# Ludics with Repetitions (Exponentials, Interactive Types and Completeness)

@article{Basaldella2009LudicsWR, title={Ludics with Repetitions (Exponentials, Interactive Types and Completeness)}, author={Michele Basaldella and Claudia Faggian}, journal={2009 24th Annual IEEE Symposium on Logic In Computer Science}, year={2009}, pages={375-384} }

We prove that is possible to extend Girard's Ludics so as to have repetitions (hence exponentials), and still have the results on semantical types which characterize Ludics in the panorama of Game Semantics. The results are obtained by using less structure than in the original paper; this has an interest on its own, and we hope that it will open the way to applying the approach of Ludics to a larger domain.

## Figures and Tables from this paper

## 34 Citations

### Inductive and Functional Types in Ludics

- MathematicsCSL
- 2017

This paper investigates the representation of inductive data types and functional types in ludics following a game semantics approach, and identifies which higher-order functions types fail to satisfy type safety.

### On the Meaning of Focalization

- Computer SciencePRELUDE Project
- 2011

Girard's ludics are used to analyze focalization, a fundamental property of the proof theory of linear logic, and show how focalization can be realized interactively thanks to suitable section-retraction pairs between semantical types.

### Ludics Characterization of Multiplicative-Additive Linear Behaviours

- Computer Science, MathematicsArXiv
- 2014

Ludics is a logical theory that J.-Y. Girard developed around 2000. At first glance, it may be considered as a Brouwer-Heyting-Kolmogorov interpretation of Logic as a formula is denoted by the set of…

### Infinitary Completeness in Ludics

- Mathematics2010 25th Annual IEEE Symposium on Logic in Computer Science
- 2010

The purpose is to provide an interactive form of completeness between infinite proofs and infinite models over formulas of infinite depth (that include recursive types), where proofs and models are homogenous.

### Type Theory in Ludics

- MathematicsArXiv
- 2014

This work introduces some notions on Ludics and the interpretation of Martin-Lof rules, and proposes a representation for simple types in Ludics, i.e., natural numbers, lists, the arrow construction and the usual constructors.

### Incarnation in Ludics and maximal cliques of paths

- MathematicsLog. Methods Comput. Sci.
- 2013

This paper gives here a constructive way to capture the incarnation of the behaviour of a set of designs, without computing the behaviour itself, which is useful in particular because being "incarnated" is one of the conditions for a design to denote a proof of a formula.

### On the Meaning of Logical Completeness

- MathematicsTLCA
- 2009

This work considers an extension of the original ludics with contraction and universal nondeterminism in order to capture a polarized fragment of linear logic and thus a constructive variant of classical propositional logic and proves a completeness theorem for proofs in this extended setting.

### Jump from parallel to sequential proofs: exponentials

- Computer ScienceMathematical Structures in Computer Science
- 2016

This work replaces the familiar linear logic notion of exponential box with a less restricting one (called cone) defined by means of jumps, and gets a syntax for polarized nets where, instead of a structure of boxes nested one into the other, there is one of cones which can be partially overlapping.

## References

SHOWING 1-10 OF 70 REFERENCES

### Ludics is a Model for the Finitary Linear Pi-Calculus

- Computer ScienceTLCA
- 2007

This work analyzes in game-semantical terms the finitary fragment of the linear π-calculus, and proves that the model is fully complete and fully abstract w.r.t. the calculus.

### Towards Ludics Programming: Interactive Proof Search

- Computer ScienceICLP
- 2008

This paper investigates how ludics could serve as a foundation for logic programming, providing a mechanism for interactive proof search, that is proof search by interaction (orProof search by cut-elimination).

### Designs, Disputes and Strategies

- PhilosophyCSL
- 2002

It is explained how Ludics basic notions correspond to those of the "innocent strategy" appraoch to Games Semantics, and thus establish a clear connection between the two subjects.

### Polarized games

- Computer ScienceProceedings 17th Annual IEEE Symposium on Logic in Computer Science
- 2002

The intuitionistic Hyland-Ong games are generalized to a notion of polarized games allowing games with plays starting by proponent moves yielding a game model for polarized linear logic with a definability result.

### Introduction to linear logic and ludics, part I

- Computer ScienceArXiv
- 2005

A survey of linear logic and ludics, which were introduced by Girard in 1986 and 2001, are offered, which covers an introduction to the connectives and proof rules oflinear logic, to its decidability properties, and to its models.

### An introduction to uniformity in Ludics

- MathematicsLICS 2003
- 2003

In these notes we develop explicit examples to help understanding the role of uniformity in Ludics. This is the key notion that underlies the move from behaviours to bihaviours. Uniformity arises in…

### Travelling on Designs

- Mathematics, Computer ScienceCSL
- 2002

An abstract machine is introduced which presents normalization as a token travelling along a net of designs, allowing a concrete approach to carry on the study of issues such as which part of a design can be recognized interactively and how to reconstruct a design from the traces of its interactions in different tests.

### On the Meaning of Logical Completeness

- MathematicsTLCA
- 2009

This work considers an extension of the original ludics with contraction and universal nondeterminism in order to capture a polarized fragment of linear logic and thus a constructive variant of classical propositional logic and proves a completeness theorem for proofs in this extended setting.

### Partial Orders, Event Structures and Linear Strategies

- Computer Science, MathematicsTLCA
- 2009

A Game Semantics where strategies are partial orders, and composition is a generalization of the merging of orders is introduced, and a compact closed category of event structures which embeds Linear Strategies is introduced.