Second-order logic: Difference between revisions

Revision as of 23:24, 30 May 2020

Revision as of 07:27, 2 June 2020

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Suppose we would like to say that a and b have the same shape. The best we could do in FOL is something like this:

(Cube(a) ∧ Cube(b)) ∨ (Tet(a) ∧ Tet(b)) ∨ (Dodec(a) ∧ DocedDodec(b))

If the only shapes are cube, tetrahedron, and dodecahedron, for a and b to have the same shape is for them either to be both cubes, both tetrahedra, or both dodecahedra. But this FOL sentence doesn’t seem to mean quite the same thing as the English sentence it is translating — for example, it doesn’t say anything about the fact that it is shape that a and b have in common<ref>Professor Marc Cohen lecture notes https://faculty.washington.edu/smcohen/120/SecondOrder.pdf</ref>.