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.