Sören Halldén. Results concerning the decision problem of Lewis's calculi S3 and S6. The journal of symbolic logic, Bd. 14 (1949), pp. 230–236.

1950 ◽  
Vol 15 (1) ◽  
pp. 70-70
Author(s):  
A. R. Turquette
Keyword(s):  
Decision Problem ◽  
Symbolic Logic

Closing the Circle: An Analysis of Emil Post's Early Work

2006 ◽  
Vol 12 (2) ◽  
pp. 267-289 ◽  
Author(s):  
Liesbeth de Mol
Keyword(s):  
Mathematical Logic ◽  
Decision Problem ◽  
Symbolic Logic ◽  
Negative Solution ◽  
Kurt Gödel ◽  
Historical Fact

AbstractIn 1931 Kurt Gödel published his incompleteness results, and some years later Church and Turing showed that the decision problem for certain systems of symbolic logic has a negative solution. However, already in 1921 the young logician Emil Post worked on similar problems which resulted in what he called an “anticipation” of these results. For several reasons though he did not submit these results to a journal until 1941. This failure ‘to be the first’, did not discourage him: his contributions to mathematical logic and its foundations should not be underestimated. It is the purpose of this article to show that an interest in the early work of Emil Post should be motivated not only by this historical fact, but also by the fact that Post's approach and method differs substantially from those offered by Gödel, Turing and Church. In this paper it will be shown how this method evolved in his early work and how it finally led him to his results.

A Boolean derivation of the Moore-Osgood theorem

1946 ◽  
Vol 11 (3) ◽  
pp. 65-70 ◽  
Author(s):  
Archie Blake
Keyword(s):  
Decision Problem ◽  
Fundamental Problem ◽  
Symbolic Logic ◽  
Logical Function ◽  
Consistent System ◽  
First Order ◽  
Methods Of Calculation ◽  
Truth Value ◽  
Function Calculus ◽  
Logical Calculi

A fundamental problem of symbolic logic is to define logical calculi sufficient to comprise important parts of mathematics, and to develop systematic methods of calculation therein.The possibility of progress in this direction has been severely limited by Gödel's proof that a consistent system sufficient to comprise arithmetic must contain propositions whose truth-value cannot be decided within the system, and by Church's extension of Gödel's method to the result that even in the first order logical function calculus the general decision problem cannot be solved.

Special Cases of the Decision Problem

1951 ◽  
Vol 49 (22) ◽  
pp. 203-221 ◽  
Author(s):  
Alonzo Church
Keyword(s):  
Decision Problem ◽  
Special Cases
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