• Title/Summary/Keyword: modal logic

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Constructivist interpretation on the modal logic (양상 논리에 대한 구성주의적 해석)

  • Eun, Eun-suk
    • Journal of Korean Philosophical Society
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    • v.116
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    • pp.257-280
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    • 2010
  • I try to formalize the system of modal logic and interpret it in view of constructivism through this study. As to the meaning of a sentence, as we saw, Frege endorsed extensions in view of the fact that they are enough to provide for a compositional account for truth, in particular that (1) the assignment of extensions to expressions is compositional ; (2) the assignment of extensions to sentences coincides with the assignment of truth values. But nobody would be willing to admit that a truth value is what a sentence means and that consequently all true sentences are synonymous. So, if what we are after is meaning in the intuitive sense, then extensions would not do. This consideration has later become the point of departure of modal and intensional semantics. So, it is clear that the language of modal logic do not allow for an extensional interpretation. ${\square}$ is syntactically on a par with ${\vdash}$, hence within the extensional framework it would have to denote a unary truth function. This means that if modal logic is to be interpreted, we need a semantics which is not extensional. The first attempt to build a feasible intensional semantics was presented by Saul Kripke. He came to the conclusion that we must let sentences denote not truth values, but rather subsets of a given set. He called elements of the underlying set possible world. Hence each sentence is taken to denote the set of those possible world in which it is true. This lets us explicate necessity as 'truth in every possible world' and possibility as 'truth in at least one possible world'. But it is clear that the system of modal logic is not only an enlargement of propositional logic, as long as the former contains the new symbols, but that it is of an other nature. In fact, the modal logic is intensional, in that the operators do not determine the functions of truth any more. But this new element is not given a priori, but a posteriori from construction by logicist.

A Study on Implementation of Model Checking Program for Verifying LTS Specification (LTS 명세 검증을 위한 모델 검증기 개발)

  • Park, Yong-Bum;Kim, Tae-Gyun;Kim, Sung-Un
    • The Transactions of the Korea Information Processing Society
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    • v.5 no.4
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    • pp.995-1004
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    • 1998
  • This paper presents an implementation of model checking tool for LTS process specification, which checks deadlock, livelock and reachability for the state and action. The implemented formal checker using modal mu-calculus is able to verify whether properties expressed in modal logic are true on specifications. We prove experimentally that it is powerful to check, safety and liveness for the state and action on LTS. The tool is implemented by $C^{++}$ language and runs on IBM PC under Windows NT.

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Yagisawa on Peacocke and van Inwagen

  • Kim, Seahwa
    • Korean Journal of Logic
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    • v.16 no.1
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    • pp.45-59
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    • 2013
  • In his book Worlds and Individuals: Possible and Otherwise, Takashi Yagisawa Yagisawa argues that his own theory is better than Lewis's theory by showing that his own theory can deal with important objections to modal realism more successfully than Lewis's. In particular, Yagisawa claims that by adopting modal tenses, he can respond to many important objections to modal realism in a uniform way. In this paper, I argue that Lewis can also successfully respond to Peacocke's objection in an exactly parallel way to Yagisawa's by distinguishing existence at the actual world from existence at other possible worlds and that Yagisawa's response to van Inwagen's objection does not succeed. I conclude that Yagisawa fails to show that his own theory is better than Lewis's.

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The Extension of BML Specification including Modal Logic (양상논리를 포함한 BML 스펙 확장)

  • Kim, Seon-Tae;Kim, Je-Min;Park, Joon-Seok;Yoo, Won-Hee
    • Proceedings of the Korea Information Processing Society Conference
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    • pp.265-268
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    • 2012
  • 검증에 사용하는 명세는 대부분 1차 술어 논리(First Order Logic)로 이루어져 있다. 1차 술어 논리가 자연언어 대부분을 표현하지만 표현하지 못하는 부분도 존재한다. 이를 해결하기위해 양상논리(Modal Logic)를 추가한 명세방법이 존재하지만 간접적인 방법으로만 존재할 뿐 이다. 본 논문에서는, 양상논리를 이용한 명세의 직접적인 표현을 위해 BML(Bytecode Modeling Language)을 확장한다. 이를 통해, 명세정보 표현의 정확성을 향상시킨다.

