Contextual Negations and Reasoning with Contradictions

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 we show that a simple logic support­ ing contradictions can be constructed translat­ ing classical logic into three-valued logics. This translation semantics offers a new interpreta­ tion to certain paraconsistent logics which al­ lows the application of them to automated rea­ soning and knowledge representation.