• Title/Summary/Keyword: modal logic

Search Result 13, Processing Time 0.085 seconds

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

  • Eun, Eun-suk
    • Journal of Korean Philosophical Society
    • /
    • v.116
    • /
    • pp.257-280
    • /
    • 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.

Logical Necessity Based on Carnap's Criterion of Adequacy

  • Cocchiarella, Nino B.
    • Korean Journal of Logic
    • /
    • v.5 no.2
    • /
    • pp.1-21
    • /
    • 2002
  • A semantics for logical necessity, based on Carnap's criterion of adequacy, is given with respect to the ontology of logical atomism. A calculus for sentential (propositional) modal logic is described and shown to be complete with respect to this semantics. The semantics is then modified in terms of a restricted notion of 'all possible worlds' in the interpretation of necessity and shown to yield a completeness theorem for the modal logic S5. Such a restricted notion introduces material content into the meaning of necessity so that, in addition to atomic facts, there are "modal facts" that distinguish one world from another.

  • PDF

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
    • /
    • v.5 no.4
    • /
    • pp.995-1004
    • /
    • 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.

  • PDF

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
    • /
    • 2012.05a
    • /
    • pp.287-288
    • /
    • 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.

  • PDF

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
    • /
    • v.23 no.1
    • /
    • pp.79-88
    • /
    • 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
    • /
    • 2006.05a
    • /
    • pp.3-6
    • /
    • 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.

  • PDF

INFRA-TOPOLOGIES REVISITED: LOGIC AND CLARIFICATION OF BASIC NOTIONS

  • Witczak, Tomasz
    • Communications of the Korean Mathematical Society
    • /
    • v.37 no.1
    • /
    • pp.279-292
    • /
    • 2022
  • In this paper we adhere to the definition of infra-topological space as it was introduced by Al-Odhari. Namely, we speak about families of subsets which contain ∅ and the whole universe X, being at the same time closed under finite intersections (but not necessarily under arbitrary or even finite unions). This slight modification allows us to distinguish between new classes of subsets (infra-open, ps-infra-open and i-genuine). Analogous notions are discussed in the language of closures. The class of minimal infra-open sets is studied too, as well as the idea of generalized infra-spaces. Finally, we obtain characterization of infra-spaces in terms of modal logic, using some of the notions introduced above.

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
    • /
    • 2012.04a
    • /
    • pp.265-268
    • /
    • 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.

  • PDF

SOME EQUIVALENTS OF L$\"{O}$B'S THEOREM

  • Kim, S.M.
    • Communications of the Korean Mathematical Society
    • /
    • v.9 no.4
    • /
    • pp.803-808
    • /
    • 1994
  • Since L$\ddot{o}$b's announcement of his solution to Henkin's problem (L$\ddot{o}$b (1954, 1955)) there has been successful and fruitful research on provability logic tied up with modal logic. Specially, L$\ddot{o}$b's Theorem is of far-reaching significance in the following meta-mathematical and philosophical sense.

  • PDF

Development of Verification and Conformance Test Generation of Communication Protocol for Railway Signaling Systems

  • Lee, Jae-Ho;Hwang, Jong-Gyu;Seo, Mi-Seon;Kim, Sung-Un;Park, Gwi-Tae
    • 제어로봇시스템학회:학술대회논문집
    • /
    • 2004.08a
    • /
    • pp.358-362
    • /
    • 2004
  • Verification and testing are complementary techniques that are used to increase the level of confidence in the correct functioning of communication systems as prescribed by their specifications. This paper presents an experience of model checking for a formal railway signaling protocol specified in LTS (Labeled Transition System). This formal approach checks deadlock, livelock and reachability for the state and action to verify whether properties expressed in modal logic are true on specifications. We also propose a formal method for semi-automated test case generation for a railway signaling protocol described in I/O FSM (Input/Output Finite State Machine). This enables the generation of more complete and consistent test sequence for conformance testing. The above functions are implemented by C++ language and included within RSPVTE (Railway Signaling Protocol Verification and Testing Environment).

  • PDF