Concurrent games and full completeness

@article{Abramsky1999ConcurrentGA,
  title={Concurrent games and full completeness},
  author={Samson Abramsky and Paul-Andr{\'e} Melli{\`e}s},
  journal={Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158)},
  year={1999},
  pages={431-442}
}
A new concurrent form of game semantics is introduced. This overcomes the problems which had arisen with previous, sequential forms of game semantics in modelling Linear Logic. It also admits an elegant and robust formalization. A Full Completeness Theorem for Multiplicative-Additive Linear Logic is proved for this semantics. 
View on IEEE
cs.ox.ac.uk
195 Citations
Highly Influential Citations
21
Background Citations
88
Methods Citations
32
Results Citations
7

195 Citations

Concurrent Strategies
TLDR
A bi category of very general nondeterministic concurrent games and strategies is presented to formalize distributed games in which both Player and Opponent can interact in highly distributed fashion, without, for instance, enforcing that their moves alternate.
An invitation to game semantics
TLDR
This work presents a gentle introduction to game semantics, focussing on high-level ideas and examples with a view to providing a bridge to more technical literature.
Sequentiality vs. concurrency in games and logic
  • S. Abramsky
  • Computer Science, Philosophy
    Mathematical Structures in Computer Science
  • 2003
Connections between the sequentiality/concurrency distinction and the semantics of proofs are investigated, with particular reference to games and Linear Logic.
Focusing in Asynchronous Games
TLDR
Interestingly, it is shown that associating a concurrent strategy to an asynchronous strategy can be seen as a semantical counterpart of the focusing property of linear logic.
Ludics nets, a game model of concurrent interaction
  • C. Faggian, F. Maurel
  • Computer Science
    20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05)
  • 2005
TLDR
This work introduces L-nets as a game model of concurrent interaction that results into partial orders, hence allowing for parallelism in Games Semantics and Ludics.
Fully-abstract concurrent games for pi
TLDR
A semantics for Milner's pi-calculus is defined, with three main novelties, based on reduction semantics, which provides a fully-abstract model for fair testing equivalence and has a strong game semantical flavor in the sense of Hyland-Ong and Nickau.
Fully-abstract concurrent games for π
TLDR
A semantics for Milner's pi-calculus is defined, with three main novelties, based on reduction semantics, which provides a fully-abstract model for fair testing equivalence and has a strong game semantical flavor in the sense of Hyland-Ong and Nickau.
Syntax vs. semantics: A polarized approach
Fully Abstract Game Semantics for Actors
TLDR
The full abstraction proof of game semantics for actors is given, based on the work on the algebraic theory of actors andgame semantics for asynchronous $\pi$ calculus.
Process Realizability
  • S. Abramsky
  • Computer Science
    Electron. Notes Theor. Comput. Sci.
  • 1999
...
...

References

SHOWING 1-10 OF 36 REFERENCES
Believe it or not, AJM's games model is a model of classical linear logic
TLDR
A subcategory of saturated strategies, closed under all possible codings in copy games, is shown to model reduction in classical linear logic.
Games and full completeness for multiplicative linear logic
TLDR
It is shown that this semantics yields a categorical model of Linear Logic and proves full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the denotation of a unique cut-free proof net.
Linear logic, totality and full completeness
  • R. Loader
  • Mathematics
    Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science
  • 1994
TLDR
This work gives a 'totality space' model for linear logic derived by taking an abstract view of computations on a datatype based upon a notion of total object and proves a full completeness result.
PROOF-NETS : THE PARALLEL SYNTAX FOR PROOF-THEORY
TLDR
The paper is mainly concerned with the extension of proof-nets to additives, for which the best known solution is presented, which is shown to be compatible with quantifiers, and the structural rules of exponentials are also accommodated.
Models of Lambda Calculi and Linear Logic: Structural, Equational and Proof-Theoretic Characterisati
Models of Lambda Calculi and Linear Logic: T his thesis is an investigation into models of typed-calculi and of linear logic. The models we investigate are denotational in nature; we construct…
Annals of Pure and Applied Logic
TLDR
A new process logic is defined, called computation paths logic (CPL), which treats lbnn~~la~ and programs essentially alike and is decidable in elementary tlmc, and also ofrcr extensions for modeling asynchronouaisynchronous concurrency and infinite computanons.
Domains and lambda-calculi
TLDR
This chapter discusses the development of lambda-calculi in CCC's of algebraic dcpo's, as well as its applications in recursion theory and category theory.
Domain Theory in Logical Form
Petri Nets
TLDR
The structure of Petr i nets, thei r markings and execution, several examples of Petm net models of computer hardware and software, and research into the analysis of Pet m nets are presented, as are the use of the reachabil i ty tree and the decidability and complexity of some Petr i net problems.
A new deconstructive logic: linear logic
TLDR
The method presented is powerful: it allows us to recover as fragments formalisms as seemingly different as Girard's LC and Parigot's λμ, FD, delineates other viable systems as well, and gives means to extend the Krivine/Leivant paradigm of ‘programming-with-proofs’ to classical logic.
...
...