@incollection {primiero2012type, title = {Type-Theoretical Dynamics. {E}xploring Belief Revision in a Constructive Framework}, booktitle = {The realism-antirealism debate in the age of alternative logics}, year = {2012}, pages = {191{\textendash}212}, publisher = {Springer}, abstract = {

In the present paper a dynamics for type theory is introduced. The formalization provides epistemic explanations for the basic notions of belief state and belief set by referring to assertion conditions for type-theoretical judgements; it interprets expectations in terms of default assumptions for such a structure and it adapts the usual revision operations and the analogous of the Ramsey test. The model, restricted to operations of revision, merging and information preference, provides a constructive type-theoretical approach to epistemic dynamics.

}, doi = {10.1007/978-94-007-1923-1_11}, author = {Primiero, Giuseppe}, editor = {Rahman, Shahid and Primiero, Giuseppe and Marion, Mathieu} } @incollection {771936, title = {Epistemic Modalities}, booktitle = {Acts of Knowledge: History, Philosophy and Logic}, series = {Tributes}, volume = {9}, year = {2009}, pages = {207{\textendash}232}, publisher = {College Publications}, abstract = {

I present an analysis of the notion of epistemic modalities, based on an appropriate interpretation of two basic constructivist issues: verification and epistemic agency. Starting from an historical analysis of conditions for judgments, I analyze first the reading of necessity with respect to apodictic judgements, and then that of possibility with respect to hypothetical judgement. The analysis results in a formal treatment of rules for judgemental modal operators, whose aim is to preserve epistemic states corresponding to verified and unverified assumptions in contexts. In the conclusion, further tracks of research are indicated for designing a semantic framework and defining multi-agents systems.

}, isbn = {978-1-904987-92-5}, author = {Primiero, Giuseppe}, editor = {Primiero, Giuseppe and Rahman, Shahid} } @incollection {417858, title = {A conceptual analysis of early arabic algebra}, booktitle = {The unity of science in the arabic tradition : science, logic, epistemology and their interactions}, year = {2008}, pages = {89{\textendash}128}, publisher = {Kluwer Academic Publishers}, address = {Dordrecht}, abstract = {

Arabic algebra derives its epistemic value not from proofs but from correctly performing calculations using coequal polynomials. This idea of ‘mathematics as calculation’ had an important influence on the epistemological status of European mathematics until the seventeenth century. We analyze the basic concepts of early Arabic algebra such as the unknown and the equation and their subsequent changes within the Italian abacus tradition. We demonstrate that the use of these concepts has been problematic in several aspects. Early Arabic algebra reveals anomalies which can be attributed to the diversity of influences in which the al-jabr practice flourished. We argue that the concept of a symbolic equation as it emerges in algebra textbooks around 1550 is fundamentally different from the ‘equation’ as known in Arabic algebra.

}, isbn = {978-1-4020-8404-1}, url = {http://dx.doi.org/1854/11276}, author = {Heeffer, Albrecht}, editor = {Rahman, Shahid and Street, Tony and Tahiri, Hassan} } @incollection {D:eial, title = {The Need for Adaptive Logics in Epistemology}, booktitle = {Logic, Epistemology, and the Unity of Science}, year = {2004}, pages = {459{\textendash}485}, publisher = {Kluwer}, address = {Dordrecht}, abstract = {

After it is argued that philosophers of science have lost their interest in logic because they applied the wrong type of logics, examples are given of the forms of dynamic reasoning that are central for philosophy of science and epistemology. Adaptive logics are presented as a means to understand and explicate those forms of reasoning. All members of a specific (large) set of adaptive logics are proved to have a number of properties that warrant their formal decency and their suitability with respect to understanding and explicating dynamic forms of reasoning. Most of the properties extend to other adaptive logics.

}, author = {Batens, Diderik}, editor = {Rahman, Shahid and Symons, John and Gabbay, Dov M. and Van Bendegem, Jean Paul} }