Modularity and relevant logic
type: Item
instance of: scholarly article
title: Modularity and relevant logic
zbMATH Open document ID: 0693.03010
published in: Notre Dame Journal of Formal Logic
publication date: 1989-01-01T00:00:00Z
review text: This paper addresses the theoretical problem of practical reasoning systems (natural and artificial) being both correct and efficient. The problem of guaranteeing both has engendered disillusionment with formal logic in the AI community [see \textit{C. Cherniak}, J. Philos. 81, 739-758 (1984), for instance]. However, the abandonment of formal logic for the sake of efficiency has led to more or less ad hoc techniques, e.g., specific-context-bound semantic nets, frames, etc., which are not known to be correct. This paper explores a model in which reasoning systems consist of an assembly of \underbar{logical} modules (each one meets the conditions of local consistency and completeness) using procedural derivations in a relevant logic, and shows that having a combination of both speed and logical accuracy is at last an open possibility. For different discussions and approaches to this issue which include using relevant logics, see \textit{P. B. Thistlewaite}, \textit{M. A. McRobbie} and \textit{R. K. Meyer} [Automatic theorem proving in non-classical logics (John Wiley and Sons, Inc.) (1988)] and \textit{N. D. Belnap} jun. [``How a computer should think'', in: Contemporary aspects of philosophy (\textit{G. Ryle} (ed.)), 30-55 (Oriel Press) (1988), and ``A useful four-valued logic'' in: Modern uses of multiple valued logic, 5-37 (1978; Zbl 0424.03012)]. A reasoner is to have a global logic G, and is to consist of a set of modules and a selector, where a module consists of i) a set of rules that define the set of sentences that comprises its domain of expertise, ii) a set of inference rules and iii) a set of sentences that serve as its data. The global data is the data in all of the modules, and the global domain is the union of domains of all the modules. The selector assigns a module to each sentence in the global domain. A sentence is correct (for G) just in case it is derivable (according to G) from the global data. A sentence is provable in a module if there is a pro…
reviewed by: Steve Giambrone
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 68T15
zbMATH DE Number: 4134010
zbMATH Keywords: modularity
zbMATH Keywords: procedural derivations
zbMATH Keywords: automated reasoning
zbMATH Keywords: relevance logic
zbMATH Keywords: correctness
zbMATH Keywords: efficiency
zbMATH Keywords: AI
zbMATH Keywords: relevant logic
zbMATH Keywords: logical modules
author: James W. Garson
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1093635079
OpenAlex ID: W1991023298
DOI: 10.1305/NDJFL/1093635079
description: scientific article; zbMATH DE number 4134010