Results 1 
3 of
3
The Craig Interpolation Theorem for Schematic Systems
, 1996
"... The notion of Schematic System has been introduced by Parikh in the early seventies. It is a metamathematical notion describing the concept of deduction system and the operation of substitution of terms and formulas in it. We show a generalization of the Craig Interpolation Theorem for a natural ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
The notion of Schematic System has been introduced by Parikh in the early seventies. It is a metamathematical notion describing the concept of deduction system and the operation of substitution of terms and formulas in it. We show a generalization of the Craig Interpolation Theorem for a natural class of schematic systems while we determine sufficient conditions for a schematic system to enjoy Interpolation.
Streams and Strings in Formal Proofs
"... Streams are acyclic directed subgraphs of the logical flow graph of a proof and represent bundles of paths with the same origin and the same end. Streams can be described with a natural algebraic formalism which allows to explain in algebraic terms the evolution of proofs during cutelimination. ..."
Abstract
 Add to MetaCart
Streams are acyclic directed subgraphs of the logical flow graph of a proof and represent bundles of paths with the same origin and the same end. Streams can be described with a natural algebraic formalism which allows to explain in algebraic terms the evolution of proofs during cutelimination. In our approach, "logic" is often forgotten and combinatorial properties of graphs are taken into account to explain logical phenomena.