Related papers: Linear Realisability over nets: multiplicatives (l…

We characterize type isomorphisms in the multiplicative-additive fragment of linear logic (MALL), and thus in *-autonomous categories with finite products, extending a result for the multiplicative fragment by Balat and Di Cosmo. This…

We examine some combinatorial properties of parallel cut elimination in multiplicative linear logic (MLL) proof nets. We show that, provided we impose a constraint on some paths, we can bound the size of all the nets satisfying this…

We prove a completeness result for Multiplicative Exponential Linear Logic (MELL): we show that the relational model is injective for MELL proof-nets, i.e. the equality between MELL proof-nets in the relational model is exactly axiomatized…

Proof nets for MLL (unit-free Multiplicative Linear Logic) are concise graphical representations of proofs which are canonical in the sense that they abstract away syntactic redundancy such as the order of non-interacting rules. We argue…

This paper presents a simple notion of proof net for multiplicative linear logic with units. Cut elimination is direct and strongly normalising, in contrast to previous approaches which resorted to moving jumps (attachments) of par units…

When predictive models are used to support complex and important decisions, the ability to explain a model's reasoning can increase trust, expose hidden biases, and reduce vulnerability to adversarial attacks. However, attempts at…

We prove that given two cut free nets of linear logic, by means of their relational interpretations one can: 1) first determine whether or not the net obtained by cutting the two nets is strongly normalizable 2) then (in case it is strongly…

Following the idea of Subexponential Linear Logic and Stratified Bounded Linear Logic, we propose a new parameterized version of Linear Logic which subsumes other systems like ELL, LLL or SLL, by including variants of the exponential rules.…

We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational complexity. This…

Each Multiplicative Exponential Linear Logic (MELL) proof-net can be expanded into a differential net, which is its Taylor expansion. We prove that two different MELL proof-nets have two different Taylor expansions. As a corollary, we prove…

We introduce two-sorted theories in the style of [CN10] for the complexity classes \oplusL and DET, whose complete problems include determinants over Z2 and Z, respectively. We then describe interpretations of Soltys' linear algebra theory…

This work introduces a novel framework of uniform realizability that unifies and generalizes various realizability interpretations of logic, particularly focussing on the treatment of atomic formulas and quantifiers. Traditional…

The quasi-normal modal logic GLS is a provability logic formalizing the arithmetical truth. Kushida (2020) gave a sequent calculus for GLS and proved the cut-elimination theorem. This paper introduces semantical characterizations of GLS and…

In this paper we present a semantics for a linear algebraic lambda-calculus based on realizability. This semantics characterizes a notion of unitarity in the system, answering a long standing issue. We derive from the semantics a set of…

While the reasoning capabilities of Large Language Models (LLMs) excel in analytical tasks such as mathematics and code generation, their utility for abstractive summarization remains widely assumed but largely unverified. To bridge this…

Standpoint linear temporal logic SLTL is a recent formalism able to model possibly conflicting commitments made by distinct agents, taking into account aspects of temporal reasoning. In this paper, we analyse the computational properties of…

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, we show its Turing-completeness and to illustrate…

The profusion of knowledge encoded in large language models (LLMs) and their ability to apply this knowledge zero-shot in a range of settings makes them promising candidates for use in decision-making. However, they are currently limited by…

While there are many applications of ML to scientific problems that look promising, visuals can be deceiving. Using numerical analysis techniques, we rigorously quantify the accuracy, convergence rates, and generalization bounds of certain…

Linearizability is a commonly accepted notion of correctness for libraries of concurrent algorithms, and recent years have seen a number of proposals of program logics for proving it. Although these logics differ in technical details, they…