Interpolation via translations

@article{Rasga2009InterpolationVT,
  title={Interpolation via translations},
  author={Jo{\~a}o Rasga and Walter Alexandre Carnielli and Cristina Sernadas},
  journal={Mathematical Logic Quarterly},
  year={2009},
  volume={55}
}
A new technique is presented for proving that a consequence system enjoys Craig interpolation or Maehara interpolation based on the fact that these properties hold in another consequence system. This technique is based on the existence of a back and forth translation satisfying some properties between the consequence systems. Some examples of translations satisfying those properties are described. Namely a translation between the global/local consequence systems induced by fragments of linear… 
Towards automated reasoning in Herbrand structures
TLDR
This paper offers several layers for coping with the inherent incompleteness and non-compactness of herbrand structures and introduces two types of infinitary proof system which manipulate infinite sequents and are sound and complete for the intended semantics.
Interpolation in Extensions of First-Order Logic
TLDR
A direct proof of interpolation is obtained for (classical and intuitionistic) first-order logic with identity, as well as interpolation for several mathematical theories, including the theory of equivalence relations, (strict) partial and linear orders, and various intuitionistic order theories such as apartness and positive partial andlinear orders.
Craig Interpolation in the Presence of Unreliable Connectives
TLDR
Arrow and turnstile interpolations are investigated in UCL, a logic that is a complete extension of classical propositional logic for reasoning about connectives that only behave as expected with a given probability.
in the Presence of Unreliable Connectives
Arrow and turnstile interpolations are investigated in UCL (introduced in [32]), a logic that is a complete extension of classical propositional logic for reasoning about connectives that only behave

References

SHOWING 1-10 OF 32 REFERENCES
The Craig Interpolation Theorem for Schematic Systems
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
Appendix on Interpolation via translations : proofs as expected
Theorem 3.2 A consequence system (L,`) enjoys Craig interpolation with respect to an L-function var, if (i) there is a Craig generalized translation schema from (L,`) to another consequence system
Interpolation in Fragments of Classical Linear Logic
TLDR
This work proves interpolation for a lot of fragments and refute it for the multiplicative fragment (→,+) , using proof nets and quantum graphs, nearly the Lambek calculus.
Completeness Proofs for Linear Logic Based on the Proof Search Method(Preliminary Report)(Type Theory and its Applications to Computer Systems)
TLDR
This paper generalizes the notion of branch in the standardProof search method to that of OR-tree, and gives a proof of the completeness theorem for intuitionistic (classical, resp.) linear logic with respect to intuitionistic phase semantics, based on a generalized form of the proof search method.
Transfers between Logics and their Applications
In this paper, logics are conceived as two-sorted first-order structures, and we argue that this broad definition encompasses a wide class of logics with theoretical interest as well as interest from
Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics over FL
TLDR
The algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices are discussed, and a weak form of the deduction theorem that is known as parametrized local deduction theorem is established.
Interpolation and Definability: Modal and Intuitionistic Logic
1. Introduction and Discussion 2. Modal and Superintuitionistic Logics: Basic Concepts 3. Superintuitionistic Logics and Normal Extensions of the Modal Logics S4 4. The Interpolation Theorem in
Proof-Theoretic Methods in Nonclassical Logic --an Introduction
TLDR
This is an introduction to proof theory of nonclassical logic, which is directed at people who have just started the study of non classical logics, using proof-theoretic methods, and why certain modifications will be necessary in some cases.
Fibring: completeness preservation
TLDR
A completeness theorem is established for logics with congruence endowed with general semantics (in the style of general frames) and completeness is shown to be preserved by fibring logic with equivalence and general semantics.
...
1
2
3
4
...