35,626 research outputs found
Etude polarisée du système L
Herbelin coined the name ``System L'' to refer to syntactical quotients of sequent calculi, in which two classes of terms interact in commands, in the manner of Curien's and Herbelin's lambda-bar-mu-mu-tilde calculus or Wadler's dual calculus. This paper introduces a system L that has constructs for all connectives of second order linear logic, and that shifts focus from the old code/environment interaction to a game between positives and negatives. L provides quotients for major second order sequent calculi, in their right-hand-side-sequents formulation as well as their two-sided-sequents formulation, namely LL, LK and LLP. The logician reader will appreciate the unifying framework for the study of sequent calculi it claims to be, whereas the computer scientist reader will appreciate the fact that it is a step toward Herbelin's project of rebuilding a theory of computation that puts ``call by name'' and ``call by value'' on an equal footing --- in particular is L involved with respect to reduction strategies, to wit that a cut elimination protocol that enjoys the Curch-Rosser property seems to stand out, and it allows to mix lazy and eager aspects. The principal tool for the study of this system is classical realizability, a consequence being that this tool is now extended to call by value
Kripke Models for Classical Logic
We introduce a notion of Kripke model for classical logic for which we
constructively prove soundness and cut-free completeness. We discuss the
novelty of the notion and its potential applications
Etude polarisée du système L
Herbelin coined the name ``System L'' to refer to syntactical quotients of sequent calculi, in which two classes of terms interact in commands, in the manner of Curien's and Herbelin's lambda-bar-mu-mu-tilde calculus or Wadler's dual calculus. This paper introduces a system L that has constructs for all connectives of second order linear logic, and that shifts focus from the old code/environment interaction to a game between positives and negatives. L provides quotients for major second order sequent calculi, in their right-hand-side-sequents formulation as well as their two-sided-sequents formulation, namely LL, LK and LLP. The logician reader will appreciate the unifying framework for the study of sequent calculi it claims to be, whereas the computer scientist reader will appreciate the fact that it is a step toward Herbelin's project of rebuilding a theory of computation that puts ``call by name'' and ``call by value'' on an equal footing --- in particular is L involved with respect to reduction strategies, to wit that a cut elimination protocol that enjoys the Curch-Rosser property seems to stand out, and it allows to mix lazy and eager aspects. The principal tool for the study of this system is classical realizability, a consequence being that this tool is now extended to call by value
From Proof Nets to the Free *-Autonomous Category
In the first part of this paper we present a theory of proof nets for full
multiplicative linear logic, including the two units. It naturally extends the
well-known theory of unit-free multiplicative proof nets. A linking is no
longer a set of axiom links but a tree in which the axiom links are subtrees.
These trees will be identified according to an equivalence relation based on a
simple form of graph rewriting. We show the standard results of
sequentialization and strong normalization of cut elimination. In the second
part of the paper we show that the identifications enforced on proofs are such
that the class of two-conclusion proof nets defines the free *-autonomous
category.Comment: LaTeX, 44 pages, final version for LMCS; v2: updated bibliograph
A System of Interaction and Structure
This paper introduces a logical system, called BV, which extends
multiplicative linear logic by a non-commutative self-dual logical operator.
This extension is particularly challenging for the sequent calculus, and so far
it is not achieved therein. It becomes very natural in a new formalism, called
the calculus of structures, which is the main contribution of this work.
Structures are formulae submitted to certain equational laws typical of
sequents. The calculus of structures is obtained by generalising the sequent
calculus in such a way that a new top-down symmetry of derivations is observed,
and it employs inference rules that rewrite inside structures at any depth.
These properties, in addition to allow the design of BV, yield a modular proof
of cut elimination.Comment: This is the authoritative version of the article, with readable
pictures, in colour, also available at
. (The published version contains
errors introduced by the editorial processing.) Web site for Deep Inference
and the Calculus of Structures at <http://alessio.guglielmi.name/res/cos
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