Consistency and interpolation in linear continuous logic (Q6053505)

Linear continuous logic is the fragment of continuous logic which restricts the connectives by only allowing one to multiply a formula by a real number or to add two formulae. In this paper, proofs are given of the classical interpolation theorems, that is, the Lyndon and Herbrand interpolation theorems, in the context of linear continuous logic. The other classical interpolation theorem, namely Craig's interpolation theorem, also holds in this context; indeed, in this paper, the linear continuous logic version of Robinson's joint consistency theorem is proven and in an earlier work it was shown how to derive the linear continuous logic version of Craig interpolation from the linear continuous logic version of Robinson consistency.