Aug 21, 2021 · Decidable means there is a Turing-machine that accepts all and only instances of that language, but also explicitly rejects when input is not that language. So, this Turing-machine will …

Mar 8, 2011 · What is difference between "recognizable" and "decidable" in context of Turing machines?

Aug 28, 2019 · So whether a theory T is decidable is an epistemological fact. A statement about what we can effectively know, but completeness is a metaphysical fact about the theory.

Dec 26, 2020 · Let's say checking if a proof is valid is decidable. Then surely we can just enumerate the proofs then check if it's valid. This seems to be a semi-decidable procedure. But why …

Oct 4, 2022 · Basically, we have to prove that if L1 L 1 and L2 L 2 are Turing-decidable then L =L1 ∩L2 L = L 1 ∩ L 2 is also Turing-decidable (a language is Turing-decidable iff a Turing machine exists …

Apr 9, 2021 · We know that a set is decidable iff the set and its complement are both semi-decidable. Thus, the undecidability of validity implies that the complement of the set of valid formulas is not semi …

Nov 28, 2018 · For example, the theory of algebraically closed fields is decidable but incomplete, whereas the set of all true first-order statements about nonnegative integers in the language with + …

Feb 13, 2022 · Since this is decidable, we know that either w ∈ A w ∈ A or w ∈ B w ∈ B. Now, I wanted to argue that, since A A is semi-decidable, so is Ac A c, where Ac A c is the complement of A A.

Jun 17, 2015 · If satisfiability were semi-decidable, then satisfiability and its complement, unsatisfiability would both be semi-decidable, so satisfiability would be decidable, in which case validity would be …

Oct 14, 2023 · A formal system comes with both a syntactic component, which determines the notion of provability (⊢ ⊢), and a semantic component, which determines the notion of truth (⊨ ⊨). For this …