We present a weighted algebraic non-monotonic logic we refer to as LogAG for reasoning with uncertain beliefs. In LogAG, the classical logical formulas could be associated with ordered grades representing measures of uncertainty. The revision of beliefs in LogAG, when contradictions arise, is done according to the grades of the contradictory propositions. Throughout the paper, we present the sy...

This paper introduces the logical basis for mod­ elling the phenomenon of reasoning in the pres­ ence of contradiction, by identifying this prob­ lem with the notion of change of context. We give here the basic definitions of a new seman­ tics, which works by interpreting one logic into a family of logics via translations, which we call semantics of translations. As a particular ap­ plication w...

The threshold behavior of the K-satisfiability problem is studied in the framework of the statistical mechanics of random diluted systems. We find that at the transition the entropy is finite and hence that the transition itself is due to the abrupt appearance of logical contradictions in all solutions and not to the progressive decreasing of the number of these solutions down to zero. A physic...

Psychologists have suggested that people from different cultures use different cognitive processes when they reason. Nisbett (2003), for example, proposes that East Asians tend to think holistically, dialectically, and on the basis of their experience, whereas Westerners tend to think analytically, logically, and abstractly. It follows that East Asians should tolerate contradictions to a greate...

A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way. In an earlier paper [Notre Dame J. Form. Log. 49 (2008), 401–424], we developed the systems of weakening of intuitionistic negation logic, called Zn and CZn, in the spirit of da Costa’s approach by preserving, differently from da Costa, the fundamental properties of negation: antitonici...

The logical structure of quantum mechanics is investigated. After some remarks on formal systems and interpretations, it is shown that Bohr’s complementarity can be seen as an undecidable proposition. The flowing of the time prevents the birth of contradictions in nature, because it poses a cut between two different, but complementary aspects of the reality. PACS-03.65.Bz Foundations, theory of...

The introduction of mass privatization policies in Russia and the Czech Republic depended on the creation of impersonal capital markets to finance the needs of privatized companies and to provide a secondary market for the trading of securities. Yet, mass privatization created the contradictory conditions of generating millions of poorly informed shareholders, with no efficient markets for the ...