After a brief introduction to algebras, in 2.1 we begin with linear spaces (LSs) and Boolean alge... more After a brief introduction to algebras, in 2.1 we begin with linear spaces (LSs) and Boolean algebras (BAs). In 2.2 we cover the basic notions of universal algebra, building up to, but not including, Birkhoff’s Theorem. Ultrafilters are introduced in 2.3. In 2.4 we turn to the propositional calculus, and the (lower) predicate calculus is discussed in 2.5. The elements of proof theory are sketched in 2.6, and some preliminaries from multivariate statistics (which are, for the most part, just linear algebra in new terminological garb) are discussed in 2.7. The material is selected for its utility in later chapters, rather than for internal cohesion, and is largely orthogonal to the standard logic prerequisites to compositional semantics covered in for example the two volumes of Gamut (1991). A first course in linear algebra (but not in multivariate statistics) is assumed.
The analysis of geographic references in natural language text involves, at least conceptually, f... more The analysis of geographic references in natural language text involves, at least conceptually, four distinct stages. Of course, implementations may vary greatly in how these stages are interleaved. The first conceptual stage is geographic entity reference detection: strings such as New York, the Amazon delta, LaGuardia, the San Diego-Tijuana border, [the] Brooklyn Bridge, a mile from downtown Manhattan, etc. are identified in the text (Rauch et al). Second, contextual information gathering may help identify the type and approximate location of geographic entities: LaGuardia Airport vs. LaGuardia Community College, the town of Manhattan (population 44,831), etc. (Manov et al, Bilhaut et al). Third is the actual disambiguation of the entity with respect to both type (New York City vs. New York State) and location (Orange County, California vs. Orange County, Florida) (Leidner et al, Waldinger et al, Li et al).
After a brief introduction to algebras, in 2.1 we begin with linear spaces (LSs) and Boolean alge... more After a brief introduction to algebras, in 2.1 we begin with linear spaces (LSs) and Boolean algebras (BAs). In 2.2 we cover the basic notions of universal algebra, building up to, but not including, Birkhoff’s Theorem. Ultrafilters are introduced in 2.3. In 2.4 we turn to the propositional calculus, and the (lower) predicate calculus is discussed in 2.5. The elements of proof theory are sketched in 2.6, and some preliminaries from multivariate statistics (which are, for the most part, just linear algebra in new terminological garb) are discussed in 2.7. The material is selected for its utility in later chapters, rather than for internal cohesion, and is largely orthogonal to the standard logic prerequisites to compositional semantics covered in for example the two volumes of Gamut (1991). A first course in linear algebra (but not in multivariate statistics) is assumed.
The analysis of geographic references in natural language text involves, at least conceptually, f... more The analysis of geographic references in natural language text involves, at least conceptually, four distinct stages. Of course, implementations may vary greatly in how these stages are interleaved. The first conceptual stage is geographic entity reference detection: strings such as New York, the Amazon delta, LaGuardia, the San Diego-Tijuana border, [the] Brooklyn Bridge, a mile from downtown Manhattan, etc. are identified in the text (Rauch et al). Second, contextual information gathering may help identify the type and approximate location of geographic entities: LaGuardia Airport vs. LaGuardia Community College, the town of Manhattan (population 44,831), etc. (Manov et al, Bilhaut et al). Third is the actual disambiguation of the entity with respect to both type (New York City vs. New York State) and location (Orange County, California vs. Orange County, Florida) (Leidner et al, Waldinger et al, Li et al).
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