Quasi-truth theories and paraconsistent databases (Draft) Luiz Henrique Silvestrini and Marcelo Esteban Coniglio August 19, 2010 Abstract The concept of quasi-truth (or pragmatic truth) was introduced by Newton da Costa and his collaborators as a formal framework to repre- sent the concept of truth in the context of Philosophy of Science. The resulting Tarskian model theory of quasi-truth is paraconsistent, but it is not clear what the underlying logic is. In this paper we show how the model theory of quasi-truth is related to the semantics of evolutionary databases introduced in [2]. Additionally, the relationship between both approaches and the formalization of quasi-truth proposed in [1] is also studied. 1 Formalizations of quasi-truth How can we provide a way of accommodating the conceptual incompleteness and partial nature inherent in scientific representations? To this openness and partiality of scientific activity, Newton da Costa and his collaborators have presented a forceful answer by introducing the notion of partial structures into the model-theoretic approach. The partial structures are obtained in a natural way, because when we study a determinate domain of knowledge Δ, we may begin by modelling it by a set- theoretic structure A. Since in general we do not know everything about Δ, A must normally be a structure that reflect our partial knowledge and under- standing of the world (see [3] and [4]). In that sense, we cannot say for certain that a particular theory under this domain Δ is true. However, we can say that, as far as our information allows us, the theory can be true, that is, it is quasi-true. Thus the concept of quasi-truth (or pragmatic truth ) was introduced by da Costa and his collaborators as a formal framework to represent the concept of truth in the context of Philosophy of Science. According to da Costa [3], science can be best understood in terms of the search for quasi-true theories, that is, theories which partially describe the phe- 1