Interaction graphs: Full linear logic

T Seiller - Proceedings of the 31st Annual ACM/IEEE Symposium …, 2016 - dl.acm.org
Interaction graphs were introduced as a general, uniform, construction of dynamic models of
linear logic, encompassing all Geometry of Interaction (GoI) constructions introduced so far …

[HTML][HTML] Interaction graphs: Graphings

T Seiller - Annals of Pure and Applied Logic, 2017 - Elsevier
Abstract In two previous papers [33],[37], we exposed a combinatorial approach to the
program of Geometry of Interaction, a program initiated by Jean-Yves Girard [16]. The …

[HTML][HTML] Interaction graphs: additives

T Seiller - Annals of Pure and Applied Logic, 2016 - Elsevier
Abstract Geometry of Interaction (GoI) is a research program initiated by Jean-Yves Girard
which aims at defining a semantics of linear logic proofs accounting for the dynamical …

Interaction graphs: Non-deterministic automata

T Seiller - ACM Transactions on Computational Logic (TOCL), 2018 - dl.acm.org
This article exhibits a series of semantic characterisations of sublinear nondeterministic
complexity classes. These results fall into the general domain of logic-based approaches to …

Characterizing co-NL by a group action

C Aubert, T Seiller - Mathematical Structures in Computer Science, 2016 - cambridge.org
In a recent paper, Girard (2012) proposed to use his recent construction of a geometry of
interaction in the hyperfinite factor (Girard 2011) in an innovative way to characterize …

[HTML][HTML] Logarithmic space and permutations

C Aubert, T Seiller - Information and Computation, 2016 - Elsevier
In a recent work, Girard proposed a new and innovative approach to computational
complexity based on the proofs-as-programs correspondence. In a previous paper, the …

Multiplicative linear logic from a resolution-based tile system

B Eng, T Seiller - arxiv preprint arxiv:2207.08465, 2022 - arxiv.org
We present the stellar resolution, a" flexible" tile system based on Robinson's first-order
resolution. After establishing formal definitions and basic properties of the stellar resolution …

Interaction graphs: Exponentials

T Seiller - Logical Methods in Computer Science, 2019 - lmcs.episciences.org
This paper is the fourth of a series exposing a systematic combinatorial approach to Girard's
Geometry of Interaction (GoI) program. The GoI program aims at obtaining particular …

On the computational meaning of axioms

A Naibo, M Petrolo, T Seiller - Epistemology, knowledge and the impact of …, 2016 - Springer
This paper investigates an anti-realist theory of meaning suitable for both logical and proper
axioms. Unlike other anti-realist accounts such as Dummett–Prawitz verificationism, the …

Linear Realisability and Cobordisms

V Maestracci, T Seiller - arxiv preprint arxiv:2310.19339, 2023 - arxiv.org
Cobordism categories are known to be compact closed. They can therefore be used to
define non-degenerate models of multiplicative linear logic by combining the Int construction …