The Penn Lambda Calculator: Pedagogical software for
natural language semantics
Lucas Champollion, Joshua Tauberer, and Maribel Romero
Abstract
This paper describes a novel pedagogical software program that can be
seen as an online companion to one of the standard textbooks of formal natural
language semantics, Heim and Kratzer (1998). The Penn Lambda Calculator
is a multifunctional application designed for use in standard graduate
and undergraduate introductions to formal semantics: Teachers can use the
application to demonstrate complex semantic derivations in the classroom
and modify them interactively, and students can use it to work on problem
sets provided by the teacher. The program supports demonstrations and exercises
in two main areas: (1) performing beta reduction in the simply typed
lambda calculus; (2) application of the bottom-up algorithm for computing
the compositional semantics of natural language syntax trees. The program
is able to represent the full range of phenomena covered in the Heim and
Kratzer textbook by function application, predicate modification, and lambda
abstraction. This includes phenomena such as intersective adjectives, relative
clauses and quantifier raising. In the student use case, emphasis has been
placed on providing "live" feedback for incorrect answers. Heuristics are
used to detect the most frequent student errors and to return specific, interactive
suggestions.
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