A parallel game semantics for Linear Logic

1997 ◽  
Vol 36 (3) ◽  
pp. 189-217
Author(s):  
Stefano Baratella ◽  
Stefano Berardi
Keyword(s):  
Linear Logic ◽  
Game Semantics

scholarly journals Games and full completeness for multiplicative linear logic

1994 ◽  
Vol 59 (2) ◽  
pp. 543-574 ◽  
Author(s):  
Samson Abramsky ◽  
Radha Jagadeesan
Keyword(s):  
Linear Logic ◽  
Winning Strategy ◽  
Game Semantics ◽  
Categorical Model ◽  
Natural Notion ◽  
Winning Strategies

AbstractWe 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 cut-free proof net. A key role is played by the notion of history-free strategy; strong connections are made between history-free 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.

scholarly journals A game semantics for linear logic

1992 ◽  
Vol 56 (1-3) ◽  
pp. 183-220 ◽  
Author(s):  
Andreas Blass
Keyword(s):  
Linear Logic ◽  
Game Semantics

scholarly journals Jump from parallel to sequential proofs: exponentials

2016 ◽  
Vol 28 (7) ◽  
pp. 1204-1252
Author(s):  
PAOLO DI GIAMBERARDINO
Keyword(s):  
Distinctive Feature ◽  
Linear Logic ◽  
The Other ◽  
Cut Elimination ◽  
Strong Normalization ◽  
Structural Rules ◽  
New Class ◽  
Game Semantics ◽  
Proof Nets

In previous works, by importing ideas from game semantics (notably Faggian–Maurel–Curien'sludics nets), we defined a new class of multiplicative/additive polarized proof nets, calledJ-proof nets. The distinctive feature of J-proof nets with respect to other proof net syntaxes, is the possibility of representing proof nets which are partially sequentialized, by usingjumps(that is, untyped extra edges) as sequentiality constraints. Starting from this result, in the present work, we extend J-proof nets to the multiplicative/exponential fragment, in order to take into account structural rules: More precisely, we replace the familiar linear logic notion of exponential box with a less restricting one (calledcone) defined by means of jumps. As a consequence, we get a syntax for polarized nets where, instead of a structure of boxes nested one into the other, we have one of cones which can bepartially overlapping. Moreover, we define cut-elimination for exponential J-proof nets, proving, by a variant of Gandy's method, that even in case of ‘superposed’ cones, reduction enjoys confluence and strong normalization.

Finiteness spaces

2005 ◽  
Vol 15 (4) ◽  
pp. 615-646 ◽  
Author(s):  
THOMAS EHRHARD
Keyword(s):  
Linear Logic ◽  
Discrete Analogue ◽  
Relational Model ◽  
Formal Similarity ◽  
Closure Condition ◽  
Linear Topology ◽  
Game Semantics ◽  
Primitive Recursion ◽  
Continuous Maps ◽  
Köthe Space

We investigate a new denotational model of linear logic based on the purely relational model. In this semantics, webs are equipped with a notion of ‘finitary’ subsets satisfying a closure condition and proofs are interpreted as finitary sets. In spite of a formal similarity, this model is quite different from the usual models of linear logic (coherence semantics, hypercoherence semantics, the various existing game semantics…). In particular, the standard fix-point operators used for defining the general recursive functions are not finitary, although the primitive recursion operators are. This model can be considered as a discrete analogue of the Köthe space semantics introduced in a previous paper: we show how, given a field, each finiteness space gives rise to a vector space endowed with a linear topology, a notion introduced by Lefschetz in 1942, and we study the corresponding model where morphisms are linear continuous maps (a version of Girard's quantitative semantics with coefficients in the field). In this way we obtain a new model of the recently introduced differential lambda-calculus.

Nominal Game Semantics

2016 ◽  
Author(s):  
Andrzej S. Murawski ◽  
Nikos Tzevelekos
Keyword(s):  
Game Semantics

Quantum Linear Logic Synthesis Algorithm Based on L-ESOP Reduction

2018 ◽  
Vol 30 (8) ◽  
pp. 1579
Author(s):  
Lihua Wei ◽  
Pengcheng Zhu ◽  
Zhijin Guan
Keyword(s):  
Linear Logic ◽  
Logic Synthesis ◽  
Synthesis Algorithm
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