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Topic: Intuitionistic linear logic

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Linear logic

List of topics in logic

	Linear Logic, Monads, and the Lambda Calculus - Benton, Wadler (ResearchIndex) (Site not responding. Last check: 2007-11-01)
		Linear Logic, Monads, and the Lambda Calculus - Benton, Wadler (ResearchIndex)
		Linear Logic, Monads, and the Lambda Calculus (1995)
		Linear Logic, Monads and the Lambda Calculus - Benton, Wadler (1996)
	citeseer.ifi.unizh.ch /9733.html (603 words)

	Pretopology Semantics for Bimodal Intuitionistic Linear Logic - HARTONAS (ResearchIndex) (Site not responding. Last check: 2007-11-01)
		Pretopology Semantics for Bimodal Intuitionistic Linear Logic - HARTONAS (ResearchIndex)
		Pretopology Semantics for Bimodal Intuitionistic Linear Logic (1997)
		87 Linear Logic: Its Syntax and Semantics - Girard - 1995
	citeseer.ist.psu.edu /158474.html (612 words)

	Linear Logic
		In the sequent calculus presentation of classical logic, the rules for the connectives "and" and "or", as well as the Cut rule and the rule for implication may be presented equivalently in an additive form (the context of the premises are the same) or a multiplicative form (the context of the premises are different).
		Many models of linear logic proofs have been proposed; we consider that, to date, the simplest and most intuitive construction is those based on the so-called “relational semantics”, where formulas are interpreted as multisets, sequents as tuples of multisets and proofs as relations over the interpretation of sequents.
		Linear logic provides this approach to computational specification new types, new declarative means for statically understand how resources may be used in a computation, and provided an appealing means for formalizing the duality between a function and the environment that supplies it with arguments.
	plato.stanford.edu /entries/logic-linear (5958 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		We also show how intuitionistic logic may be embedded in intuitionistic (and classical) linear logic, proving that we gain structure without a loss of expressive power.
		Such a linear type reconstruction can be seen either as a compilation from lambda calculus to a linear term language (remember that a linear term language is lower level as it includes resource usage information), or equivalently as strictness and/or sharing analysis for the lambda calculus.
		A linear decoration of a proof in IL or CL is a proof in the corresponding linear logic, with the same structure as the original proof.
	www.cs.cmu.edu /afs/cs/user/fp/courses/95-linear/lectures.txt (2435 words)

	Logic programming in a fragment of linear logic (Site not responding. Last check: 2007-11-01)
		Logic Programming in a Fragment of Intuitionistic Linear Logic Joshua S. Hodas and Dale Miller Computer Science Department University of Pennsylvania Philadelphia, PA 19104-6389 USA When logic programming is based on the proof theory of intuitionistic logic, it is natural to allow implications in goals and in the bodies of clauses.
		While such an intuitionistic notion of context provides for elegant specifications of many computations, contexts can be made more expressive and flexible if they are based on linear logic.
		Logic programs based on the intuitionistic theory of hereditary Harrop formulas can be modularly embedded into this linear logic setting.
	www.cis.upenn.edu /~bcpierce/types/archives/1992/msg00065.html (500 words)

	Wadler: Linear Logic
		This paper introduces a new way of attaching proof terms to proof trees for classical linear logic, which bears a close resemblance to the way that pattern matching is used in programming languages.
		Call-by-name, call-by-value, call-by-need, and the linear lambda calculus
		The presentation of linear logic is simplified by basing it on the Logic of Unity.
	homepages.inf.ed.ac.uk /wadler/topics/linear-logic.html (1065 words)

	Logic Programming in ILL
		Abstract: Logic programming languages based on fragments of intuitionistic logic have recently been developed and studied by several researchers In such languages, implications are permitted in goals and in the bodies of clauses.
		While an intuitionistic notion of context has many uses, it has turned out to be either too powerful or too limiting in several settings.
		We refine the intuitionistic notion of context by using a fragment of Girard's linear logic that includes additive and multiplicative conjunction, linear implication, universal quantification, the ``of course'' exponential, and the constants 1 (the empty context) and T (for ``erasing'' contexts).
	www.lfcs.inf.ed.ac.uk /reports/91/ECS-LFCS-91-158 (246 words)

