assertions about what is logically possible through an appeal to what exists in the set-theoretic hierarchy. In chapter one, I illustrate the modal involvement of the major modal nominalist views (Chihara\u27s Constructibility Theory, Field\u27s fictionalism, and Hellman\u27s Modal Structuralism). Chapter two provides an analysis of Shapiro\u27s criticism, and a partial response to it. A response is provided in full in chapter three, in which I argue that reducing modality does not provide a means for justifying modal assertions, vitiating the accusation that modal nominalists are particularly burdened by their inability to justify modal assertions. Chapter four discusses Burgess\u27s naturalistic objection that nominalism is unscientific. I argue that Burgess\u27s naturalism is inadequately resourced to expose nominalism (modal or otherwise) as unscientific in a way that would compel a naturalist to reject nominalism. I also argue that Burgess\u27s favored moderate platonism is also guilty of being unscientific. Chapter five discusses some objections derived from Maddy\u27s naturalism, one according to which modal nominalism fails to affirm or support mathematical method, and a second according to which modal nominalism fails to be contained or accommodated by mathematical method. Though both objections serve as evidence that modal nominalism is incompatible with Maddy\u27s naturalism, I argue that Maddy\u27s naturalism is implausibly strong and that modal nominalism is compatible with forms of naturalism that relax the stronger of Maddy\u27s naturalistic principles