Difference between revisions of "User:IssaRice/Computability and logic/List of possibilities for completeness and decidability"

From Machinelearning
Jump to: navigation, search
Line 35: Line 35:
 
| No || No || No || No ||
 
| No || No || No || No ||
 
|}
 
|}
 +
 +
==References==
 +
 +
<references/>

Revision as of 19:50, 20 February 2019

Decidable logic? Complete logic? (semantic completeness) Decidable theory? Complete theory? (negation-completeness) Example or proof of non-existence
Yes Yes Yes Yes Empty theory (theory with no non-logical axioms) inside propositional logic
Yes Yes Yes No Smith's example of T_1 with just \neg p as an axiom inside a propositional logic with propositional atoms p,q,r.[1]
Yes Yes No Yes
Yes Yes No No
Yes No Yes Yes
Yes No Yes No
Yes No No Yes
Yes No No No
No Yes Yes Yes
No Yes Yes No
No Yes No Yes Empty theory (theory with no non-logical axioms) inside first-order logic
No Yes No No The theory of Robinson arithmetic inside first-order logic
No No Yes Yes
No No Yes No
No No No Yes
No No No No

References

  1. Peter Smith. An Introduction to Gödel's Theorems (2nd ed). p. 32.