• Title, Summary, Keyword: symbolic logic

### Variations and Series Expansions of the Symbolic Multiple-Valued Logic functions (기호 다치 논리함수와 그 변화 및 전개)

• 이성우;정환묵
• Journal of the Korean Institute of Telematics and Electronics
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• v.20 no.5
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• pp.1-7
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• 1983
• Generally, multiple-valued logic algebra is based on the number system of modulo-M. In this paper, characters a, b, c‥… each of them represents the independent state, are regarded as the elements of the symbolic multiple-valued logic. By using the set theory, the symbolic multiple - valued logic and their functions are defined. And Varation for the symbolic logic function due to the variation of a variable and their properties are suggested and analized. With these variations, the MacLaurin's and Taylor's Series expansions of the symbolic logic functions are proposed and proved.

### Adaptive Automata using Symbolic Multi-Valued Logic Function (기호 다치 논리 함수를 이용한 적응오토마타)

• 정환묵;손병성
• Journal of the Korean Institute of Intelligent Systems
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• v.6 no.4
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• pp.10-16
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• 1996
• In this paper, we construct the state table of the automata according to input, state, and change of state and transform that state table into symbolic multi-valued logic formula. Also, we propose an adaptive automata which adapts dynamically change of state aqording to the input string of automata by using the properties of derivative about the symbolic multi-valued logic function. And we analyze the properties of the adaptive automata.

### A Study on the Minimization of Fuzzy Rule Using Symbolic Multi-Valued Logic (기호다치논리를 이용한 Fuzzy Rule Minimization에 관한 연구)

• 김명순
• Journal of the Korea Society of Computer and Information
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• v.4 no.4
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• pp.1-8
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• 1999
• In the logic where we study the principle and method of human, the binary logic with the proposition which has one-valued property that it can be assigned the truth value 'truth'or 'false'. Although most of the traditional binary logic which was drawn by human includes fuzziness hard to deal with, the knowledge for expressing it is not precise and has less degree of credit. This study uses multi-valued logic in order to slove the problem above that .When compared with the data processing ability of the binary logic, Multi-valued logic has an at a high speed. Therefore the Inference can be possible by minimization multi-valued logic in stead of using the information stead of using the information system based on the symbolic binary logic.

### SymCSN : a Neuro-Symbolic Model for Flexible Knowledge Representation and Inference (SymCSN : 유연한 지식 표현 및 추론을 위한 기호-연결주의 모델)

• 노희섭;안홍섭;김명원
• Korean Journal of Cognitive Science
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• v.10 no.4
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• pp.71-83
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• 1999
• Conventional symbolic inference systems lack flexibility because they do not well reflect flexible semantic structure of knowledge and use symbolic logic for their basic inference mechanism. For solving this problem. we have recently proposed the 'Connectionist Semantic Network(CSN)' as a model for flexible knowledge representation and inference based on neural networks. The CSN is capable of carrying out both approximate reasoning and commonsense reasoning based on similarity and association. However. we have difficulties in representing general and structured high-level knowledge and variable binding using the connectionist framework of the CSN. In this paper. we propose a hybrid system called SymCSN(Symbolic CSN) that combines a symbolic module for representing general and structured high-level knowledge and a connectionist module for representing and learning low-level semantic structure Simulation results show that the SymCSN is a plausible model for human-like flexible knowledge representation and inference.

### A Historical Background of Mathematical Logic and $G{\ddot{o}}del$ (수리논리학의 역사적 배경과 괴델)

• Park, Chang-Kyun
• Journal for History of Mathematics
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• v.21 no.1
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• pp.17-28
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• 2008
• This Paper introduces a historical background of mathematical logic. Logic and mathematics were not developed dependently until the mid of the nineteenth century, when two streams of logic and mathematics came to form a river so that brought forth synergy effects. Since the mid-nineteenth century mathematization of logic were proceeded while attempts to reduce mathematics to logic were made. Against this background $G{\ddot{o}}del's$ proof shows the limitation of formalism by proving that there are true arithmetical propositions that are not provable.

### Symbolic Reliability Evaluation of Combinational Logic Circuit (조합논리회로의 기호적 신뢰도 계정)

• 오영환
• The Journal of Korean Institute of Communications and Information Sciences
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• v.7 no.1
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• pp.25-28
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• 1982
• A method for finding the symbolic reliability expressision of a conbinational logic circuit is presented. The evaluation of the probabilities of the outputs can be symbolically evaluated by the Boolean operation named sharp operation, provided that every input of such a circuit can be treated as random variables with values set(0, 1) and the output of a circuit can be represented by a Boolean sum of produt expression.

