منابع مشابه
Intuitionistic Dual-intuitionistic Nets
The intuitionistic sequent calculus (at most one formula on the right-hand side of sequents) comes with a natural dual system: the dual-intuitionistic sequent calculus (at most one formula on the left-hand side). We explain how the duality between these two systems exactly corresponds to the intensively studied duality between call-by-value systems and call-by-name systems for classical logic. ...
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We consider a logic which is semantically dual (in some precise sense of the term) to intuitionistic. This logic can be labeled as “falsification logic”: it embodies the Popperian methodology of scientific discovery. Whereas intuitionistic logic deals with constructive truth and non-constructive falsity, and Nelson’s logic takes both truth and falsity as constructive notions, in the falsificati...
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Until the beginning of the 20th century, there was no way to reason formally about proofs. In particular, the question of proof equivalence had never been explored. When Hilbert asked in 1920 for an answer to this very question in his famous program, people started looking for proof formalizations. Natural deduction and sequent calculi, which were invented by Gentzen in 1935, quickly became two...
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We present a new intuitionistic linear logic, Dual Intuitionistic Linear Logic, designed to reflect the motivation of exponentials as translations of intuitionistic types, and provide it with a term calculus, proving associated standard type-theoretic results. We give a sound and complete categorical semantics for the type-system, and consider the relationship of the new type-theory to the more...
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We define pure intuitionistic differential proof nets, extending Ehrhard and Regnier’s differential interaction nets with the exponential box of Linear Logic. Normalization of the exponential reduction and confluence of the full one is proved. These results are directed and adjusted to give a translation of Boudol’s untyped λ-calculus with resources extended with a linear-non linear reduction à...
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ژورنال
عنوان ژورنال: Journal of Logic and Computation
سال: 2009
ISSN: 0955-792X,1465-363X
DOI: 10.1093/logcom/exp044