Handbook of philosophical logic. Vol. 9
type: Item
instance of: scholarly article
title: Handbook of philosophical logic. Vol. 9
zbMATH Open document ID: 1055.03001
published in: Handbook of Philosophical Logic
publication date: 2004-11-25T00:00:00Z
review text: This volume of this Handbook series is to a large extent concerned with proof-theoretic matters. It offers only chapters which do not have companions in the first edition. Their common feature is a tendency toward computer science applications. The first chapter (pp. 1--88) by \textit{N. Martí-Oliet} and \textit{J. Meseguer} is on ``Rewriting logic as a logical and semantic framework''. The authors aim is to explain the basic ideas of rewriting logic, as introduced by \textit{J. Meseguer} [Theor. Comput. Sci. 96, 73--155 (1992; Zbl 0758.68043)], and to offer it as a general semantical framework for a unified understanding of a broad class of different logics. The next chapter (pp. 89--164) discusses ``Logical frameworks'' again from a general point of view and is written by \textit{D. Basin} and \textit{S. Matthews}. Here, logics are mainly understood as being determined by syntactic calculi. The aim again is to offer a unifying metalogical framework which covers quite different systems of logic. Following this, \textit{G. Sundholm} explains in his chapter on ``Proof theory and meaning'' (pp. 165--198) the understanding that, and to what extent, the logical calculi, particularly the rules governing the behavior of the connectives, determine the meaning of these connectives, and to what extent a truth-conditional definition of the meaning of the connectives is problematic. Essentially a particular type of logical framework is presented in the fourth chapter (pp. 199--286) by \textit{D. M. Gabbay} and \textit{N. Olivetti}: ``Goal directed deductions''. This chapter's main goal is a generalized methodology for automated deduction inspired by the logic programming paradigm. The (formal) ``goals'' within the deductions may be formulas which have to be checked for satisfiability or derivability or validity, of course in certain situations. The methodology is based upon backward reasoning which comes into considerations via the splitting of goals into subgoals which imply,…
reviewed by: Siegfried J. Gottwald
Mathematics Subject Classification ID: 03-00
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03F03
Mathematics Subject Classification ID: 03B60
Mathematics Subject Classification ID: 03B22
Mathematics Subject Classification ID: 03B70
Mathematics Subject Classification ID: 68T99
zbMATH DE Number: 2118884
zbMATH Keywords: rewriting logic
zbMATH Keywords: metalogic
zbMATH Keywords: general proof theory
zbMATH Keywords: theory of meaning
zbMATH Keywords: consequence relations
zbMATH Keywords: negations
zbMATH Keywords: philosophy of logic
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2118884