	Logic and Critical Thinking at Erratic Impact's Philosophy Research Base
		Linear logic was developed by J.Y.Girard as part of his investigation into the semantics of Intuitionistic Logic.
		Linear Logic has now matured into a rich area of active research: a workshop devoted to linear logic was held at Cornell in 1993, and another workshop was held at Keio University in Tokyo in 1996.
		Many papers have been published regarding linear logic semantics, proof theory, complexity, and expressiveness, and there is an electronic mailing list devoted to linear logic (to join send email to linear-request@cs.stanford.edu).
	www.erraticimpact.com /~topics/html/logic.htm (954 words)

	natural deduction for linear logic; corrections;bibliography (Site not responding. Last check: 2007-11-01)
		ABSTRACT Natural deduction for intuitionistic linear logic by A.S. Troelstra The paper deals with two versions of the fragment with unit, tensor, linear implication and storage operator (the exponential !) of intuitionistic linear logic.
		It is relatively easy to adapt Prawitz's treatment of natural deduction for intuitionistic logic to ILLP; in particular one can formulate a notion of strong validity (as in Prawitz's ``Ideas and Results in Proof Theory'') permitting a proof of strong normalization.
		The file nat.ps is the postscript file of the paper "Natural deduction for intuitionistic linear logic", report ML-93-09 of The Institute for Logic.
	www.cis.upenn.edu /~bcpierce/types/archives/1993/msg00086.html (315 words)

	Bibliography on Linear Logic
		An introduction to `On the pi-calculus and linear logic' by Gianluigi Bellin and Philip Scott.
		The Horn fragment of linear logic is NP-complete.
		The complexity of the Horn fragment of linear logic.
	www-2.cs.cmu.edu /~carsten/linearbib/llb.html (6680 words)

	Introduction to Linear Logic (Site not responding. Last check: 2007-11-01)
		Linear Logic was introduced by J.-Y. Girard in 1987 and it has attracted much attention from computer scientists, as it is a logical way of coping with resources and resource control.
		Cut-elimination for Classical Logic is highly non-deterministic; it is shown how this can be remedied either by moving to Intuitionistic Logic or to Linear Logic.
		In the case on Linear Logic we consider Intuitionistic Linear Logic as well as Classical Linear Logic.
	www.brics.dk /LS/96/6/BRICS-LS-96-6/BRICS-LS-96-6.html (210 words)

	Semantics and Logics of Computation (University of Turin) - People - Dipartimento di Informatica - Università di ...
		It has been developed by introducing Light linear logic, and it is based on a careful control of the expressiveness of the logical rule contraction.
		The distinguishing feature of FALL is that it is a proof-theoretic system that both embodies the quite restrictive structural constraints `a la Linear logic to control the reduction complexity, and keeps such constraints flexible enough to encode, and simulate, the more programming-oriented terms of BC.
		Given the lambda terms admitting Curry types as a source language, and considered the implicative fragment of the linear lambda terms as an object language, we define a compiler from the first to the second language exclusively driven by the structure of the proof which gives a type to a source program.
	www.di.unito.it /~rover/RESEARCH/BIBLIOGRAPHY (2050 words)

	papers.html
		On an Intuitionistic Modal Logic (with Gavin Bierman), Studia Logica (65):383-416, 2000.
		Linear Logic in Isabelle (with S. Kalvala) in Proceedings of the Isabelle Users Workshop, Technical Report TR379, Computer Laboratory, University of Cambridge, September 1995.
		Linear Logic and Applications R. Crouch, Josef van Genabith, V. de Paiva and E. Ritter (editors) Dagstuhl-Seminar-Report, 248, IBFI gem GmbH, Schloss Dagstuhl, D-66687 Wadern, Germany, ISSN 0940-1121, 22.08.99-27.08.99.
	www.cs.bham.ac.uk /~vdp/publications/papers.html (1660 words)

	[No title]
		Linear Explicit Substitutions (with Neil Ghani and Eike Ritter), in the Journal of the IGPL, vol 8, Issue 1, January 2000, 7-31.
		Explicit Substitutions for Linear Logical Frameworks (with Iliano Cervesato and Eike Ritter), Proc.
		Yet another intuitionistic modal logic (with G. Bierman) Abstract of a contributed paper in the Logic Colloquium 1994, The Bulletin of Symbolic Logic, vol 1(2), June 1995.
	www2.parc.com /spl/members/paiva/publications/papers.html (1166 words)

