Categorical logic with partial elements
Marcelo E. Coniglio · Contemporary mathematics - American Mathematical Society · 1999
In this paper we extend the usual categorical semantics by redening the interpretation of the constant symbols. The key idea is the utilisation of extent (or support) for the objects, interpreting the constants as partial elements. In this extension we can now combine dierent theories in which the objects \\with constants" do not necessarily have maximum extent. The sequent calculus is appropriately modied, and soundness and completeness theorems are proved.