The talk peeks at the current interactions between mathematics and LLMs. I will start by recalling some recent breakthroughs to frame the current state of affairs and later move to comment on their relevance and impact on the subject and its underlying community.

Public defence of Orvar Lorimer Olsson’s Licentiate thesis.

Opponent Assistant Professor Fan Yang, Utrecht University
Examiner Professor Graham E Leigh, Göteborgs universitet

Abstract

This thesis concerns semantic set-lifting procedures in logic, particularly plurivalence and team semantics. These are methods of constructing new logical semantics in terms of collections of semantic objects from an initial logical semantic (for the studied cases in terms of sets of truth values or teams of assignments respectively). By representing the underlying semantics in terms of algebraic structures we present versions of these set-lifting constructions in terms of power algebras [Brink, 1992], that is, algebras of subsets with pointwise operations in an underlying algebraic structure. Doing so, and by considering the classes of such algebras, we present versions of the set-lifting procedures that are independent of the semantic representation of the original logic.

This thesis includes three papers presenting applications of the power-algebra interpretation of set-lifting procedures in three different cases. Paper I presents two new syntactic categorisations of a family of eight logics called the FDE-family, previously categorised semantically by Priest. These categorisations are also extended to larger families of logics. Paper II describes Priest’s notion of plurivalence in terms of power matrices and shows that reiterating the plurivalent construction is logically equivalent to a single application. Paper III (joint work with Fredrik Engström) instead deals with team semantics, and presents the logic of team properties (LTP) as a natural algebraically defined abstract team-semantic extension of classical propositional logic. LTP is a team logic closed under substitution (a property that is missing for most logics with team semantics) and still expressive enough to encode many traditional team logics as axiomatisable syntactic fragments.

The thesis can be accessed via the Gothenburg University Library Archive at https://hdl.handle.net/2077/93583

Articles contained within the thesis

This thesis is a compilation of the following articles

• Paper I: Forthcoming in The Australasian Journal of Logic.
• Paper II: Published in Proceedings of the ESSLLI 2026 Student Session, available via: https://philpapers.org/rec/JOSPOT-2
• Paper III: Unpublished. Also available via: https://arxiv.org/abs/2303.14022.

Two agents with the same information and awareness may hold different beliefs because of inattention. Attention differs from awareness: while awareness determines what is available for reasoning, attention determines what is actually taken into account. Existing epistemic logics do not typically address this distinction explicitly.

In this talk, I will discuss how attention and awareness can be represented in epistemic logic, what distinguishes them, and how they shape belief.