Corpus ID: 118169513

First-Order Intuitionistic Logic with Decidable Propositional Atoms

@article{Sakharov2004FirstOrderIL,
  title={First-Order Intuitionistic Logic with Decidable Propositional Atoms},
  author={Alexander Sakharov},
  journal={arXiv: General Mathematics},
  year={2004}
}
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as a framework for investigating this extension. Admissibility of cut is retained. Constrained Kripke structures are introduced for modeling intuitionistic logic with decidable propositional atoms. The extent of the disjunction and existence properties is… Expand

References

SHOWING 1-10 OF 12 REFERENCES
TR-2004003: Intuitionistic Logic with Classical Atoms
In this paper, we define a Hilbert-style axiom system IPCCA that conservatively extends intuitionistic propositional logic (IPC) by adding new classical atoms for which the law of excluded middleExpand
A Short Introduction to Intuitionistic Logic
Introduction. I: Intuitionistic Propositional Logic. 1. Preliminaries. 2. Natural Deduction for Propositional Logic. 3. Negative Translation: Glivenko's Theorem. 4. Program Interpretation ofExpand
Combining Classical and Intuitionistic Logic
We study how a logic C+J conbining classical logic C and intuitionistic logic J can be defined. We show that its Hilbert axiomatization cannot be attained by simply extending the union of theExpand
On maximal intermediate logics with the disjunction property
TLDR
It is proved that the logic of finite binary trees is not maximal among intermediate logics withDP and introduced is a logicND, which has the only maximal extension withDP, namely, the logicML of finite problems. Expand
Counting the Maximal Intermediate Constructive Logics
A proof is given that the set of maximal intermediate propositional logics with the disjunction property and the set of maximal intermediate predicate logics with the disjunction property and theExpand
On Extensions of Intermediate Logics by Strong Negation
  • M. Kracht
  • Mathematics, Computer Science
  • J. Philos. Log.
  • 1998
TLDR
It is shown that the mapping from Λ to n(Λ) is a homomorphism of complete lattices, preserving and reflecting finite model property, frame-completeness, interpolation and decidability, and a general characterization of those constructive logics are given. Expand
Modulated fibring and the collapsing problem
TLDR
Modulated fibring allows a finer control of the combination, solving the collapsing problem both at the semantic and deductive levels. Expand
...
1
2
...