Abstract
The authors show that a very general framework of set approximation can be the set-theoretical base of semantics of a partial first-order logic. The most general problem is what happens if in the semantics of first-order logic one uses the approximations of sets as semantic values of predicate parameters instead of sets given by their total interpretation in order to determine the truth values of formulas? The authors show some unexpected properties connected with logical constants directly. The goal of the investigation is to show the possible connections between the result of different approximative and exact evaluation of formulas – or the lack of them. At the end, the authors present the practical example, in which we can see the discussed behavior of approximation.
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Kádek, T., Mihálydeák, T. (2014). Some Fundamental Laws of Partial First-Order Logic Based on Set Approximations. In: Cornelis, C., Kryszkiewicz, M., Ślȩzak, D., Ruiz, E.M., Bello, R., Shang, L. (eds) Rough Sets and Current Trends in Computing. RSCTC 2014. Lecture Notes in Computer Science(), vol 8536. Springer, Cham. https://doi.org/10.1007/978-3-319-08644-6_5
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DOI: https://doi.org/10.1007/978-3-319-08644-6_5
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