# Games and Full Completeness for Multiplicative Linear Logic

arXiv: https://arxiv.org/abs/1311.6057 · HTML: https://mlsanity.com/paper/1311.6057/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Nov 2013.

## Built on by (most cited first, 1 of 1)

- [Object Recognition by a Minimally Pre-Trained System in the Process of Environment Exploration](https://mlsanity.com/paper/2111.11965/) (2021)

## Abstract (arXiv)

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 cut-free proof net. A key role is played by the notion of em 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.