Showing papers on "Paraconsistent logic published in 1981"
01 Jan 1981
TL;DR: This paper argues that a proper theory of conditional obligation, like one of “conditional quantification”, will be the product of two separate components: a theories of the conditional, and a theory of obligation.
Abstract: Most of the recent work in deontic logic has concentrated on problems concerning “conditional obligation”. I’ve felt for a long time that this has been a mistake. A proper theory of conditional obligation, like one of “conditional quantification”, will be the product of two separate components: a theory of the conditional, and a theory of obligation.
94 citations
60 citations
01 Jan 1981
TL;DR: Paraconsistent logic as discussed by the authors is a generalization of the notion of non-trivial logic, and it can be seen as a type of logic that is not overcomplete.
Abstract: Let us consider informally a theory T (deductive system). We say that T is trivial (or overcomplete) if all formulas of T are theorems of T ; otherwise, we say that T is non-trivial (or not overcomplete). T is inconsistent if it has a negation symbol and there are, at least, two theorems of T such that one is the negation of the other; if this is not the case, T is consistent. If the underlying logic of T is the classical logic, T is inconsistent if and only if it is trivial. The same occurs with a great part of well-known systems of logic. So, if we intend to study inconsistent but non-trivial theories, we must construct new types of logic as a foundation to those theories. The logical systems constructed with this intention, have been called paraconsistent systems (see [1]). In general, the systems of paraconsistent logic must satisfy the following conditions:
23 citations
01 Jan 1981
TL;DR: Two dual axiomatizations of minimal quantum logic, (QL and QL), are discussed, which are linguistical and axiomatical extensions of classical logic, which can take as QL implication the same classical implication or, by suitably changing the basic logical frame, the intuitionistic one.
Abstract: In this paper we discuss two dual axiomatizations of minimal quantum logic, (QL), which are linguistical and axiomatical extensions of classical logic. We know that implication is one of the more problematic quantum logical notions. One of the features of the present axiomatization is that we can take as QL implication the same classical implication or, by suitably changing the basic logical frame, the intuitionistic one. We can take, in general, whatever notion of implication has the same properties of the lattice ordering relation and for which a cut elimination theorem holds. Indeed the notion of implication will be used as a “deduction” relation rather than a true connective.
2 citations