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Intersection types for light affine lambda calculus
 In Proceedings of 3rd Workshop on Intersection Types and Related Systems (ITRS’04
, 2004
"... Light Affine Lambda Calculus is a term calculus for polynomial time computation ([12]). Some of the terms of Light Affine Lambda Calculus must however be regarded as errors. Intuitionistic Light Affine Logic (ILAL) types only terms without errors, but not all of them. We introduce two type assignmen ..."
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Light Affine Lambda Calculus is a term calculus for polynomial time computation ([12]). Some of the terms of Light Affine Lambda Calculus must however be regarded as errors. Intuitionistic Light Affine Logic (ILAL) types only terms without errors, but not all of them. We introduce two type assignment systems with intersection types: in the first one, typable pseudoterms are exactly the terms without errors; in the second one, they are exactly those that reduce to normal terms without errors.
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"... Abstract: It is known that a number of inference principles can be used to trivialise the axioms of naïve comprehension — the axioms underlying the naïve theory of sets. In this paper we systematise and extend these known results, to provide a number of general classes of axioms responsible for triv ..."
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Abstract: It is known that a number of inference principles can be used to trivialise the axioms of naïve comprehension — the axioms underlying the naïve theory of sets. In this paper we systematise and extend these known results, to provide a number of general classes of axioms responsible for trivialising naïve comprehension. Keywords: Abelian logic, contraction, Curry’s paradox, naïve comprehension, Nonclassical implicational logics, Peirce’s law.