TY - Generic T1 - Kennissystemen selectief wieden Y1 - 2018 A1 - Batens, Diderik ED - Van Kerkhove, Bart ED - François, Karen ED - Ducheyne, Steffen ED - Allo, Patrick JA - Laat ons niet ernstig blijven. Huldeboek voor Jean Paul Van Bendegem PB - Academia Press CY - Gent, België SP - 227–244 SN - 978-94-014-5589-3 ER - TY - Generic T1 - The Consistency of Peano Arithmetic. A Defeasible Perspective Y1 - 2014 A1 - Batens, Diderik ED - Allo, Patrick ED - Van Kerkhove, Bart AB -

This paper proposes to replace \sys{PA}, Peano Arithmetic, by a theory \sys{APA} defined in terms of (i) a set of axioms that is classically equivalent to the Peano axioms and (ii) a defeasible logic that minimizes inconsistency, viz.\ an inconsistency-adaptive logic. If \sys{PA} is consistent, its set of theorems coincides with the set of \sys{APA}-theorems. If \sys{PA} is inconsistent, \sys{APA} is non-trivial and has the following remarkable property: there is a unique non-standard number that is its own successor and every `desirable' \sys{PA}-theorem is retained if restricted to the other numbers. The restriction can be expressed in the language of arithmetic. And there is much more.

JA - Modestly Radical or Radically Modest. Festschrift for Jean Paul Van Bendegem on the Occasion of His 60th Birthday PB - College Publications SP - 11–59 ER - TY - Generic T1 - Reasoning with computer-assisted experiments in mathematics T2 - Third Workshop in the Philosophy of Information Y1 - 2012 A1 - De Mol, Liesbeth ED - Primiero, Giuseppe ED - Allo, Patrick JA - Third Workshop in the Philosophy of Information PB - Koninklijke Vlaamse Academie van België door Wetenschappen en Kunsten SP - 80-92 ER - TY - Generic T1 - On the necessity of (sometimes) being synthetic. Comment on Poggiolesi. Y1 - 2011 A1 - Primiero, Giuseppe ED - Allo, Patrick ED - Primiero, Giuseppe JA - Third Workshop in the Philosophy of Information PB - Koninklijke Vlaamse Academie van België CY - Brussels SP - 63-68 ER - TY - JOUR T1 - Report 3rd Workshop in the Philosophy of Information JF - The Reasoner Y1 - 2011 A1 - Allo, Patrick A1 - Primiero, Giuseppe VL - 1 SP - 6-7 ER -