A critical view of the alleged significance of Belnap four-valued logic for reasoning under inconsistent and incomplete information is provided. The difficulty lies in the confusion between truth-values and information states, when reasoning about Boolean propositions. So our critique is along the lines of previous debates on the relevance of many-valued logics and especially of the extension of the Boolean truth-tables to more than two values as a tool for reasoning about uncertainty. The critique also questions the significance of partial (...) logic. (shrink)

Two kinds of justification logics are studied. Then, this article shows how the notion of quasi-truth can be defined in these systems.

In 1986, Mikenberg et al. introduced the semantic notion of quasi-truth defined by means of partial structures. In such structures, the predicates are seen as triples of pairwise disjoint sets: the set of tuples which satisfies, does not satisfy and can satisfy or not the predicate, respectively. The syntactical counterpart of the logic of partial truth is a rather complicated first-order modal logic. In the present article, the notion of predicates as triples is recursively extended, in a natural way, to (...) any complex formula of the first-order object language. From this, a new definition of quasi-truth is obtained. The proof-theoretic counterpart of the new semantics is a first-order paraconsistent logic whose propositional base is a 3-valued logic belonging to hierarchy of paraconsistent logics known as Logics of Formal Inconsistency, which was proposed by Carnielli and Marcos in 2002. (shrink)

We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t: F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a (...) robust system of justifications. This renders a new, evidence-based foundation for epistemic logic. As a case study, we offer a resolution of the GoldmanRed Barns in Justification Logic. Furthermore, we formalize the well-known Gettier example and reveal hidden assumptions and redundancies in Gettier’s reasoning. (shrink)

Our aim is to propose a non-referential semantics for the principle of logical charity: neither logical universalism (one logic, one way of thinking), nor logical relativism (several logics, several ways of thinking) afford an adequate conceptual framework to interpret the meaning of any speech act. But neither of them is totally wrong, either. The point is to know to which extent each of these views is partly right, thus leading to a more consensual but paradoxical-sounding "relative principle of charity". After (...) recalling the theoretical background of logical charity, we suggest a four-valued logic of acceptance and rejection (hereafter: AR4); then we explain how such a non-referential semantics does justice both to the champions of logical charity and its opponents. While endorsing coherence as a precondition for rationality, we argue that such a criterion does not entail that classical logic is a necessary conceptual scheme to interpret the others' beliefs. A better application of charity should take account of the questions implicitly asked by a statement, and we bring these questions out in replacing Quine's truth-functions by Quine’s verdict functions while emphasizing upon their varying degrees of strength. (shrink)

The present paper wants to promote epistemic pluralism as an alternative view of non-classical logics. For this purpose, a bilateralist logic of acceptance and rejection is developed in order to make an important di erence between several concepts of epistemology, including information and justi cation. Moreover, the notion of disagreement corresponds to a set of epistemic oppositions between agents. The result is a non-standard theory of opposition for many-valued logics, rendering total and partial disagreement in terms of epistemic negation and (...) semi-negations. (shrink)