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38
Games and Full Completeness for Multiplicative Linear Logic
 JOURNAL OF SYMBOLIC LOGIC
, 1994
"... We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the den ..."
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Cited by 210 (26 self)
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We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the denotation of a unique cutfree proof net. A key role is played by the notion of historyfree strategy; strong connections are made between historyfree strategies and the Geometry of Interaction. Our semantics incorporates a natural notion of polarity, leading to a refined treatment of the additives. We make comparisons with related work by Joyal, Blass et al.
A Brief Guide to Linear Logic
, 1993
"... An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation. ..."
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Cited by 53 (8 self)
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An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation.
Full completeness of the multiplicative linear logic of chu spaces
 Proc. IEEE Logic in Computer Science 14
, 1999
"... We prove full completeness of multiplicative linear logic (MLL) without MIX under the Chu interpretation. In particular we show that the cutfree proofs of MLL theorems are in a natural bijection with the binary logical transformations of the corresponding operations on the category of Chu spaces on ..."
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Cited by 22 (8 self)
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We prove full completeness of multiplicative linear logic (MLL) without MIX under the Chu interpretation. In particular we show that the cutfree proofs of MLL theorems are in a natural bijection with the binary logical transformations of the corresponding operations on the category of Chu spaces on a twoletter alphabet. This is the online version of the paper of the same title appearing in the LICS’99 proceedings. 1
From proof nets to the free * autonomous category
 Logical Methods in Computer Science, 2(4:3):1–44, 2006. Available from: http://arxiv.org/abs/cs/0605054. [McK05] Richard McKinley. Classical categories and deep inference. In Structures and Deduction 2005 (Satellite Workshop of ICALP’05
, 2005
"... Vol. 2 (4:3) 2006, pp. 1–44 www.lmcsonline.org ..."
Chu spaces and their interpretation as concurrent objects
, 2005
"... A Chu space is a binary relation =  from a set A to an antiset X defined as a set which transforms via converse functions. Chu spaces admit a great many interpretations by virtue of realizing all small concrete categories and most large ones arising in mathematical and computational practice. Of pa ..."
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Cited by 21 (0 self)
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A Chu space is a binary relation =  from a set A to an antiset X defined as a set which transforms via converse functions. Chu spaces admit a great many interpretations by virtue of realizing all small concrete categories and most large ones arising in mathematical and computational practice. Of particular interest for computer science is their interpretation as computational processes, which takes A to be a schedule of events distributed in time, X to be an automaton of states forming an information system in the sense of Scott, and the pairs (a, x) in the =  relation to be the individual transcriptions of the making of history. The traditional homogeneous binary relations of transition on X and precedence on A are recovered as respectively the right and left residuals of the heterogeneous binary relation =  with itself. The natural algebra of Chu spaces is that of linear logic, made a process algebra by the process interpretation.
First Order Linear Logic without Modalities Is NEXPTIMEHard
 Theoretical Computer Science
, 1994
"... The decision problem is studied for the nonmodal or multiplicativeadditive fragment of first order linear logic. This fragment is shown to be nexptime hard. The hardness proof combines Shapiro's logic programming simulation of nondeterministic Turing machines with the standard proof of the pspace ..."
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Cited by 15 (11 self)
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The decision problem is studied for the nonmodal or multiplicativeadditive fragment of first order linear logic. This fragment is shown to be nexptime hard. The hardness proof combines Shapiro's logic programming simulation of nondeterministic Turing machines with the standard proof of the pspace hardness of quantified boolean formula validity, utilizing some of the surprisingly powerful and expressive machinery of linear logic. 1 Introduction Linear logic, introduced by Girard, is a resourcesensitive refinement of classical logic [10, 29]. Linear logic gains its expressive power by restricting the "structural" proof rules of contraction (copying) and weakening (erasing). The contraction rule makes it possible to reuse any stated assumption as often as desired. The weakening rule makes it possible to use dummy assumptions, i.e., it allows a deduction to be carried out without using all of the hypotheses. Because contraction and weakening together make it possible to use an assu...
On the axiomatisation of Boolean categories with and without medial, 2005. Preprint, available at http://arxiv.org/abs/cs.LO/0512086
"... Abstract. In its most general meaning, a Boolean category is to categories what a Boolean algebraic structure underlying the proofs in Boolean Logic, in the same sense as a ..."
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Cited by 15 (8 self)
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Abstract. In its most general meaning, a Boolean category is to categories what a Boolean algebraic structure underlying the proofs in Boolean Logic, in the same sense as a
Higher Dimensional Automata Revisited
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 2000
"... ..."
On proof nets for multiplicative linear logic with units
 In Jerzy Marcinkowski and Andrzej Tarlecki, editors, Computer Science Logic, CSL 2004, volume 3210 of LNCS
, 2004
"... Abstract. In this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the wellknown theory of unitfree multiplicative proof nets. A linking is no longer a set of axiom links but a tree in which the axiom links are subtrees. Th ..."
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Cited by 14 (4 self)
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Abstract. In this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the wellknown theory of unitfree 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. Furthermore, the identifications enforced on proofs are such that the proof nets, as they are presented here, form the arrows of the free (symmetric) *autonomous category. 1
Chu Spaces as a Semantic Bridge Between Linear Logic and Mathematics
 Theoretical Computer Science
, 1998
"... The motivating role of linear logic is as a "logic behind logic." We propose a sibling role for it as a logic of transformational mathematics via the selfdual category of Chu spaces, a generalization of topological spaces. These create a bridge between linear logic and mathematics by soundly interp ..."
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Cited by 12 (2 self)
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The motivating role of linear logic is as a "logic behind logic." We propose a sibling role for it as a logic of transformational mathematics via the selfdual category of Chu spaces, a generalization of topological spaces. These create a bridge between linear logic and mathematics by soundly interpreting linear logic while fully and concretely embedding a comprehensive range of concrete categories of mathematics. Our main goal is to treat each end of this bridge in expository detail. In addition we introduce the dialectic lambdacalculus, and show that dinaturality semantics is not fully complete for the Chu interpretation of linear logic. 1 Introduction Linear logic was introduced by J.Y. Girard as a "logic behind logic." It separates logical reasoning into a core linear part in which formulas are merely moved around, and an auxiliary nonlinear part in which formulas may be deleted and copied. The core, multiplicative linear logic (MLL), is a substructural logic whose basic connect...