Logic is generally defined as the science of reasoning. Mathematical logic is mainly concerned with forms of reasoning that lead from true premises to true conclusions. Thus we say that the argument from σ0;σ1; · · · ;σn−1 to δ is logically correct if whenever σi is true for all i < n, then so is δ. In place of ‘argument’ one also speaks of a ‘rule’ or an ‘inference’ and says that the rule is v...

UNLABELLED The genomic mutation consequence calculator (GMCC) is a tool that will reliably and quickly calculate the consequence of arbitrary genomic mutations. GMCC also reports supporting annotations for the specified genomic region. The particular strength of the GMCC is it works in genomic space, not simply in spliced transcript space as some similar tools do. Within gene features, GMCC can...

The title of my lecture derives from a statement by the great lexicographer Dr Samuel Johnson in the course of a review of the Essay on Waters, by Dr Charles Lucas. Lucas extolled the healing powers of the waters at Bath (where he was physician) and elsewhere during an enforced hiatus in his political life in Dublin. Dr Johnson was evidently not persuaded: “It is incident to physicians, I am af...

In this paper I argue that a variety of consequence relations can be subsumed under a common core. The reduction proceeds by taking the unconditional consequence, or judgment, as basic and deriving the conditional consequence via a uniform abstraction scheme. A specific outcome is that it is better not to base such a scheme on the semantic notion of a matrix and valuation but rather on theories...

306 REFERENCES Damasio AR (1999) The Feeling of What Happens: Body and Emotion in the Making of Consciousness. New York, NY, USA: Harcourt Brace Dennett D (1991) Consciousness Explained. Boston, MA, USA: Little, Brown & Co. Farah MJ, Illes J, Cook-Deegan R, Gardner H, Kandel E, King P, Parens E, Sahakian B, Wolpe PR (2004) Neurocognitive enhancement: what can we do and what should we do? Nat Re...

In this paper we will investigate the possibility of reducing derivability in a modal consequence relation to consistency in unimodal and polymodal K by means of so–called reduction functions. We will present new and easy methods to prove standard results on decidability, complexity, finite model property, interpolation and Halldén–completeness using only the reduction functions. Some new resul...

In this short paper, I compare and contrast the kind of symmetric treatment of negation favoured in different ways by Huw Price (in “Why ‘Not’?”) and by me (in “Multiple Conclusions”) with Robert Brandom’s analysis of scorekeeping in terms of commitment, entitlement and incompatibility. Both kinds of account are what Brandom calls a normative pragmatics. They are both semantic anti-realist acco...

Tarski’s 1936 paper, “On the concept of logical consequence”, is a rather philosophical, non-technical paper that leaves room for conflicting interpretations. My purpose is to review some important issues that explicitly or implicitly constitute its themes. My discussion contains four sections: (1) terminological and conceptual preliminaries, (2) Tarski’s definition of the concept of logical co...

One of the most successful approaches to the formalization of commonsense reasoning is the work by Lehmann and colleagues, known as the KLM approach, in which defeasible consequence relations with a preferential semantics are studied. In spite of its success, KLM is limited to propositional logic. In recent work we provided the semantic foundation for extending defeasible consequence relations ...

n engl j med 358;14 www.nejm.org april 3, 2008 1496 From the Departments of Medicine (N.S., C.L.A.) and Surgery (D.J.), University of Wisconsin School of Medicine, Madison; and the Department of Internal Medicine, University of Michigan Medical School (D.R.K., S.S.), and the Ann Arbor Veterans Affairs Health Services Research and Development Center of Excellence (S.S.) — both in Ann Arbor. Addr...