• Journal for History of Mathematics
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• v.25 no.4
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• pp.21-36
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• 2012

It is commonly believed that the model-theoretic account of logical consequence is originated from Tarski' s 1936 paper. But Etchemendy has denied this. This paper discusses and evaluates the recent controversies over whether the definition of logical consequence presented in Tarski' s paper is based on the fixed-domain conception or the variable-domain conception.

• Korean Journal of Logic
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• v.17 no.1
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• pp.71-109
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• 2014

Gila Sher believes that Tarskian definition of logical consequence is a conceptually and extensionally adequate explanation. She has tried to show this on the basis of Mostowskian conceptions of generalized quantifiers as being invariant under isomorphic structures and her own conceptions of models. In this paper I try to show that her attempt to justify the Tarskian definition is only partially successful. I admit that her conceptions of the logical as being invariant under isomorphic structures are enough to show the logical formality of logical consequence relations. But I think that since her conceptions of meanings of terms are quite inadequate for dealing with the problem of empty predicates, she fails to distinguish logically necessary truths from other kinds of truths.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.13 no.21
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• pp.29-41
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• 1990

An assessment of risk in industrial and urban environments is essential in the prevention of accident and in the analysis of situations which are hazardous to public health and safety. The risk imposed by a particular hazard increases with the likelihood of occurence of the event, the exposure and the possible consequence of that event. In a traditional approach, the calculation of a quantitative value of risk is usually based on an assignment of numerical values of each of the risk factors. Then the product of the values of likelihood, exposure and consequences called risk score is derived. However vagueness and imprecision in mathematical quantification of risk are equated with fuzziness rather than randomness. In this paper, a fuzzy set theoretic approach to risk analysis is proposed as an alternative to the techniques currently used in the area of systems safety. Then the concept of risk evaluation using linguistic representation of the likelihood, exposure and consequences is introduced. A risk assessment model using approximate reasoning technique based on fuzzy logic is presented to drive fuzzy values of risk and numerical example for risk analysis is also presented to illustrate the results.