@incollection {D:JP65, title = {Kennissystemen selectief wieden}, booktitle = {Laat ons niet ernstig blijven. Huldeboek voor Jean Paul Van Bendegem}, year = {2018}, pages = {227{\textendash}244}, publisher = {Academia Press}, address = {Gent, Belgi{\"e}}, isbn = {978-94-014-5589-3}, author = {Batens, Diderik}, editor = {Van Kerkhove, Bart and Fran{\c c}ois, Karen and Ducheyne, Steffen and Allo, Patrick} } @incollection {D:JP, title = {The Consistency of {P}eano {A}rithmetic. {A} Defeasible Perspective}, booktitle = {Modestly Radical or Radically Modest. Festschrift for Jean Paul Van Bendegem on the Occasion of His 60th Birthday}, year = {2014}, pages = {11{\textendash}59}, publisher = {College Publications}, abstract = {

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 {\textquoteleft}desirable{\textquoteright} \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.

}, author = {Batens, Diderik}, editor = {Allo, Patrick and Van Kerkhove, Bart} } @proceedings {dereasoning, title = {Reasoning with computer-assisted experiments in mathematics}, journal = {Third Workshop in the Philosophy of Information}, year = {2012}, pages = {80-92}, publisher = {Koninklijke Vlaamse Academie van Belgi{\"e} door Wetenschappen en Kunsten}, author = {De Mol, Liesbeth}, editor = {Primiero, Giuseppe and Allo, Patrick} } @incollection {primieronecessity, title = {On the necessity of (sometimes) being synthetic. {C}omment on {P}oggiolesi.}, booktitle = {Third Workshop in the Philosophy of Information}, year = {2011}, pages = {63-68}, publisher = {Koninklijke Vlaamse Academie van Belgi{\"e}}, address = {Brussels}, author = {Primiero, Giuseppe}, editor = {Allo, Patrick and Primiero, Giuseppe} } @article {Allo2011, title = {Report 3rd Workshop in the Philosophy of Information}, journal = {The Reasoner}, volume = {1}, number = {5}, year = {2011}, pages = {6-7}, author = {Allo, Patrick and Primiero, Giuseppe} }