@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} } @incollection {D:cg_fpsp, title = {Content Guidance in Formal Problem Solving Processes}, booktitle = {Abduction and the Process of Scientific Discovery}, year = {2007}, pages = {121{\textendash}156}, publisher = {Centro de Filosofia das Ci{\^e}ncias da U. de Lisboa}, address = {Lisboa}, abstract = {

In this paper, a formal framework to problem-solving processes is presented. The framework is not complete. Nevertheless, even its present sophistication allows one to see that it is promising.\par The framework demonstrably allows one to understand scientific change as content-guided. It will be argued that a formal framework is required in order to make definite and precise statements about the content-guided aspects of scientific problem solving.

}, author = {Batens, Diderik}, editor = {Pombo, Olga and Gerner, Alexander} } @article {D:gluts, title = {Criteria Causing Inconsistencies. {G}eneral Gluts as Opposed to Negation Gluts}, journal = {Logic and Logical Philosophy}, volume = {11/12}, year = {2003}, pages = {5{\textendash}37}, abstract = {

This paper studies the question: how should one handle inconsistencies that derive from the inadequacy of the criteria by which one approaches the world. I compare the approaches underlying several inconsistency-adaptive logics. I consider the Rescher{\textendash}Manor consequence relations as well as adaptive logics defined from CLuN, CLuNs, LP, AN, and AL. The adaptive systems defined from CLuN appear to be superior to the others. They isolate inconsistencies rather than spreading them, and at the same time allow for genuine deductive steps from inconsistent and mutually inconsistent premises.

Nevertheless, the systems based on CLuN introduce an asymmetry between negated and non-negated formulas that seems hard to justify. To clarify and understand the source of the problem, the epistemological presuppositions of CLuN, viz. inadequate criteria, are investigated. This leads to a new type of paraconsistent logic that involves gluts with respect to all other logical constants. The larger part of the paper is devoted to this logic, to the adaptive logics defined from it, and to the study of the properties of these systems.

While this resulting logics are sensible and display interesting features, the search for variants of the justification leads to an unexpected justification for CLuN.

}, author = {Batens, Diderik} } @article {DLn:induct2, title = {On Classical Adaptive Logics of Induction}, journal = {Logique et Analyse}, volume = {44}, number = {173-175}, year = {2001}, pages = {255{\textendash}290}, abstract = {

This paper concerns the inference of inductive generalizations and of predictions derived from them. It improves on the adaptive logic of induction from \emph{On a Logic of Induction} (Batens, Logic and Philosophy of Science, IV, 1, 2006, pp. 3-32) by presenting logics that are formulated strictly according to the usual adaptive standards. It moreover extends that paper with respect to background knowledge.

We present logics that handle inductive generalizations as well as logics that handle prioritized background knowledge of three kinds: background generalizations, pragmatic background generalizations (the instances of which may be invoked even after the generalizations are falsified), and background theories. All logics may be combined into a single system.

}, author = {Batens, Diderik and Haesaert, Lieven} } @article {D:cps, title = {Contextual Problem Solving and Adaptive Logics In Creative Processes}, journal = {Philosophica}, volume = {64}, year = {1999}, note = {Appeared 2001}, pages = {7{\textendash}31}, abstract = {

Creativity is commonly seen as beyond the scope of rationality. In the present paper, it is argued that available insights in epistemology and available results in logic enable us to incorporate creativity within an independently sensible view on human rationality.

}, author = {Batens, Diderik} } @incollection {D:catm\&k, title = {A contextual approach to meaning and knowledge}, booktitle = {Science and Society}, year = {1987}, pages = {84{\textendash}110}, publisher = {VUB-Uitgaven}, author = {Batens, Diderik}, editor = {Gosselin, M. and Demeyere, F.} } @incollection {D:cwm, title = {Creativiteit in wetenschap en muziek}, booktitle = {Liber Amicorum J.L. Broeckx}, year = {1986}, pages = {29{\textendash}55}, publisher = {Grafisch Bureau M \& Team}, author = {Batens, Diderik}, editor = {De Hen, Ferdinand J. and Riessauw, Anne-Marie and Sabbe, Herman} } @article {D:cpm, title = {A completeness-proof method for extensions of the implicational fragment of the propositional calculus}, journal = {Notre Dame Journal of Formal Logic}, volume = {21}, year = {1980}, pages = {509{\textendash}517}, author = {Batens, Diderik} }