Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/undecidability-of-the-problem-of-recognizing-axiomatizations-of-V6sgQ5RSHF
References (40)
-
L. Maksimova (1977)
Craig's theorem in superintuitionistic logics and amalgamable varieties of pseudo-boolean algebrasAlgebra and Logic, 16
-
(1949)
Recursive unsolvability of the deducibility, Tarski’s completeness, and independence of axioms problems of propositional calculus -
(1997)
Modal Logic, Vol. 35 of Oxford Logic Guides -
M. Minsky (1961)
Recursive Unsolvability of Post's Problem of "Tag" and other Topics in Theory of Turing MachinesAnnals of Mathematics, 74
-
G. V. Bokov (2009)
(Russian), http://www -
A. Urquhart (2009)
Logic from Russell to Church -
Hao Wang (1963)
Tag systems and lag systemsMathematische Annalen, 152
-
Ann Ihrig (1965)
The Post-Lineal theorems for arbitrary recursively enumerable degrees of unsolvabilityNotre Dame J. Formal Log., 6
-
(1982)
Undecidable propositional calculi, in Problems of Cybernetics -
J. Marcinkowski (1993)
A Horn Clause that Implies and Undecidable Set of Horn Clauses -
W. Singletary (1968)
Results regarding the axiomatization of partial propositional calculiNotre Dame J. Formal Log., 9
-
A. Kuznecov, E. Mendelson (1972)
Undecidability of the General Problems of Completeness, Decidability and Equivalence for Propositional Calculi -
J. Łukasiewicz (1970)
Łukasiewicz, J., The shortest axiom of the implicational calculus of propositions, in L. Borowski, and J. Łukasiewicz, (eds.), Selected Works, North-Holland Publishing Company, London, 1970, pp. 295–305. -
V. B. Shehtman (1978)
(Russian) -
J. Marcinkowski (1994)
223–237 -
Z. Ariola, Hugo Herbelin (2003)
Minimal Classical Logic and Control Operators -
N. I. Fel’dman (1966)
Fel’dman, N. I., A. V. Kuznecov and J. I. Manin et al., Twelve Papers on Logic and Algebra, Vol. 59 of American Mathematical Society Translations, series 2, American Mathematical Society, USA, 1966. -
V. B. Shehtman (1982)
Shehtman, V. B., Undecidable propositional calculi, in Problems of Cybernetics. Non-Classical Logics and Their Applications, Vol. 75, Nauka, Moscow, 1982, pp. 74–116, (Russian). -
Z. M. Ariola (2003)
Ariola, Z. M., and H. Herbelin, Minimal classical logic and control operators, in J. C. M. Baeten, J. K. Lenstra, J. Parrow, and G. J. Woeginger (eds.), Proceedings of the 30th International Colloquium on Automata, Languages and Programming (ICALP 2003), Vol. 2719 of Lecture Notes in Computer Science, Springer, Berlin, 2003, pp. 871–885. -
J. Łukasiewicz (1948)
25–33 -
R. Harrop (1964)
A Relativization Procedure for Propositional Calculi, with an Application to a Generalized form of Post's TheoremProceedings of The London Mathematical Society
-
A. Chagrov, M. Zakharyaschev (1993)
The undecidability of the disjunction property of propositional logics and other related problemsJournal of Symbolic Logic, 58
-
W. Singletary (1967)
A note on finite axiomatization of partial propositional calculiJournal of Symbolic Logic, 32
-
(1958)
Computability and Unsolvability, McGraw-Hill -
A. Church (1948)
Review: Jan Lukasiewicz, The Shortest Axiom of the Implicational Calculus of PropositionsJournal of Symbolic Logic, 13
-
R. Harrop (1958)
On the existence of finite models and decision procedures for propositional calculiMathematical Proceedings of the Cambridge Philosophical Society, 54
-
(2009)
Completeness problem in the propositional calculus, Intellectual Systems -
A. Urquhart (1081)
1083, 1985 -
(1953)
A single axiom of positive logic -
M. Gladstone (1965)
Some ways of constructing a propositional calculus of any required degree of unsolvabilityTransactions of the American Mathematical Society, 118
-
M. L. Minsky (1967)
Finite and Infinite Machines -
W. Singletary (1964)
A complex of problems proposed by PostBulletin of the American Mathematical Society, 70
-
L. Maksimova (1972)
Pretabular superintuitionist logicAlgebra and Logic, 11
-
M. Yntema (1964)
A detailed argument for the Post-Linial theoremsNotre Dame J. Formal Log., 5
-
Lilia Chagrova (1991)
An undecidable problem in correspondence theoryJournal of Symbolic Logic, 56
-
A Chagrov (1994)
Chagrov, A, Undecidable properties of superintuitionistic logics, in S. V. Jablonskij, (ed.), Mathematical Problems of Cybernetics, Physmatlit, Moscow, Vol. 5, 1994, pp. 62–108, (Russian). -
W. E. Singletary (1964)
(A correction in 70(6):826) -
M. Davis (1958)
Computability and Unsolvability -
Emil Post (1943)
Formal Reductions of the General Combinatorial Decision ProblemAmerican Journal of Mathematics, 65
-
B. Wells, S. Popov (1985)
An Undecidable Superintuitionistic Propositional Calculus
- Publisher
- Springer Journals
- Copyright
- 2013 Springer Science+Business Media Dordrecht
- ISSN
- 0039-3215
- eISSN
- 1572-8730
- DOI
- 10.1007/s11225-013-9520-5
- Publisher site
- See Article on Publisher Site
Abstract
Abstract We give a new proof of the following result (originally due to Linial and Post): it is undecidable whether a given calculus, that is a finite set of propositional formulas together with the rules of modus ponens and substitution, axiomatizes the classical logic. Moreover, we prove the same for every superintuitionistic calculus. As a corollary, it is undecidable whether a given calculus is consistent, whether it is superintuitionistic, whether two given calculi have the same theorems, whether a given formula is derivable in a given calculus. The proof is by reduction from the undecidable halting problem for the so-called tag systems introduced by Post. We also give a historical survey of related results.
Journal
"Studia Logica" – Springer Journals
Published: Oct 1, 2014