	Lolli: A Linear Logic Programming Language
		It is based on the logic of Higher-Order Hereditary Harrop Formulas, a fragment of ordinary (that is, not Linear) Intuitionistic logic.
		The logic and meta-theory are presented in detail with full proofs; more and longer examples are given, and the implementation of the language is discussed at length.
		This paper presents a variant of the logic of Lolli in which it is possible to directly specify the Relevant (clauses may be copied but not discarded) and Affine (clauses may be discarded but not copied) constraints.
	www.lix.polytechnique.fr /Labo/Dale.Miller/lolli (1643 words)

	Re: Higher-order linear logic
		The earliest uses were with Horn clauses [nadathur90jacm] and intuitionistic logic [miller91apal].
		Later versions mixed higher-order quantification (as in Church's Simple Theory of Types) with intuitionistic linear logic [hodas94ic] and all of linear logic [miller96tcs].
		Numerous examples mixing higher-order quantification with linear logic are illustrated in these last two papers.
	www.seas.upenn.edu /~sweirich/types/archive/1999-2003/msg00638.html (140 words)

	BI
		The logic of bunched implications, BI, is a substructural system which freely combines an additive (intuitionistic) and a multiplicative (linear) implication via bunches (contexts with two combining operations, one which admits Weakening and Contraction and one which does not).
		Specifically, we start with the multiplicative fragment of linear logic and extend, on the one hand, to linear logic with its additives and, on the other, to the additives of the logic of bunched implications (BI).
		The logic of bunched implications, BI, provides a logical analysis of a basic notion of resource rich enough, for example, to form the logical basis for ``pointer logic'' and ``separation logic'' semantics for programs which manipulate mutable data structures.
	www.cs.bath.ac.uk /~pym/BI.html (1338 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		Series: Logic Seminar Date: Tuesday, September 28, 1999 Speaker: Dale Miller (Penn State, CSE) Title: A Meta-Logic for Sequent Calculus Time: 2:30 - 3:20 PM Place: 122 Thomas Building Abstract: Linear logic can be used as a meta-logic to specify a variety of sequent calculus proof systems for classical, intuitionistic, and linear logic.
		The operational semantics of linear logic arising from goal-directed search translates directly into object-level proof search semantics.
		Finally, we show how the meta-theory of linear logic can be used to prove various properties of object-level proof systems.
	www.math.psu.edu /simpson/logic/seminar/990928.txt (118 words)

	Linear Logic on Petri Nets. (Site not responding. Last check: 2007-11-01)
		An aim is to use Petri nets to give an understanding of linear logic and give some appraisal of the value of linear logic as a specification logic for Petri nets.
		This logic is shown sound and complete with respect to atomic nets (this include nets in which every transition leads to a nonempty multiset of places).
		The logic is remarkably expressive, enabling descriptions of the kinds of properties one might wish to show of nets; in particular, negative properties, asserting the impossibility of an assertion, can also be expressed.
	www.informatik.uni-hamburg.de /TGI/pnbib/e/engberg_u2.html (236 words)

	Seminar on Linear Logic and Applications (CS 359)
		Classical and intuitionistic sequent calculi; role of structural rules; interpretation from classical into intuitionistic logic; inversion principles; permutability of inference rules; normal and long normal forms; cut elimination.
		Additive, multiplicative, and exponential connectives; intuitionistic and classical versions; traditional and zonal presentations; interpretations from classical and intuitionistic into linear logic; cut-elimination; examples.
		Linear intuitionistic natural deductions; proof term assignments; reductions and equality; normal forms; normalization; relation to sequent calculi Bie94
	theory.stanford.edu /~iliano/courses/99-winter-linear/topics.html (1171 words)

