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Beyond FO Within SO

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Logic: Reference Book for Computer Scientists

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 245))

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Abstract

In Sects. 3.19 and 3.20, we discussed problems of expressive power of FO. The general formulation of the problem for FO was: given a class F of closed formulae and a class \(\mathcal {M}\) of FO structures, determine properties which can be expressed by formulae in F within structures in \(\mathcal {M}\). We discussed the problem EVEN and the problem CONN of connectivity for finite graphs showing that these problems cannot be expressed within FO.

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  1. Department of Mathematics and Informatics, University of Warmia and Mazury, Olsztyn, Poland

    Lech T. Polkowski

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Polkowski, L.T. (2023). Beyond FO Within SO. In: Logic: Reference Book for Computer Scientists. Intelligent Systems Reference Library, vol 245. Springer, Cham. https://doi.org/10.1007/978-3-031-42034-4_8

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