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The extension of BIRS to Translate the BML with Modal Logic (양상논리를 포함한 BML 변환을 위한 BIRS의 확장)

  • Lee, sang-hyup;Kim, seon-tae;Kim, je-min;Park, joon-seok;Yoo, weon-hee
    • Proceedings of the Korea Contents Association Conference
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    • pp.287-288
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    • 2012
  • 프로그램의 정적 검증을 위한 명세는 1차 술어 논리(First Order Logic)가 주로 사용된다. 하지만 1차 술어 논리가 모든 정보를 표현할 수가 없기에 이를 보완하기위해 양상논리(Modal Logic)를 사용할 수가 있다. 정적 프로그램 검증을 위해 양상 논리를 이용하여 확장된 BML(Bytecode Modeling Language)은 BIRS로 변환 되어야 한다. 본 논문에서는 확장된 BML을 중간 표현 언어인 BIRS(Bytecode Intermediate Representation Specification)로 표현하기 위하여 BIRS 문법을 확장한다.

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G$\ddot{o}$del's Mathematical Proof of the Existence of God (신의 존재에 대한 괴델의 수학적 증명)

  • Hyun, Woo-Sik
    • Journal for History of Mathematics
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    • v.23 no.1
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    • pp.79-88
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    • 2010
  • G$\ddot{o}$del's proof attempts to establish the existence of God by the definition that God is a being having all positive properties. The proof uses here second order modal logic system $S_5$ with the axiom ${\diamondsuit}{\Box}p{\rightarrow}{\Box}p$. We review the G$\ddot{o}$del's own version and prove his ontological theorems.

Soft Computing as a Methodology to Risk Engineering

  • Miyamoto Sadaaki
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • pp.3-6
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    • 2006
  • Methods for risk engineering is a bundle of engineering tools including fundamental concepts and approaches of soft computing with application to real issues of risk management. In this talk fundamental concepts and soft computing approaches of risk engineering will be introduced. As the term of risk implies both advantageous and hazardous uncertainty in its origins, a fundamental theory to describe uncertainties is introduced that includes traditional probability and statistical models, fuzzy systems, as well as less popular modal logic. In particular, modal logic capabilities to express various kinds of uncertainties are emphasized and relations with rough sets and evidence theory are described. Another topic is data mining related to problems in risk management. Some risk mining techniques including fuzzy clustering are introduced and a recently developed algorithm is overviewed. A numerical example is shown.

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How has belief modality contributed to formal semantics?

  • Tojo, Satoshi
    • Proceedings of the Korean Society for Language and Information Conference
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    • pp.42-53
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    • 2007
  • Looking back the history of formal treatment of linguistics, we cannot disregard the contribution of possible world semantics. Intensional logic of Montague semantics, DRT (Discourse Representation Theory), mental space, and situation theory are closely related to or compared with the notion of possible world. All these theories have commonly clarified the structure of belief context or uncertain knowledge, employing hypothesized worlds. In this talk, I firstly brief the pedigree of these theories. Next, I will introduce the recent development of modal logic for the representation of (i) knowledge and belief and (ii) time, in which belief modality is precisely discussed together with the accessibility among possible worlds. I will refer to BDI (belief-desire-intention) logic, CTL (computational tree logic), and sphere-based model in belief revision. Finally, I will discuss how these theories could be applied to the further development of analyses of natural language.

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Steganography based Multi-modal Biometrics System

  • Go, Hyoun-Joo;Chun, Myung-Geun
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.7 no.2
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    • pp.148-153
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    • 2007
  • This paper deals with implementing a steganography based multi-modal biometric system. For this purpose, we construct a multi-biometrics system based on the face and iris recognition. Here, the feature vector of iris pattern is hidden in the face image. The recognition system is designed by the fuzzy-based Linear Discriminant Analysis(LDA), which is an expanded approach of the LDA method combined by the theory of fuzzy sets. Furthermore, we present a watermarking method that can embed iris information into face images. Finally, we show the advantages of the proposed watermarking scheme by computing the ROC curves and make some comparisons recognition rates of watermarked face images with those of original ones. From various experiments, we found that our proposed scheme could be used for establishing efficient and secure multi-modal biometric systems.

Steganography based Multi-modal Biometrics System

  • Go, Hyoun-Joo;Moon, Dae-Sung;Moon, Ki-Young;Chun, Myung-Geun
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.7 no.1
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    • pp.71-76
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    • 2007
  • This paper deals with implementing a steganography based multi-modal biometric system. For this purpose, we construct a multi-biometrics system based on the face and iris recognition. Here, the feature vector of iris pattern is hidden in the face image. The recognition system is designed by the fuzzy-based Linear Discriminant Analysis(LDA), which is an expanded approach of the LDA method combined by the theory of fuzzy sets. Furthermore, we present a watermarking method that can embed iris information into face images. Finally, we show the advantages of the proposed watermarking scheme by computing the ROC curves and make some comparisons recognition rates of watermarked face images with those of original ones. From various experiments, we found that our proposed scheme could be used for establishing efficient and secure multi-modal biometric systems.