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A general description of a continuous (‐valued) logic is given, basic operations of the logic are defined, and some problems and particulars of their solutions are discussed. First, we define algebra of continuous logic and enumerate its basic unary, binary and ternary functions. All laws of continuous logic are compared with laws of discrete binary logic. We discuss how to enumerate all functions of continuous logic with specified number of variables and how to represent the functions in a standard form. Procedures of minimization of continuous logical functions and their decomposition into the functions with less clarity are exploited. The procedures are compared with their counterparts from binary logic. We also tackle problems of analysis and synthesis of continuous logical functions, and show that the problem of synthesis may not have a solution. Basics of differential and integral calculus are applied to continuous valued logic. We demonstrate that any continuous logical function has the points where a derivative does not exist. At the end of the paper we briefly discuss an incompleteness problem of continuous logic, application of continuous logic in mathematics, engineering and economy, give examples, draw a perspective of further development and supply extensive bibliography of Russian works in the field.
There have been several document ranking methods to calculate the conceptual distance or closeness between a Boolean query and a document. Though they provide good…
There have been several document ranking methods to calculate the conceptual distance or closeness between a Boolean query and a document. Though they provide good retrieval effectiveness in many cases, they do not support effective weighting schemes for queries and documents and also have several problems resulting from inappropriate evaluation of Boolean operators. We propose a new method called Knowledge‐Based Extended Boolean Model (kb‐ebm) in which Salton's extended Boolean model is incorporated. kb‐ebm evaluates weighted queries and documents effectively, and avoids the problems of the previous methods. kb‐ebm provides high quality document rankings by using term dependence information from is‐a hierarchies The performance experiments show that the proposed method closely simulates human behaviour.
Malaria is one of the most sinister life-threatening disease and generally transmitted by the bite of an Anopheles mosquito which was infected. These mosquitoes carry the…
Malaria is one of the most sinister life-threatening disease and generally transmitted by the bite of an Anopheles mosquito which was infected. These mosquitoes carry the Plasmodium parasite. Worldwide risk of malaria thread is very hard to deal, because of extreme temperature and climate changes which lead to uncontrolled changes in the mosquito population, as many deaths from malaria occur outside the healthcare system and other infections might be misdiagnosed as malaria unless a diagnostic test is done. The purpose of this study is creating a system which is early diagnosing malaria for settlements adequate healthcare units and non-immune travellers.
In this study’s system, the authors developed a new medical expert system (MES) process using the decreased rule base to detect malaria. The authors’ purpose was to successfully identify the illness by taking all symptoms of malaria into consideration in the MES (six basic signs, 64 different conditions). In the proposed MES process, in place of inspecting all the malaria-related signs, the authors used the decreased rule bases.
So as to take the lessen decreased bases, Boolean functions are used in a two-level simplification method. Using this method, decreased cases were evaluated by taking six symptoms of malaria into account instead of assessing 64 individual conditions.
The system can be used in diagnosis of asthma and chronic obstructive respiratory disease.
The system can be used in absence of adequate healthcare units. Thus, malaria can be diagnosed early.
The authors hope that the system they have developed will be useful for settlements in the absence of adequate healthcare units and non-immune travellers.
Specialist physicians, specialist nurses and personnel in the intensive care unit (ICU) work to treat patients. Compared with other hospital units, ICUs are full-fledged…
Specialist physicians, specialist nurses and personnel in the intensive care unit (ICU) work to treat patients. Compared with other hospital units, ICUs are full-fledged and provide 24-h services. However, patients are admitted to this unit because of conditions such as severe trauma, organ failure or dysfunction and poisoning. The life expectancy of such patients is considerably low.
This study developed a reduced rule-based expert system to determine life expectancy. The purpose of this study is to determine the life expectancy of patients using ten variables. The rules were determined by evaluating 210 = 1,024 results. These rules were minimized using Boolean rules for simplification.
Conclusions were drawn by evaluating the minimized cases rather than evaluating 1,024 different cases. ICU patients were evaluated using this method, and the mean success rate was 63.75 per cent.
No rule-based expert system has been designed to determine the death risks of patients in the ICU.
Boolean algebra, Karnaugh map method and Quine‐McClusky algorithm are usually the tools used for minimizing logic functions using gates. However, with the advent of IC chips, the criteria for implementing a low‐cost circuit have been changed from logic gate reduction to IC chip reduction. In this paper, the IC chip reduction problem is systematically analyzed and illustrated by examples. More specifically, the direct mapping method, the IC chip diagram, the IC chip usage table, the reduced IC chip usage table and the reduced IC chip diagram are created and used for IC chip reduction. The reduction process is illustrated step by step with examples. In addition, six substitution rules for reducing the IC chip usage table are also presented. The IC chip reduction problem is both theoretically challenging and practically useful. The results may have useful applications in picture description reduction, picture semantic network reduction as well as in other related areas. It illustrates the effectiveness of a cybernetic approach.
This paper discusses a knowledge based information retrieval model with hierarchical thesaurus. The model computes the conceptual distance between a query and an object…
This paper discusses a knowledge based information retrieval model with hierarchical thesaurus. The model computes the conceptual distance between a query and an object and both are indexed with weighted terms from a hierarchical thesaurus. The hierarchical thesaurus is represented by a hierarchical‐concept graph (HCG) in which nodes represent concepts and directed edges represent generalisation relationships. Rada et al. have developed a similar model. However, their model considered only a binary indexing scheme and revealed some counter‐intuitive results. Our proposed model extends theirs by allowing the index term and the edge of the HCG to be weighted. A new concept mapping method is devised to overcome Rada's counter‐intuitive results. In addition, a scheme for allowing Boolean operators in user queries is provided with a formula for computing conceptual distance from negated index terms. Experimental results have shown that our model simulates human performance more closely than Rada's model.
The L‐map method is an innovative method for sequential machine state minimization. More specifically, the L‐map method consists of five steps. This method uses a portion…
The L‐map method is an innovative method for sequential machine state minimization. More specifically, the L‐map method consists of five steps. This method uses a portion of the partitioning method (step 1), and a portion of the implication table method (step 4). Steps 2 (eliminate singleton blocks), 3 (order non‐singleton blocks) and 5 (process the block implication table cells) are developed in this paper. The resultant method is more effective than both the partitioning method and the implication table method. The L‐map method is best illustrated by examples. In addition, 11 theorems are proven with illustrative examples. The advantages of this method over the partitioning method and the implication table method are stated. Furthermore, an algorithm which has four steps for finding the shortest input sequences for separating all pairs of distinguishable states using the L‐map method is developed. Illustrative examples are given to demonstrate this algorithm. The results obtained in this may have useful applications in logic design, computer design, as well as VLSI design.