An introduction to differential linear logic: proof-nets, models and antiderivatives
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DOI: 10.1017/s0960129516000372
Abstract: Differential linear logic enriches linear logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for differential linear logic and a… read more here.
Keywords: proof nets; nets models; differential linear; introduction differential ... See more keywords
Deep inference and expansion trees for second-order multiplicative linear logic
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DOI: 10.1017/s0960129518000385
Abstract: In this paper, we introduce the notion of expansion tree for linear logic. As in Miller's original work, we have a shallow reading of an expansion tree that corresponds to the conclusion of the proof,… read more here.
Keywords: deep inference; expansion; expansion trees; linear logic ... See more keywords
Encodings of Turing machines in linear logic
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DOI: 10.1017/s0960129520000109
Abstract: Abstract The Sweedler semantics of intuitionistic differential linear logic takes values in the category of vector spaces, using the cofree cocommutative coalgebra to interpret the exponential and primitive elements to interpret the differential structure. In… read more here.
Keywords: linear logic; machines linear; semantics; encodings turing ... See more keywords
A linear logic framework for multimodal logics
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DOI: 10.1017/s0960129522000366
Abstract: Abstract One of the most fundamental properties of a proof system is analyticity, expressing the fact that a proof of a given formula F only uses subformulas of F. In sequent calculus, this property is… read more here.
Keywords: linear logic; cut admissibility; mathsf; framework ... See more keywords