### An Empirical Study for Satisfiability Problems in Propositional Logic Using Set Covering Formulation (집합 피복 공식화를 이용한 명제논리의 만족도 문제에 대한 계산실험 연구)

• Cho, geon
• Journal of the Korean Operations Research and Management Science Society
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• v.27 no.4
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• pp.87-109
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• 2002
• A satisfiability problem in propositional logic is the problem of checking for the existence of a set of truth values of atomic prepositions that renders an input propositional formula true. This paper describes an empirical investigation of a particular integer programming approach, using the set covering model, to solve satisfiability problems. Our satisfiability engine, SETSAT, is a fully integrated, linear programming based, branch and bound method using various symbolic routines for the reduction of the logic formulas. SETSAT has been implemented in the integer programming shell MINTO which, in turn, uses the CPLEX linear programming system. The logic processing routines were written in C and integrated into the MINTO functions. The experiments were conducted on a benchmark set of satisfiability problems that were compiled at the University of Ulm in Germany. The computational results indicate that our approach is competitive with the state of the art.

### A study on implementation of optical high-speed multiplier using multiplier bit-pair recoding derived from Booth algorithm (Booth 알고리즘의 승수 비트-쌍 재코딩을 이용한 광곱셈기의 구현에 관한 연구)

• 조웅호;김종윤;노덕수;김수중
• Journal of the Korean Institute of Telematics and Electronics D
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• v.35D no.10
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• pp.107-115
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• 1998
• A multiplier bit-pair recoding technique derived from Booth algorithm is used as an effective method that can carry out a fast binary multiplication regardless of a sign of both multiplicand and multiplier. In this paper, we propose an implementation of an optical high-speed multiplier which consists of a symbolic substitution adder and an optical multiplication algorithm, which transforms and enhances the multiplier bit-pair recoding algorithm to be fit for optical characteristics. Specially, a symbolic substitution addition rules are coded with a dual-rail logic, and so the complement of the logic of the symbolic substitution adder is easily obtained with a shift operation because it is always present. We also construct the symbolic substitution system which makes superposition image by superimposing two shifted images in a serial connection and recognizes a reference image by feeding this superimposed image to a mask. Thus, the optical multiplier, which is compared with a typical system, is implemented to the smaller system by reducing the number of optical passive elements and the size of this system.

### The State CHDL Description and Symbolic Minimization Algorithm Development for State Machine Synthesizer (상태합성기 설계를 위한 상태 CHDL 기술 및 기호최소화 알고리듬개발)

• Kim, Hi-Seok
• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.5
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• pp.127-136
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• 1989
• A Symbolic cover Minimization Algorithm and State CHDL Description for Finite State Machine Synthesizer are Presented. State CHDL are used for design of PLA based finite state machine, also the symbolic cover minimization algorithms are based upon single cube containment and distance 1 merging algorithms. The procedure for state machine synthesizer has been applied to practical example, including traffic light controller by using Boulder Optimal Logic Design System.

### Die Leibniz' $bin\ddot{a}re$ Arithmetik und das I-Ching' Symbolik der Hexagramme vom Standpunkt der modernen Logik

• Bae, Sun-Bok
• Korean Journal of Logic
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• v.5 no.1
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• pp.147-157
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• 2001
• In this study I try to show some numerical analogy between Leibniz's binary system anc I-ching's symbolic system of duo rerum principia, imagines quator, octo figurae am 64 hexagrams. But, there is really a formal logical accordance in their symbolic foundations, on which are based especially the Wittgenstein's 16 truth-tables in his Tractatus-logico-philosophicus(5.101) am 16 hexagrams, as long as we interpret with the binary values 0 am 1, i.e. the Bi-Polarity, the logical tradition from J. Boole, G. Frege through B. Russell and AN. Whitehead to R. Wittgenstein. So, I argue that the historical and theoretical root of that tradition goes back to the debate between Bouvet and Leibniz about the mathematical structure of I-ching' symbols and the Leibnizian binary arithmetic. In the letter on 4. 11. 1701 from Peking to Leibniz, Bouvet wrote that the I-Ching's symbolism has an analogous structure with Leibniz's binary arithmetic. Corresponding to his suggestion, but without exact knowledge, in the letter of 2. January 1967 to the duke August in Braunschweig-Lueneburg-Wolfenbuettel had Leibniz shown already an original idea for the creation of the world with imago Dei which comes from binary progression, dark and light on water.