NOL Seminar with Fredrik Engström
published: 2025-01-15
event date:
2025-01-27
The Nordic Online Logic Seminar
is organised monthly over Zoom, with expository talks on topics of interest for
the broader logic community. The seminar is open for professional or aspiring
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Date Monday, 27 January 2025 at 16:00 CET (UTC+1) on Zoom
Speaker Fredrik Engström (Senior lecturer, University of Gothenburg)
Title Team semantics and substitutional logics
Abstract
Team semantics extends traditional semantics by shifting the interpretation of
formulas from individual semantic objects (e.g., assignments, valuations, or
worlds) to sets of such objects, commonly referred to as teams. This approach
enables the expression of properties, such as variable dependency, that are
inaccessible in traditional semantics. Since its introduction by Hodges and
subsequent refinement by Väänänen, team semantics has been used to develop
expressively enriched logics that retain desirable properties such as
compactness.
However, these logics are typically non-substitutional, limiting their algebraic treatment and preventing the development of schematic proof systems. This limitation can be attributed to the flatness principle which is commonly adhered to in many constructions of team semantics for logics.
In this talk, we approach the formation of propositional logic of teams from an algebraic perspective, explicitly discarding the flatness principle. We propose a substitutional logic of teams that is expressive enough to axiomatize key propositional team logics, such as propositional dependence logic.
Our construction parallels the algebraic construction of classical propositional logic from Boolean algebras. The algebras we are using are powersets of Boolean algebras equipped with both internal (pointwise) and external (set-theoretic) operations. The resulting logic is clearly substitutional, and is shown to be sound and complete with respect to a labelled natural deduction system.
If time permits, we will also discuss how we might do to extend this construction to the framework of first-order logic.