Rice theorem says every non-trivial property of languages of Turing machines is undecidable.  As David Richerby said in here : Undecidable means not decidable. Undecidable problems may or may not be semi-decidable.I would like to know how to find out Rice Theorem leads to semi-decidability or non-semi-decidability?As an example Rice Theorem is applicable to this r.e. language $A = \{x | \phi_x$ is defined for at least one input$ \}$and also this non-r.e. language as well:$\psi_p = x^2$There is no algorithm to determine $\psi_p$ has that property at all while for $A$ we can simply run the program forever an see whether it accepts one input or not. I would like to know using Rice Theorem is there any way to determine this difference?
Type of undecidability in Rice Theorem
terminology;computability;semi decidability
Rice's Theorem just says it's undecidable. Some undecidable languages are semi-decidable; some (almost all, in fact) of them aren't.