Abstract
Most theories of computation start with the following:
-
a set of states S;
-
the initial states I — a subset of S;
-
the terminal states τ — a subset of S;
-
a set of moves M — mapping S in S.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Archimedes. “The Sandreckoner”.
W. F. Clocksin and C. S. Mellish, “Programming in Prolog”, Springer Verlag (1981).
H. Friedmann, S. Simpson and S. Smith, Countable algebras and set existence axioms, Annals of Pure & App. Logic (1983).
G. Gentzen, Untersuchungen über das logische Schliessen, Mathematische Zeitschrift. 39:176–210, 405–431 (1935).
J-Y. Girard, II<Stack><Subscript>2</Subscript><Superscript>1</Superscript></Stack>-logic, Part I: Dilators, Annals of Math. Logic, vol. 21:75–219 (1981).
J-Y. Girard, The Ω-Rule. Proceedings International Congress of Mathematicians, Warszawa (1983).
J-Y. Girard and J. P. Ressayre, Elements de logique Π<Stack><Subscript>n</Subscript><Superscript>1</Superscript></Stack> Proceedings of the AMS Symposium on Recursion Theory, Cornell (1982).
K. Gödel, Ueber eine bisher noch nicht benützte Erweiterung des finiten Standpunktes, Dialectica, 12:280–287 (1958).
H. R. Jervell, Introducing Π<Stack><Subscript>2</Subscript><Superscript>1</Superscript></Stack>-logic. Proceedings from a Symposium in Oslo. To appear in Springer Lecture Notes.
H. R. Jervell, Π<Stack><Subscript>n</Subscript><Superscript>1</Superscript></Stack>-completeness. Proceedings from a Symposium in Oslo. To appear in Springer Lecture Notes.
A. Mostowski, Formal systems of analysis based on an infinistic rule, in: “Infinitistic Methods”, Warszawa (1960).
D. Prawitz, Mekanisk bevisföring i predikatkalkylen, Uppsats för seminariet i teoretisk filosofi (mimeographed), Stockholm (1957).
J. A. Robinson, Theorem-Proving on the Computer, J. Assoc. for Computing Machinery, Vol. 10, No. 2, April (1963).
A. M. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, Ser. 2, Vol. 42:230–265 (1936–1937);
A. M. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, Ser. 2, Vol. 43:544–546 (1937).
H. Wang, Proving theorems by pattern recognition: I, Communications of the Assoc. Computing Machinery, Vol. 3, No. 4, April (1960). (“H. Wang” should be “W. Hao”.)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Plenum Press, New York
About this chapter
Cite this chapter
Jervell, H.R. (1987). Reasoning in Trees. In: Skordev, D.G. (eds) Mathematical Logic and Its Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0897-3_8
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0897-3_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-8234-1
Online ISBN: 978-1-4613-0897-3
eBook Packages: Springer Book Archive