Intuitionistic completeness of first-order logic
@article{Constable2014IntuitionisticCO, title={Intuitionistic completeness of first-order logic}, author={R. Constable and M. Bickford}, journal={Ann. Pure Appl. Log.}, year={2014}, volume={165}, pages={164-198} }
Abstract We constructively prove completeness for intuitionistic first-order logic, iFOL, showing that a formula is provable in iFOL if and only if it is uniformly valid in intuitionistic evidence semantics as defined in intuitionistic type theory extended with an intersection operator. Our completeness proof provides an effective procedure that converts any uniform evidence into a formal iFOL proof. Uniform evidence can involve arbitrary concepts from type theory such as ordinals, topological… CONTINUE READING
18 Citations
Completeness Theorems for First-Order Logic Analysed in Constructive Type Theory
- Mathematics, Computer Science
- LFCS
- 2020
- 8
- Highly Influenced
- PDF
Virtual Evidence: A Constructive Semantics for Classical Logics
- Computer Science, Mathematics
- ArXiv
- 2014
- 1
- PDF
Intuitionistic Ancestral Logic as a Dependently Typed Abstract Programming Language
- Computer Science
- WoLLIC
- 2015
- PDF
Validating Brouwer's continuity principle for numbers using named exceptions
- Mathematics, Computer Science
- Math. Struct. Comput. Sci.
- 2018
- 9
- PDF
Proof Assistants and the Dynamic Nature of Formal Theories
- Computer Science, Mathematics
- ATx/WInG@IJCAR
- 2012
- PDF
On Building Constructive Formal Theories of Computation Noting the Roles of Turing, Church, and Brouwer
- Computer Science
- 2012 27th Annual IEEE Symposium on Logic in Computer Science
- 2012
- 3
- PDF
References
SHOWING 1-10 OF 101 REFERENCES
Completeness and incompleteness for intuitionistic logic
- Mathematics, Computer Science
- J. Symb. Log.
- 2008
- 15
An Abstract Notion of Realizability for Which Intuitionistic Predicate Calculus is Complete
- Mathematics
- 1970
- 78
Uniform provability realization of intuitionistic logic, modality and lambda-terms
- Computer Science, Mathematics
- Electron. Notes Theor. Comput. Sci.
- 1999
- 14
Continuation-passing style models complete for intuitionistic logic
- Mathematics, Computer Science
- Ann. Pure Appl. Log.
- 2013
- 12
- PDF
Some Intuitions Behind Realizability Semantics for Constructive Logic: Tableaux and Läuchli Countermodels
- Mathematics, Computer Science
- Ann. Pure Appl. Log.
- 1996
- 10
- PDF
An Intuitionistically Plausible Interpretation of Intuitionistic Logic
- Mathematics, Computer Science
- J. Symb. Log.
- 1977
- 16