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Syntax vs. semantics: a polarized approach
 THEORETICAL COMPUTER SCIENCE
, 2005
"... We present a notion of sliced proofnets for the polarized fragment of Linear Logic and a corresponding game model. We show that the connection between them is very strong through an equivalence of categories (this contains soundness, full completeness and faithful completeness). ..."
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Cited by 14 (3 self)
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We present a notion of sliced proofnets for the polarized fragment of Linear Logic and a corresponding game model. We show that the connection between them is very strong through an equivalence of categories (this contains soundness, full completeness and faithful completeness).
A Game Semantics For Generic Polymorphism
, 1971
"... Genericity is the idea that the same program can work at many dierent data types. Longo, Milstead and Soloviev proposed to capture the inability of generic programs to probe the structure of their instances by the following equational principle: if two generic programs, viewed as terms of type 8X ..."
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Cited by 9 (4 self)
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Genericity is the idea that the same program can work at many dierent data types. Longo, Milstead and Soloviev proposed to capture the inability of generic programs to probe the structure of their instances by the following equational principle: if two generic programs, viewed as terms of type 8X:A[X ], are equal at any given instance A[T ], then they are equal at all instances. They proved that this rule is admissible in a certain extension of System F, but nding a semantically motivated model satisfying this principle remained an open problem.
Game semantics for firstorder logic
, 2010
"... We refine HO/N game semantics with an additional notion of pointer (mupointers) and extend it to firstorder classical logic with completeness results. We use a Church style extension of Parigot’s lambdamucalculus to represent proofs of firstorder classical logic. We present some relations with ..."
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Cited by 4 (0 self)
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We refine HO/N game semantics with an additional notion of pointer (mupointers) and extend it to firstorder classical logic with completeness results. We use a Church style extension of Parigot’s lambdamucalculus to represent proofs of firstorder classical logic. We present some relations with Krivine’s classical realizability and applications to type isomorphisms.
Game Semantics in String Diagrams
"... equipped with a notion of tensorial negation. We establish that the free dialogue category is a category of dialogue games and total innocent strategies. The connection clarifies the algebraic and logical nature of dialogue games, and their intrinsic connection to linear continuations. The proof of ..."
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equipped with a notion of tensorial negation. We establish that the free dialogue category is a category of dialogue games and total innocent strategies. The connection clarifies the algebraic and logical nature of dialogue games, and their intrinsic connection to linear continuations. The proof of the statement is based on an algebraic presentation of dialogue categories inspired by knot theory, and a factorization theorem established by rewriting techniques. Index Terms—Dialogue games, innocent strategies, linear continuations, string diagrams, ribbon categories, coherence theorems, 2dimensional algebra. I.
Compressing Polarized Boxes
"... Abstract—The sequential nature of sequent calculus provides a simple definition of cutelimination rules that duplicate or erase subproofs. The parallel nature of proof nets, instead, requires the introduction of explicit boxes, which are global and synchronous constraints on the structure of graph ..."
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Abstract—The sequential nature of sequent calculus provides a simple definition of cutelimination rules that duplicate or erase subproofs. The parallel nature of proof nets, instead, requires the introduction of explicit boxes, which are global and synchronous constraints on the structure of graphs. We show that logical polarity can be exploited to obtain an implicit, compact, and natural representation of boxes: in an expressive polarized dialect of linear logic, boxes may be represented by simply recording some of the polarity changes occurring in the box at level 0. The content of the box can then be recovered locally and unambiguously. Moreover, implicit boxes are more parallel than explicit boxes, as they realize a larger quotient. We provide a correctness criterion and study the novel and subtle cutelimination dynamics induced by implicit boxes, proving confluence and strong normalization.