Akka

The Scandinavian Logic Society

NOL Seminar with Ian Pratt-Hartmann

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 logicians and logic aficionados worldwide. If you wish to receive the Zoom ID and password for it, as well as further announcements, please subscribe here:
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Date Monday, 31 August 2026 at 16:00 CEST (UTC+2) on Zoom
Speaker Ian Pratt-Hartmann (Senior Lecturer, University of Manchester and Professor, Uniwersytet Opolski)
Title Variable-ordering fragments of first-order logic

Abstract
In the context of first-order logic, a ‘variable-ordering fragment’ is a subset of formulas identified by restricting the permitted sequences of variables appearing as arguments of atomic subformulas. Examples include W.V.O. Quine’s ‘fluted fragment’, A. Herzig’s ‘forward fragment’ and the recently identified ‘adjacent fragment’. All three of these fragments possess the finite model property and hence are decidable for satisfiability. The largest of these, the adjacent fragment, extends a wide range of propositional modal logics (under the standard translation into first-order logic) as well as the two-variable fragment. In this talk, I shall give an overview of the possible variable-ordering fragments, and explain how bounds on complexity of satisfiability can be derived. I shall also survey various extensions of these logics, in particular with counting quantification.