Tootfinder

This https://arxiv.org/abs/2505.12899 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Interpolation for the two-way modal mu-calculus
The two-way modal mu-calculus is the extension of the (standard) one-way mu-calculus with converse (backward-looking) modalities. For this logic we introduce two new sequent-style proof calculi: a non-wellfounded system admitting infinite branches and a finitary, cyclic version of this that employs annotations. As is common in sequent systems for two-way modal logics, our calculi feature an analytic cut rule. What distinguishes our approach is the use of so-called trace atoms, which serve to ap…

This https://arxiv.org/abs/2405.03536 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Extensional and Non-extensional Functions as Processes
Following Milner's seminal paper, the representation of functions as processes has received considerable attention. For pure $λ$-calculus, the process representations yield (at best) non-extensional $λ$-theories (i.e., $β$ rule holds, whereas $η$ does not). In the paper, we study how to obtain extensional representations, and how to move between extensional and non-extensional representations. Using Internal $π$, $\mathrm{I}π$ (a subset of the $π$-calculus in which all outputs are boun…

Recursive Difference Categories and Topos-Theoretic Universality
Andreu Ballus Santacana
https://arxiv.org/abs/2505.22931 https://arx…

Recursive Difference Categories and Topos-Theoretic Universality
We introduce a radically minimal categorical foundation for logic, semantics, and computation, built from a single generative axiom of recursive difference. From the null mnema M0 and iterated labeled extensions by D, we form the free category M and its sheaf topos Sh(M). We prove: Modal completeness: Lawvere-Tierney topologies on Sh(M) classify all standard modal logics (K, T, S4, S5) purely via submonoids of the free monoid D*. Fixed-point expressivity: The internal mu-calculus over infin…

My favourite thing about the monarchy is that it's transparently BS. Like, no one actually believes that the King of England has some sort of divine right to rule over Canada. The trouble with republican forms of government is that the will of the people, often imagined in terms of the political calculus of the US's electoral college or first-past-the-post or whatever, is far less transparently BS, though perhaps equally so. Artifice, when it's obvious, can have a positive effect…

I'm very good at integral and differential calculus,
I know the scientific names of beings animalculous;
In short, in matters vegetable, animal, and mineral,
I am the very model of a modern Major-General.
-- Gilbert & Sullivan, "Pirates of Penzance"

Teaching Mathematics for Economists
Eric Hillebrand
https://arxiv.org/abs/2505.22671 https://arxiv.org/pdf/2505.22671

Teaching Mathematics for Economists
In this chapter, I discuss teaching mathematical tools specifically tailored for economics students. A typical one-semester course in this area seeks to blend a range of topics: from foundational elements of subjects such as linear algebra and multivariate calculus to intermediate areas like real and convex analysis and further into advanced topics such as dynamic optimization in both continuous and discrete time. This breadth of coverage corresponds to material usually spread across multiple y…

Agent Interpolation for Knowledge
Marta B\'ilkov\'a, Wesley Fussner, Roman Kuznets
https://arxiv.org/abs/2505.23401 https://a…

Agent Interpolation for Knowledge
We define a new type of proof formalism for multi-agent modal logics with S5-type modalities. This novel formalism combines the features of hypersequents to represent S5 modalities with nested sequents to represent the T-like modality alternations. We show that the calculus is sound and complete, cut-free, and terminating and yields decidability and the finite model property for multi-agent S5. We also use it to prove the Lyndon (and hence Craig) interpolation property for multi-agent S5, consi…

This https://arxiv.org/abs/2505.20314 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

$Δ$-Nets: Interaction-Based System for Optimal Parallel $λ$-Reduction
I present a model of universal parallel computation called $Δ$-Nets, and a method to translate $λ$-terms into $Δ$-nets and back. Together, the model and the method constitute an algorithm for optimal parallel $λ$-reduction, solving the longstanding enigma with groundbreaking clarity. I show that the $λ$-calculus can be understood as a projection of $Δ$-Nets -- one that severely restricts the structure of sharing, among other drawbacks. Unhindered by these restrictions, the $Δ$-Nets model…

This https://arxiv.org/abs/2306.17541 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csMS_…

Rigorous Function Calculi in Ariadne
Almost all problems in applied mathematics, including the analysis of dynamical systems, deal with spaces of real-valued functions on Euclidean domains in their formulation and solution. In this paper, we describe the the tool Ariadne, which provides a rigorous calculus for working with Euclidean functions. We first introduce the Ariadne framework, which is based on a clean separation of objects as providing exact, effective, validated and approximate information. We then discuss the function c…

Term Ordering Diagrams
M\'arton Hajdu, Robin Coutelier, Laura Kov\'acs, Andrei Voronkov
https://arxiv.org/abs/2505.22181 https://

Term Ordering Diagrams
The superposition calculus for reasoning in first-order logic with equality relies on simplification orderings on terms. Modern saturation provers use the Knuth-Bendix order (KBO) and the lexicographic path order (LPO) for discovering redundant clauses and inferences. Implementing term orderings is however challenging. While KBO comparisons can be performed in linear time and LPO checks in quadratic time, using the best known algorithms for these orders is not enough. Indeed, our experiments sh…

This https://arxiv.org/abs/2412.19961 has been replaced.
initial toot: https://mastoxiv.page/@arXi…

Incentivizing supplemental math assignments and using AI-generated hints is associated with improved exam performance
Inequities in student access to trigonometry and calculus are often associated with racial and socioeconomic privilege, and often influence introductory physics course performance. To mitigate these disparities in student preparedness, we developed a two-pronged intervention consisting of (1) incentivized supplemental math assignments and (2) AI-generated learning support tools in the form of optional hints embedded in the physics homework assignments. Both interventions are grounded in the Sit…