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A note on full intuitionistic linear logic

G.M. Bierman
1996 Annals of Pure and Applied Logic  
This short note considers the formulation of Full Intuitionistic Linear Logic (FILL) given by Hyland and de Paiva (1993) .  ...  This note proposes an alternative formulation based on the notion of patterns.  ...  The resulting logic, Full Intuitionistic Linear Logic (FILL), has two notable features. Firstly it contains a connective, the multiplicative disjunction ('par' or '%?  ... 
doi:10.1016/0168-0072(96)00004-8 fatcat:fb3br5f7gvblzbvabuijiyfhvy

Simulating Computations in Second Order Non-Commutative Linear Logic (Preliminary Report)

Max I. Kanovich
1996 Electronical Notes in Theoretical Computer Science  
Emms did the same for intuitionistic second order non-commutative linear logic.  ...  SynopsisLincoln, Scedrov and Shankar proved undecidability of intuitionistic second order multiplicative commutative linear logic by embedding LJ2 into this logic.  ...  Emms did the same for intuitionistic second order non-commutative linear logic.  ... 
doi:10.1016/s1571-0661(05)80408-6 fatcat:7rz2hpgv3bcpbmrtpakyvgscvi

Page 3414 of Mathematical Reviews Vol. , Issue 97F [page]

1997 Mathematical Reviews  
M. (4-CAMBG; Cambridge) A note on full intuitionistic linear logic. (English summary) Ann. Pure Appl. Logic 79 (1996), no. 3, 281-287.  ...  This note comments upon a bug in Hyland and de Paiva’s system of full intuitionistic linear logic (FILL) (i.e. a linear logic incorpo- rating an intuitionistic restriction on its entailment, but keeping  ... 

Page 6077 of Mathematical Reviews Vol. , Issue 2001I [page]

2001 Mathematical Reviews  
The logic associated with ILT is obtained as a combination of intuitionistic logic with intuitionistic linear logic, and can be em- bedded in Barber and Plotkin’s dual intuitionistic linear logic (DILL  ...  However, unlike DILL, the logic for ILT lacks an ex- plicit modality ! that translates intuitionistic proofs into linear ones.  ... 

Multiple Conclusion Linear Logic: Cut Elimination and More [chapter]

Harley Eades, Valeria de Paiva
2015 Lecture Notes in Computer Science  
par, and implication, into an intuitionistic linear logic.  ...  Full Intuitionistic Linear Logic (FILL) was first introduced by Hyland and de Paiva, and went against current beliefs that it was not possible to incorporate all of the linear connectives, e.g. tensor,  ...  This definition is the one given by Bierman in his thesis, see [3] for full definitions. Intuitionistic logic can be interpreted in a linear category as a full subcategory of the category of !  ... 
doi:10.1007/978-3-319-27683-0_7 fatcat:2nhvi55vmjhchcpibozx4jpkiu

Experiments in linear natural deduction

Simone Martini, Andrea Masini
1997 Theoretical Computer Science  
The addition of a further pre-tensorial connective yields (a natural deduction version of) Full Intuitionistic Linear Logic.  ...  We investigate several fragments of multiplicative linear logic, in a natural deduction setting and with the aim of a better understanding of the par connective.  ...  Note, moreover, that even in an intuitionistic setting (traditionally single-conclusion), the Full Intuitionistic Linear Logic (FILL) of [3] , which is an input-output interpretation, is formulated as  ... 
doi:10.1016/s0304-3975(96)00055-2 fatcat:joifiho4bncndoucbe5z3qpcpq

A taste of linear logic [chapter]

Philip Wadler
1993 Lecture Notes in Computer Science  
The presentation of linear logic is simpli ed by basing it on the Logic of Unity. An application to the array update problem is brie y discussed.  ...  This tutorial paper provides an introduction to intuitionistic logic and linear logic, and shows how they correspond to type systems for functional languages via the notion of'Propositions as Types'.  ...  Embedding intuitionistic logic in linear logic One reason for incorporating ! into our logic is so that it has su cient power that intuitionistic logic can be embedded within it.  ... 
doi:10.1007/3-540-57182-5_12 fatcat:rqrdqjxzkfegdeuvopist55urm

Page 4099 of Mathematical Reviews Vol. , Issue 98G [page]

1998 Mathematical Reviews  
After some proof-theoretic results on these intermediate systems, the authors prove that the system N-FILL is deductively equivalent to the calculus FILL (“full intuitionistic linear logic”) investigated  ...  To this end a natural deduction style system of linear logic N-FILL is developed in a number of intermediate steps: the implicative fragment of linear logic is extended by a pre-tensorial connective, which  ... 

