| Summary: | On a descriptive level, this paper presents a number of logical fragments which require the Boolean algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">B</mi><mn>5</mn></msub></semantics></math></inline-formula>, i.e., bitstrings of length five, for their semantic analysis. Two categories from the realm of natural language quantification are considered, namely, proportional quantification with fractions and percentages—as in <i>two thirds/66 percent of the children are asleep</i>—and normative quantification—as in <i>not enough/too many children are asleep</i>. On a more theoretical level, we study two distinct Aristotelian subdiagrams in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">B</mi><mn>5</mn></msub></semantics></math></inline-formula>, which are the result of moving from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">B</mi><mn>5</mn></msub></semantics></math></inline-formula> to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">B</mi><mn>4</mn></msub></semantics></math></inline-formula> either by collapsing bit positions or by deleting bit positions. These two operations are also argued to shed a new light on earlier results from Logical Geometry, in which the collapsing or deletion of bit positions triggers a shift from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">B</mi><mn>4</mn></msub></semantics></math></inline-formula> to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">B</mi><mn>3</mn></msub></semantics></math></inline-formula>.
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