Non-traditional squares of predication and quantification

Logica Universalis 2 (1):77-85 (2008)
.  Three logical squares of predication or quantification, which one can even extend to logical hexagons, will be presented and analyzed. All three squares are based on ideas of the non-traditional theory of predication developed by Sinowjew and Wessel. The authors also designed a non-traditional theory of quantification. It will be shown that this theory is superfluous, since it is based on an obscure difference between two kinds of quantification and one pays a high price for differentiating in this way: losing the definability between the existence- and all-quantifier. Therefore, a combination of non-traditional predication and classical quantification is preferred here.
Keywords Internal negation  predication  denying  quantification  logical squares
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DOI 10.1007/s11787-007-0029-4
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