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...

Amongst possible choices for identifying complicated processes for prediction, simulation, and approximation applications, high-order Takagi-Sugeno (TS) fuzzy models are fitting tools. Although they can construct models with rather high complexity, they are not as interpretable as first-order TS fuzzy models. In this paper, we first propose to use Deformed Linear Models (DLMs) in consequence pa...

NeuroFAST is an on-line fuzzy modeling learning algorithm, featuring high function approximation accuracy and fast convergence. It is based on a first-order Takagi-Sugeno-Kang (TSK) model, where the consequence part of each fuzzy rule is a linear equation. Structure identification is performed by a fuzzy adaptive resonance theory (ART)-like mechanism, assisted by fuzzy rule splitting and adding...

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...

We discuss some consequence relations in DRT useful to discourse semantics. We incorporate some consequence relations into DRT using se-quent calculi. We also show some connections of these consequence relations and existing partial logics. Our attempt enables us to display several versions of DRT by employing different consequence relations.