  Languages may encode similar meanings using different sentence structures.
This makes it a challenge to provide a single set of formal rules that can
derive meanings from sentences in many languages at once. To overcome the
challenge, we can take advantage of language-general connections between
meaning and syntax, and build on cross-linguistically parallel syntactic
structures. We introduce UD Type Calculus, a compositional, principled, and
language-independent system of semantic types and logical forms for lexical
items which builds on a widely-used language-general dependency syntax
framework. We explain the essential features of UD Type Calculus, which all
involve giving dependency relations denotations just like those of words. These
allow UD-TC to derive correct meanings for sentences with a wide range of
syntactic structures by making use of dependency labels. Finally, we present
evaluation results on a large existing corpus of sentences and their logical
forms, showing that UD-TC can produce meanings comparable with our baseline.
