A consequence relation in the framework of preferential semantics based on the four-valued Belnap-Dunn logic is constructed which proves that the sorites paradoxes are unsound or invalid inferences .

We consider modal epistemic and doxastic logics as intuitively inadequate logics of information, and we outline a modal system of the operator being informed that which avoids inconsistency with our intuitive concept of information. The system has modal structure of the normal modal logic K4, and is sound and complete on the class of all transitive frames. We compare this logic with Floridi’s KTB information logic, and we consider a possibility of extending our system to a dynamic logic.

The concept of inconsistency has become recently the subject of many studies focused on the principle ex contradictione sequitur quodlibet which is a hallmark of the classical inconsistency. Stanisław Jaśkowski was the first who took a non-classical standpoint toward this principle building a system of propositional logic which rejects this classical principle. Rejecting it implies important consequences for the concept of classical negation, and poses the question in which properties the op-eration of negation should be endowed. The intention of this (...) article is to define the concept of inconsistency as well as the concept of negation in a way satisfying the main intuitions natural language users connect with the two notions occurring in propositions containing vague concepts. The vagueness of natural language dis-course leads to the phenomenon of the seeming contradiction characteristic of natural language. A non-standard consequence relation for such a language has been defined in terms of preferential semantics making use of the concept of most classical model. This non-standard consequence relation is applied to the ethical discourse. The concepts introduced in this article have been used to an interpretation of the contradictories of Plato's Parmenides, as well as to the rejection of dialetheism. (shrink)

The paradoxes of vagueness are unsound or invalid reasoning on the ground of preferential semantics based on the four-valued Belnap-Dunn logic.

The main aim of the present article is an outline of an intuitively adequate system of logic of the operator "being informed". Such a system should be different from the familiar systems of epistemic and doxastic logic. The principle of veracity occurring in epistemic logics does not describe adequately the information operator, since the information may be true as well as false. On the other hand, the principle of consistency of beliefs, occurring in doxastic logics, cannot be applied to information, (...) because the information can be inconsistent. Our logic of information, although it is based on Kripke's semantics, includes principles not occurring in the systems of epistemic and doxastic logics, such as the principle of incompleteness of information and the Brouwerian Axiom. We prove that this system is incomplete. We also suggest that it can be generalized to a dynamic logic in the sense of van Benthem. (shrink)

All empirical concepts belonging to natural language are vague. The vagueness of empirical discourse is a source of many semantical problems which have been known since ancient times. One of those problems concerns the so called sorites paradoxes. This article is an attempt to show that the paradoxes are either invalid or unsound inferences. Since classical logic is useless for semantical analysis of such inferences, the article makes use of the Belnap four-valued logic based on the bilattice FOUR. Belnap's logic (...) is the base logic for defining a nonmonotonic consequence relation which prefers models with classical valuations among all valuations of the four-valued logic whenever it is possible. The approach outlined in this article is intuitive, and has more advantages than the supervaluational approach. (shrink)