Systems of Natural Logic with Adjectives and Their Completeness
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Date
2010
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Indiana University Department of Mathematics
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Abstract
In natural logic, the goal is to create a system of logic that is as sim-
ilar to natural language as possible. In order to build a natural logic,
simple sentence forms are considered, slowly incorporating more language
throughout time. As background, we rst consider the fragments of the
form All X are Y and then add No X are Y , where X and Y are nouns.
We will look at the rules of logic and completeness of their proof sys-
tems. Next, we will introduce the idea of intersecting adjectives which
are adjectives with meaning separate from the noun being modifying. For
example, the plural noun red cars means the intersection of everything
red and everything that is a car. This paper will then present versions
of the simple systems that contain intersecting adjectives and will discuss
their completeness.
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Preprint