# Questions tagged [lo.logic]

Computational and mathematical logic.

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### Cut-elimination for calculus with nats or other inductive datatype?

Does anyone direct me to a paper detailing a cut-elimination theorem for propositional intuitionistic logic, including an inductive datatype such as the natural numbers (lists or trees would be fine, ...
397 views

### About the correspondence of left introduction and elimination of implication in Sequent Calculus and in Natural Deduction resp.

Could anyone give an intuitive (not intutionistic) explanation of the correspondence of left introduction and elimination of implication in Sequent Calculus (SC) and Natural Deduction (ND) ...
2k views

### What are “$\mu$-recursive functions” and $\mu$-calculus?

I saw in this question a reference to $\mu$-recursive functions or $\mu$-calculus as some computation model equivalent to Turing machines and $\lambda$-calculus. I know about these two but never heard ...
793 views

### An example of a totally computable function that is not definable in system T?

Could you give me an example of a totally computable function of type N × N → N that is not definable in System T? Thanks.
518 views

### What happens if we try to extract a witness but it actually does not exist from a term of existential type?

Given a term t : ∀x.∃y.(¬(x = 0) ⇒ x = S(y)) in Martin-Lof's type theory, what's the value of w(t(0)), where ...
709 views

### NP vs co-NP and second-order logic

Assume that NP=co-NP and polynomial $p(x)$ bounds the length of the proof of unsatisfiability for a 3-CNF instance $x$. Then are there any results on what form any proof of unsatisfiability for $x$ of ...
404 views

### Can relativization results be used to prove sentences formally independent?

Is it possible to demonstrate that a sentence must be formally independent based on the fact that it is non-relativizing? In other words, are there examples of sentences in computability/complexity ...
244 views

### A direct sum theorem for Resolution clause space complexity?

Resolution is a scheme to prove unsatisfiability of CNFs. A proof in resolution is a logical deduction of the empty clause for the initial clauses in of the CNF. In particular any initial clause can ...
373 views

### Computational consequences of Friedman's (unprovable) Upper Shift Fixed Point theorem?

Harvey Friedman showed that there is a neat fixed point result that cannot be proved in ZFC (the usual Zermelo-Frankel set theory with the Axiom of Choice). Many modern logics are built on fixed ...
792 views

### Curriculum: Logical/Formal Methods in Security

At present I teach a small course (Four two hour lectures at the Masters level) on Logical Methods in Security, though the title Formal Methods in Security might be more apt. It covers briefly the ...
3k views

### Are there any proofs the undecidability of the halting problem that does not depend on self-referencing or diagonalization ?

This is a question related to this one. Putting it again in a much simpler form after a lot of discussion there, that it felt like a totally different question. The classical proof of the ...
2k views

### What do we know about restricted versions of the halting problem

(UPDATE: a better formed question is posed here as the comments for the accepted answer below show that this question is not well-defined) The classical proof of the impossibility of the halting ...
494 views