How to Construct a Logic for Your Application

Abstract

1 I n t r o d u c t i o n The purpose of this note is to present and evaluate the options available to a practically minded researcher wishing to use logic for the representation, reasoning and computa t ion in his application area. We begin by listing the properties of classical logic agMnst the needs of a typical case study. The basic notions involved in classicM logic are the following: 1. The notion of a well formed formula, which is the basic declarative unit available for the representation of the knowledge of the case study. 2. The notion of a database A or a theory, which is the aggregation of declarative units. In this case it is a set of wits. 3. The consequence relation ~of the form A F A between databases and declarative units. This can be presented in various forms, semantically, p roof theoretically, etc. Some systems are formulated using consequence relations between two databases A ~F. This notion for arbi trary F can be defined in some cases from the fragment consequence where there is a single declarative unit in F. Different logics, such as intuitionistic or many valued logics, share with classical logic the notions of a declarative unit and a database, but differ on the consequence relation. In contrast to the above, a typical case study may indeed have identifiable basic semantic declarative units, but these declarative units are naturMly organised in a structure. This structure is external to the declarative units. Thus the * SERC Senior Research Fellow. I am grateful to H.-.]. Ohlbach for stimulating discussions and for going through an earlier version of the paper. notion of a database as a set is not found in applictions, but rather the notion of a database as a structured constellation/network of formulas seems more appropriate. The following are examples of sources of structures imposed natrual ly on declarative units of application areas: T ime stamps, earlier-later relations among data items. Sources of the data. The structure is inherited from the social relationships among the sources. Causal relations among data (in e.g. medical networks). Accessibility relations among formulas holding in different possible worlds. Priorities among data. Artificial structuring among data clauses for the purpose of efficient computation. Numerical s tamps, giving reliability or plausibility. The structure is induced from numerical relationships. The above are enough widespread examples to justify focussing our discussion on a typical case study where the declarative units are structured, say in a graph form with nodes and several types of edges. Fig 1 illustrates such a structure.

DOI: 10.1007/BFb0018989

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Cite this paper

@inproceedings{Gabbay1992HowTC, title={How to Construct a Logic for Your Application}, author={Dov M. Gabbay}, booktitle={GWAI}, year={1992} }