The modern view of logical reasoning as modeled by a consequence operator (instead of simply by a set of theorems) has allowed for huge developments in the study of logic as an abstract discipline. Still, it is unable to explain why it is often the case that the same designation is used, in an ambiguous way, to describe several distinct modes of reasoning over the same logical language. A parad...

In this paper we present a systematic study of abductive consequence relations. We show that a monotone abductive consequence relation satisses the properties of a cumulative monotonic system as deened by Kraus, Lehmann and Magidor when the disjunction of all abductive explanations is the explanation used to justify the observations. We also show that, in general, for this class of abductive co...

We provide a general investigation of Logic in which the notion of a simple consequence relation is taken to be fundamental. Our notion is more general than the usual one since we give up monotonicity and use multisets rather than sets. We use our notion for characterizing several known logics (including Linear Logic and non-monotonic logics) and for a general, semantics-independent classi cati...

We present an extensive experimental study of consequence-finding algorithms based on kernel resolution, using both a trie-based and a novel ZBDD-based implementation, which uses ZeroSuppressed Binary Decision Diagrams to concisely store and process very large clause sets. Our study considers both the full prime implicate task and applications of consequence-finding for restricted target langua...

Research on reasoning in description logics has traditionally focused on the standard inference tasks of (un)satisfiability, subsumption, and instance checking. In recent years, however, there has been a growing interest in so-called non-standard inference services (cf. [1]) which prove useful in the creation, evolution, and utilisation of description logic knowledge bases (KBs). In this paper,...

The shift of interest in logic from just reasoning to all forms of information flow has considerably widened the scope of the discipline, as amply illustrated in Johan van Benthem’s recent book Logical Dynamics of Information and Interaction. But how much does this change when it comes to the study of traditional logical notions such as logical consequence? We propose a systematic comparison be...

To test the hypothesis that atrial enlargement can develop as a consequence of atrial fibrillation, left and right atrial dimensions were measured echocardiographically at two different time points in patients with atrial fibrillation. Patients were selected who initially had normal atrial sizes and who had no evidence of significant structural or functional cardiac abnormalities other than atr...

In this chapter we first provide a general introduction to the research area methodology and relevance, then we discuss normative reasoning for multi-agent systems, and finally we discuss current research challenges. We cover the main issues in modern deontic logic, which is much broader than the traditional modal logic framework of deontic logic, with an emphasis to our intended audience. To e...

In the second volume of his Wissenschaftslehre from 1837, the Bohemian philosopher, theologian, and mathematician Bernard Bolzano (1781-1848) introduced his concept of consequence, named derivability (Ableitbarkeit), together with a variety of theorems and further considerations. Derivability is an implication relation between sentences in themselves (Sätze an sich), which are not meant to be l...

Sir Austin Bradford Hill, honorary fellow of the London School of Hygiene and Tropical Medicine, dean of the school from 1955 to 1957, and professor of medical statistics from 1946 to 1961, died on 18 April 1991. With his death the country lost a man who has been described as the greatest medical statistician of the twentieth century, despite the fact that he held no degree in either medicine o...