Propositional calculus

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  • This text is directed toward the sophomore through senior levels of uni- versity mathematics, with a tilt toward the former. It presumes that the student has completed at least one semester, and preferably a full year, of calculus. The text is a product of fourteen years of experience, on the part of the author, in teaching a not-too-common course to students with a very common need. The course is taken predominantly by sophomores and juniors from various fields of concentration who...

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  • This proposition is more complicated. The symbol 8 is read “for all”, and the symbol N stands for the set of natural numbers, {0, 1, 2, 3, . . .}. (There is some disagreement about whether 0 is a natural number; in this course, it is.) So this proposition asserts that the final phrase is true for all natural numbers n. That phrase is actually a proposition in its own right:

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  • Categorial grammar has traditionally used the λ-calculus to represent meaning. We present an alternative, dependency-based perspective on linguistic meaning and situate it in the computational setting. This perspective is formalized in terms of hybrid logic and has a rich yet perspicuous propositional ontology that enables a wide variety of semantic phenomena to be represented in a single meaning formalism. Finally, we show how we can couple this formalization to Combinatory Categorial Grammar to produce interpretations compositionally....

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