## 8 Citations

### Uniform interpolation via nested sequents and hypersequents

- Computer Science, MathematicsWoLLIC
- 2021

This paper develops a constructive method for proving uniform interpolation via nested sequents and applies it to reprove the uniform interpolations property for normal modal logics K, D, and T, and obtains the first direct proof of uniforms interpolation for S5 via a cut-free sequent-like calculus.

### Interpolation for Intermediate Logics via Hyper- and Linear Nested Sequents

- Philosophy, Computer ScienceAdvances in Modal Logic
- 2018

The goal of this paper is extending to intermediate logics the constructive prooftheoretic method of proving Craig and Lyndon interpolation via hypersequents and nested sequents developed earlier for classical modal logics, and answering in the positive the open question of whether Gödel logic enjoys the Lyndon interpolations property.

### Syntactic Interpolation for Tense Logics and Bi-Intuitionistic Logic via Nested Sequents

- Philosophy, Computer ScienceCSL
- 2020

This work provides a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality, and a novel feature of the proof includes an orthogonality condition for defining duality between interpolants.

### Interpolation in Extensions of First-Order Logic

- Philosophy, MathematicsStud Logica
- 2020

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.

### Interpolation in Extensions of First-Order Logic

- Philosophy, MathematicsStudia Logica
- 2019

We prove a generalization of Maehara’s lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms,…

### Hypersequent calculi for non-normal modal and deontic logics: Countermodels and optimal complexity

- Computer ScienceJ. Log. Comput.
- 2021

It is shown that from every failed proof of a formula or hypersequent it is possible to directly extract a countermodel of it in the bi-neighbourhood semantics of polynomial size for coNP logics, and for regular logics also in the relational semantics.

### Through an Inference Rule, Darkly

- Computer Science, PhilosophyMathesis Universalis, Computability and Proof
- 2019

The complexity of the underlying objects is abstracted away to give way for a simple syntactic description, a kind of mathesis universalis, however, the complexity continues affecting which ways of reasoning are valid.

### Interpolation for intermediate logics via injective nested sequents

- Computer ScienceJ. Log. Comput.
- 2021

A novel, semantically inspired method of constructing nested sequent calculi for propositional intermediate logics and constructive proofs of the interpolation property for most non-trivial interpolable intermediateLogics, as well as Lyndon interpolation for Gödel logic.

## References

SHOWING 1-10 OF 78 REFERENCES

### Craig Interpolation in Displayable Logics

- Computer ScienceTABLEAUX
- 2011

This uniform method is given for proving interpolation for a spectrum of display calculi differing in their structural rules, including those for multiplicative linear logic, multiplicative additive linear logic and ordinary classical logic.

### Proving Craig and Lyndon Interpolation Using Labelled Sequent Calculi

- Computer ScienceJELIA
- 2016

It is shown that classes of frames definable by quantifier-free Horn formulas correspond to logics with the IPs and capture the modal cube and the infinite family of transitive Geach logics.

### Interpolation for Intermediate Logics via Hyper- and Linear Nested Sequents

- Philosophy, Computer ScienceAdvances in Modal Logic
- 2018

The goal of this paper is extending to intermediate logics the constructive prooftheoretic method of proving Craig and Lyndon interpolation via hypersequents and nested sequents developed earlier for classical modal logics, and answering in the positive the open question of whether Gödel logic enjoys the Lyndon interpolations property.

### Proof Analysis. A Contribution to Hilbert's Last Problem

- Philosophy
- 2013

Proof theory — one of the main research fields of logic — is generally composed of the following two aspects: on the one hand, it is based on two types of calculi, the sequent calculus and the…

### The Logic of Exact Covers: Completeness and Uniform Interpolation

- Mathematics, Philosophy2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
- 2013

We show that all (not necessarily normal or monotone) modal logics that can be axiomatised in rank-1 have the interpolation property, and that in fact interpolation is uniform if the logics just have…

### Proof Analysis in Modal Logic

- PhilosophyJ. Philos. Log.
- 2005

A general method for generating contraction- and cut-free sequent calculi for a large family of normal modal logics and it can be extended to treat also Gödel–Löb provability logic.

### GEOMETRISATION OF FIRST-ORDER LOGIC

- MathematicsThe Bulletin of Symbolic Logic
- 2015

It is shown that every infinitary first-order theory, suitably restricted, has a geometric conservative extension, hence the title, and these results are applied to simplify methods used in reasoning in and about modal and intermediate logics.

### Hypersequent Calculi for Gödel Logics - a Survey

- PhilosophyJ. Log. Comput.
- 2003

This work describes analytic calculi for propositional finite and infinite-valued Gödel logics and shows that the framework of hypersequents allows one to move straightforwardly from the propositional level to first-order as well as propositional quantification.

### Nested Sequents

- MathematicsArXiv
- 2010

This work sees how nested sequents, a natural generalisation of hypersequents, allow for syntactic cut-elimination and thus allow us to obtain an ordinal upper bound on the length of proofs.