	Proof theory for full intuitionistic linear logic, bilinear logic, and MIX categories (Site not responding. Last check: 2007-11-01)
		This note applies techniques we have developed to study coherence in monoidal categories with two tensors, corresponding to the tensor-par fragment of linear logic, to several new situations, including Hyland and de Paiva's Full Intuitionistic Linear Logic (FILL), and Lambek's Bilinear Logic (BILL).
		Note that the latter is a noncommutative logic; we also consider the noncommutative version of FILL.
		We define the appropriate notion of proof nets for these logics, and use them to describe coherence results for the corresponding categorical structures.
	www.tac.mta.ca /tac/volumes/1997/n5/3-05abs.html (197 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		Series: Logic Seminar Speaker: Dale Miller, Computer Science and Engineering, Penn State Title: Sequent Calculus and the Specification of Computation Date: Tuesday, March 17, 1998, 2:30 PM Location: 308 Boucke Building Abstract: In recent years, sequent calculus presentations of proof systems have been used in a number of applications of logic to computer science.
		From such a foundation, various logic programming languages have been designed that exploit subsets of classical, intuitionistic, and linear logic.
		Given their foundation in logic and proof theory, novel ways to reason about logic programs are also possible.
	www.math.psu.edu /simpson/logic/seminar/980317.txt (137 words)

	Amazon.com: Labelled Deduction (APPLIED LOGIC SERIES Volume 17): Books: David Basin,M. D'Agostino,D.M. Gabbay,Seán ... (Site not responding. Last check: 2007-11-01)
		Labelled deduction is an approach to providing frameworks for presenting and using different logics in a uniform and natural way by enriching the language of a logic with additional information of a semantic proof-theoretical nature.
		Labelled deduction systems often possess attractive properties, such as modularity in the way that families of related logics are presented, parameterised proofs of metatheoretic properties, and ease of mechanisability.
		His research focuses on the theory and applications of non-classical logics, of proof development systems, of logical frameworks, and of logics for security.
	www.amazon.com /Labelled-Deduction-APPLIED-LOGIC-17/dp/0792362373 (676 words)

	15-816 Linear Logic
		This graduate course provides an introduction to linear logic with an emphasis on its applications in computer science.
		We will also develop a linear type theory which will serve as a meta-language in which the theory of programming languages with state can be formalized effectively.
		(10/4) Handout 5 on Pi Calculus in Linear Logic for lecture 7 is now available (picalc.ps).
	www-2.cs.cmu.edu /~fp/courses/linear (480 words)

	[2-7] Free Logic Programming Systems
		The foundation of ALF is Horn clause logic with equality which consists of predicates and Horn clauses for logic programming, and functions and equations for functional programming.
		Like Prolog and other existing logic programming languages, it is a very high-level language that allows programmers to concentrate on the problem rather than the low-level details such as memory management.
		Mercury's type system is based on many-sorted logic with parametric polymorphism, very similar to the type systems of modern functional languages such as ML and Haskell.
	www.faqs.org /faqs/prolog/resource-guide/part2/section-8.html (590 words)

	Cut-Elimination for Full Intuitionistic Linear Logic - Brauner, de Paiva (ResearchIndex) (Site not responding. Last check: 2007-11-01)
		Abstract: We describe in full detail a solution to the problem of proving the cut elimination theorem for FILL, a variant of (multiplicative and exponential-free) Linear Logic introduced by Hyland and de Paiva.
		Hyland and de Paiva's work used a term assignment system to describe FILL and barely sketched the proof of cut elimination.
		In this paper, as well as correcting a small mistake in their paper and extending the system to deal with exponentials, we introduce a di#erent formal system describing the...
	citeseer.ist.psu.edu /218615.html (365 words)

	Information and Computation Bibliography (Site not responding. Last check: 2007-11-01)
		When logic programming is based on the proof theory of intuitionistic logic, it is natural to allow implications in goals and in the bodies of clauses.
		An interpreter for this logic programming language must address the problem of splitting contexts; that is, when attempting to prove a multiplicative conjunction (tensor), say
		The abstract is also available as a LaTeX file, a DVI file, or a PostScript file.
	theory.lcs.mit.edu /~iandc/References/hodasm1994:327.html (601 words)

	Ordered Linear Logic Programming - Polakow, Pfenning (ResearchIndex) (Site not responding. Last check: 2007-11-01)
		Abstract: We begin with a review of intuitionistic non-commutative linear logic (INCLL), a refinement of linear logic with an inherent notion of order proposed by the authors in prior work.
		We then develop a logic programming interpretation for INCLL in two steps: (1) we give a system of ordered uniform derivations which is sound and complete with respect to INCLL, and (2) we present a model of resource consumption which removes non-determinism from ordered resource allocation during search for uniform...
		0.2: A Judgmental Reconstruction of Modal Logic - Pfenning, Davies
	citeseer.ifi.unizh.ch /2629.html (557 words)

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