Page 5301 of Mathematical Reviews Vol. , Issue 2000h [page]

2000 Mathematical Reviews  
of FILL and we provide a full proof of the cut-elimination theorem.  ...  linear logic.  ... 

Page 8597 of Mathematical Reviews Vol. , Issue 2001M [page]

2001 Mathematical Reviews  
The first part of the present text is a survey of results on valid intuitionistic propositional and predicate logical schemes for constructive arithmetical theories.  ...  Logic Lang. Inform. 10 (2001), no.2, 211-232. Summary: “In this paper we discuss the first order multiplicative intuitionistic fragment of linear logic, MILLI, and its applications to linguistics.  ... 

Classical and Intuitionistic Subexponential Logics Are Equally Expressive [chapter]

Kaustuv Chaudhuri
2010 Lecture Notes in Computer Science  
It is standard to regard the intuitionistic restriction of a classical logic as increasing the expressivity of the logic because the classical logic can be adequately represented in the intuitionistic  ...  We show here that subexponential logic, which is a family of substructural refinements of classical logic, each parametric over a preorder over the subexponential connectives, does not suffer from this  ...  In the work on LJF [11] there is a focally adequate encoding of classical logic in intuitionistic linear logic, which can be seen as a combination of the second and third of the above instances.  ... 
doi:10.1007/978-3-642-15205-4_17 fatcat:2wu4xiliovdatgokl2mb6abzva

Backtrackable state with linear affine implication and Assumption Grammars [chapter]

Paul Tarau, Veronica Dahl, Andrew Fall
1996 Lecture Notes in Computer Science  
A general framework of handling state information for logic programming languages on top of backtrackable assumptions (linear a ne and intuitionistic implications ranging over the current continuation)  ...  Keywords: state in logic and functional programming, linear a ne and intuitionistic implication, accumulator processing, alternative DCG implementations, destructive assignment, logical global variables  ...  Special thanks to the anonymous referee pointing out the relationships between our work and a ne linear logic.  ... 
doi:10.1007/bfb0027779 fatcat:nmwmj6ecsje57plfqjgum42a6e


2006 International Journal of Uncertainty Fuzziness and Knowledge-Based Systems  
The construction of a new categorical fuzzy model for linear logic is presented. The construction is based on a general posetvalued model.  ...  In this note, we give a brief overview of the method developed by Schalk and de Paiva. Then we build a new fuzzy model of linear logic based on this method.  ...  To get a model of intuitionistic linear logic, P has to be both a lineale and a complete lattice.  ... 
doi:10.1142/s0218488506003881 fatcat:zv2qwbjybvabrauljvhtbrmgki

Focusing and Polarization in Intuitionistic Logic [article]

Chuck Liang, Dale Miller
2007 arXiv   pre-print
Our approach to the design and analysis of these systems is based on the completeness of focusing in linear logic and on the notion of polarity that appears in Girard's LC and LU proof systems.  ...  We present a new, focused proof system for intuitionistic logic, called LJF, and show how other proof systems can be mapped into the new system by inserting logical connectives that prematurely stop focusing  ...  The work reported here was carried out while the first author was on sabbatical leave from Hofstra University to LIX.  ... 
arXiv:0708.2252v1 fatcat:octiyttzhbcsbkuylt42mehnsm

Page 2 of Mathematical Reviews Vol. , Issue 94i [page]

1994 Mathematical Reviews  
Summary: “We show how high-level algebraic nets give rise to a model of intuitionistic predicate linear logic.  ...  Finally we show as an example how to express an algebraic high-level net by a set of formulas in intuitionistic predicate linear logic.”  ... 
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