Aristotelian Fragments and Subdiagrams for the Boolean Algebra B[sub.5]

On a descriptive level, this paper presents a number of logical fragments which require the Boolean algebra B[sub.5] , i.e., bitstrings of length five, for their semantic analysis. Two categories from the realm of natural language quantification are considered, namely, proportional quantification wi...

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Bibliographic Details
Published in:Axioms 2023-06, Vol.12 (6)
Main Authors: Roelandt, Koen, Smessaert, Hans
Format: Article
Language:English
Subjects:
Algebra, Boolean
Computational linguistics
Language processing
Methods
Natural language interfaces
Semantics
Online Access:Get full text
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Summary:On a descriptive level, this paper presents a number of logical fragments which require the Boolean algebra B[sub.5] , 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 two thirds/66 percent of the children are asleep—and normative quantification—as in not enough/too many children are asleep. On a more theoretical level, we study two distinct Aristotelian subdiagrams in B[sub.5] , which are the result of moving from B[sub.5] to B[sub.4] 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 B[sub.4] to B[sub.3] .
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12060604