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first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.

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What is the conditional probability or probablity of classes of languages?

The probability measure you're asking about is nonatomic, but your events of interest are countable. Therefore the unconditional probability of each is zero, and the conditional probabilities are und …
Noah Stein's user avatar
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10 votes

Existence of unknowable algorithms ?

The Robertson-Seymour graph minor theorem shows that membership in any given minor-closed family of graphs can be checked in polynomial time. It even shows this can be done in $\mathcal{O}(n^3)$ time …
Noah Stein's user avatar
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8 votes

Is there research on Machine Learning techniques to discover conjectures (theorems) in a wid...

One example that is close to, if not exactly of this type, is Veit Elser's demonstration that machine learning techniques can learn how to do fast matrix multiplication from examples of matrix product …
Noah Stein's user avatar
  • 8,501