NOL Seminar with Ian Pratt-Hartmann
published: 2026-08-20
event date:
2026-08-31
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, 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.