The Propositional Logic of Team Properties

Fredrik Engström; Orvar Lorimer-Olsson

Home/Archive/arXiv

arXiv · 2303.14022

The Propositional Logic of Team Properties

Fredrik Engström·Orvar Lorimer-Olsson

View original source ↗Read source document ↗Export metadata ↓

Abstract

Since its introduction by Hodges and refinement by Väänänen, team semantic constructions have been used to generate expressively enriched logics preserving some desirable properties, such as compactness or decidability. By contrast, these logics fail to be substitutional, limiting any algebraic treatment and rendering schematic uniform proof systems impossible. This shortcoming can be attributed to the flatness principle, commonly adhered to when generating team semantics. Investigating the formation of team semantics from algebraic semantics, and disregarding the flatness principle, we present the Logic of Team Properties (LTP), a substitutional logic in which important propositional team logics are axiomatisable as fragments. Starting from classical propositional logic and Boolean algebras, we give a semantics for LTP by considering the algebras that are powersets of Boolean algebras B, that is, of the form P(B), equipped with internal pointwise and external set-theoretic connectives. Furthermore, we present a well-motivated sound and complete labelled natural deduction system for LTP.

Explore related subjects

math.LO

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Fredrik Engström, Orvar Lorimer-Olsson. 2026-06-30. The Propositional Logic of Team Properties. https://arxiv.org/abs/2303.14022

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Loops, Inverse Limits and Non-Determinism

We introduce an operator on problems in Weihrauch complexity, which we call the infinite loop or inverse limit, and which corresponds to an infinite compositional product. This operation arises naturally whenever one implements algorithms that produce a sequence of results in an infinite loop, using some fixed subroutine. We prove that the corresponding operator is monotone with respect to (strong) Weihrauch reducibility but that it is not a closure operator. One of our findings is that weak Kőnig's lemma is closed under infinite loops, which implies that the class of non-deterministically computable problems is also closed under this operation. Consequently, this class allows for a high degree of flexibility in programming. As our main technical tools, we present an injective version of the recursion theorem and an infinitary version of the so-called independent choice theorem. We also show that, in general, the infinite loop operator is more powerful than the composition of the diamond operator followed by the parallelization operator. However, in many practical scenarios, these compositions yield a result, which coincides with the application of the infinite loop operator. Finally, we discuss the special situation of loops for single-valued problems and for problems on Turing degrees.

math.LO↗

arXiv2026

Scott topologies on meet-continuous domains

We study Scott products and sobriety of countable meet-continuous domains, meaning meet-continuous dcpos without any additional continuity or least-element assumption. Using the complete-lattice test-family theorem of Xu and Ji, we prove finite-product equality for those domains that are $L$-dcpos, and for the weaker class whose principal ideals have suprema of all nonempty subsets. For an arbitrary family of nonempty countable meet-continuous $L$-dcpos, we prove that the Scott topology on the order product equals the product of the factor Scott topologies if and only if only finitely many factors lack a least element. We also establish sobriety under bounded completeness and under additional common-upper-bound conditions. Assuming square-product equality, sobriety is characterized by Scott closedness of common-upper-bound sections associated with irreducible Scott-closed sets, with an equivalent sequential formulation in the countable case. Two extraction lemmas extend to meet-semilattice dcpos. The finite-product and sobriety questions for general countable meet-continuous domains remain unresolved here.

math.LO↗

arXiv2026

Randomized Borel $(2d+1)$-coloring of digraphs

Let $G$ be a Borel digraph with maximum out-degree $d \in \mathbb{N}$. We show that $G$ admits a random Borel $(2d+1)$-coloring for which every edge is almost surely not monochromatic. This gives a simpler proof of a recent result of Pelayo-Gómez: such a graph $G$ admits a measurable proper $(2d+1)$-coloring with respect to any Borel probability measure on $V(G)$. Our proof is an adaptation of Pelayo-Gómez's proof to the randomized Borel setting.

math.LO↗