Mauricio Martins Reis

In this paper, we propose and axiomatically characterize residual contractions, a new kind of contraction operators for belief bases. We establish that the class of partial meet contractions is a strict subclass of the class of residual contractions. We identify an extra condition that may be added to the definition of residual contractions, which is such that the class of residual contractions that satisfy it coincides with the class of partial meet contractions. We investigate the interrelations in the sense of inclusion among the class of residual contractions and other classes of well known contraction operators for belief bases.

Two of the most well-known belief contraction operators are partial meet contractions (PMCs) and kernel contractions (KCs). In this paper we propose two new classes of contraction operators, namely the class of generalized partial meet contractions (GPMC) and the class of generalized kernel contractions (GKC), which strictly contain the classes of PMCs and of KCs, respectively. We identify some extra conditions that can be added to the definitions of GPMCs and of GKCs, which give rise to some interesting subclasses of those classes of functions, namely the classes of extensional and of uniform GPMCs/GKCs. In the context of contractions on belief sets the classes of partial meet contractions, uniform GPMCs and extensional GPMCs are all identical. Nevertheless, when considered as operations on belief bases, the class of uniform GPMCs coincides with the class of partial meet contractions, but the extensional GPMCs constitute a new kind of belief base contraction functions whose characterizing postulate of irrelevance of syntax is extensionality—the same postulate of irrelevance of syntax which occurs in the classical axiomatic characterization of partial meet contractions for belief sets—rather than the postulate of uniformity—which is the irrelevance of syntax postulate used in the axiomatic characterization for partial meet contractions on belief bases. Analogous results are obtained regarding the classes of extensional and of uniform GKCs. We present the interrelations in the sense of inclusion among all the new classes of operators presented in this paper and several well known classes of PMCs and of KCs.

In this article we present a new class of multiple contraction functionswhich are a generalization of the epistemic entrenchment-based contractions (Grdenfors & Makinson, 1988) to the case of contractions by (possibly nonsingleton) sets of sentences and provide an axiomatic characterization for that class of functions. Moreover, we show that the class of epistemic entrenchment-based multiple contractions coincides with the class of system of spheres-based multiple contractions introduced in Fermé & Reis (2012)

In the logic of theory change, the standard model is AGM, proposed by Alchourrón et al. (J Symb Log 50:510–530, 1985 ). This paper focuses on the extension of AGM that accounts for contractions of a theory by a set of sentences instead of only by a single sentence. Hansson (Theoria 55:114–132, 1989 ), Fuhrmann and Hansson (J Logic Lang Inf 3:39–74, 1994 ) generalized Partial Meet Contraction to the case of contractions by (possibly non-singleton) sets of sentences. In this paper we present the possible worlds semantics for partial meet multiple contractions.

This paper deals with the questions of emergence and complex (mental and social) systems and with downward determination from the viewpoint of perspectival realism. These are issues concerning the foundations of the human sciences, generally speaking, and particularly psychology and sociology. A criterion is put forward, which distinguish metaphysicalfrom ontological (conceptual) problems, and the notions of complex, hierarchic system and causation that would be suitable for those that defend emergence and perspectivist foundations of the human sciences are discussed. Este artigo trata das questões da emergência de sistemas complexos (mentais e sociais) e da determinação descendente do ponto de vista do realismo perspectivista. Essas são questões sobre os fundamentos das ciências humanas em geral e, em particular, da psicologia e da sociologia. É proposto um critério para distinguir problemas metafísicos de problemas ontológicos (ou conceituais), e são discutidas as noções de sistema complexo hierárquico e de causação que seriam adequadas para uma fundamentação emergentista e perspectivista das ciências humanas