In a broad sense, logic is the field of formal languages for knowledge and truth that have a
formal semantics. It tends to be difficult to give a narrower definition because very different
kinds of logics exist. One of the most fundamental contrasts is between the different methods
of assigning semantics. Here two classes can be distinguished: model theoretical semantics
based on a foundation of mathematics such as set theory, and proof theoretical semantics
based on an inference system possibly formulated within a type theory. Logical frameworks …

We give a comprehensive formal representation of first-order logic using the recently
developed module system for the Twelf implementation of the Edinburgh Logical Framework
LF. The module system places strong emphasis on signature morphisms as the main
primitive concept, which makes it particularly useful to reason about structural translations,
which occur frequently in proof and model theory. Syntax and proof theory are encoded in
the usual way using LF's higher order abstract syntax and judgments-as-types paradigm, but …