# On the Notion of Substitution

@article{Crabb2004OnTN, title={On the Notion of Substitution}, author={Marcel Crabb{\'e}}, journal={Log. J. IGPL}, year={2004}, volume={12}, pages={111-124} }

We consider a concept of substitutive structure, called "logos", in order to study simple substitution, independently of formal or programming languages. We provide a definition of simultaneous substitution in an arbitrary logos and use it to prove a completeness theorem expressing that the equational properties of the usual substitution can be proved from the logos axioms only.

## 6 Citations

### Capture-avoiding substitution as a nominal algebra

- PhilosophyFormal Aspects of Computing
- 2007

A special feature of this method is the use of nominal techniques, which give us access to a stronger assertion language, which includes so-called ‘freshness’ or ‘capture-avoidance’ conditions.

### A study of substitution, using nominal techniques and Fraenkel-Mostowksi sets

- Computer ScienceTheor. Comput. Sci.
- 2009

### Cuts and gluts

- EconomicsJ. Appl. Non Class. Logics
- 2005

The notion of validity relatively to models, for comprehension axioms, containing gluts, is characterized as well as other concepts related to ontological validity, such as consistency and adequacy.

### Logical Calculi for Reasoning with Binding

- Computer Science
- 2008

This paper presents a meta-level version of Gentzen’s sequent calculus for one-and-a-halfth-order logic, with a focus on the role of meta-equivalence in the development of knowledge representation.

### Freeoids: a semi-abstract view on endomorphism monoids of relatively free algebras

- Mathematics
- 2011

A freeoid over a (normally, infinite) set of variables X is defined to be a pair (W, E), where W is a superset of X, and E is a submonoid of WW containing just one extension of every mapping X → W.…

## References

SHOWING 1-6 OF 6 REFERENCES

### The Hauptsatz for Stratified Comprehension: A Semantic Proof

- MathematicsMath. Log. Q.
- 1994

We prove the cut-elimination theorem, Gentzen's Hauptsatz, for the system for stratified comprehension, i.e. Quine's NF minus extensionality.