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... set of equations axiomatising the variety of Boolean algebras with operators and additional equations corresponding the axioms of L. A closely related algorithmic problem for L is the admissibility problem for inference rules: given an inference rule ϕ1 , . . . , ϕn /ϕ, decide whether it is admissib ...
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... does! This result, known as the Completeness Theorem for first-order logic, was proved by Kurt Gödel in 1929. According to the Completeness Theorem provability and semantic truth are indeed two very different aspects of the same phenomena. In order to prove the Completeness Theorem, we first need a ...
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... gave an axiomatisation of star-free DL-PA and stated that the addition of the Kleene star does not increase the expressivity because “an arbitrary [program] π∗ only affects a finite number of atomic propositions”. He however observes that “[f]inding an efficient method for translating π∗ [programs] ...
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Halting problem

In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running or continue to run forever.Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist. A key part of the proof was a mathematical definition of a computer and program, which became known as a Turing machine; the halting problem is undecidable over Turing machines. It is one of the first examples of a decision problem.Jack Copeland (2004) attributes the term halting problem to Martin Davis.
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