Name
Abstract | ||
|---|---|---|
In Volume 33:1 of the Notre Dame Journal of Formal Logic , a system for diagramming syllogistic inferences using strai ght line segments is presented by Englebretsen. In light of recent research on th e representational power of diagrammatic representation systems by the authors, we point out some problems with the proposal, and indeed, with any proposal for represent- ing logically possible situations diagrammatically. We sh all first outline the pro- posed linear diagrammatic system of Englebretsen, and then show by means of counterexamples that it is inadequate as a representatio n scheme for general logical inferences (the task for which the system is intende d). We also show that modifications to the system fail to remedy the problems. The considera- tions we present are not limited to the particular proposal o f Englebretsen; we thus draw a more general moral about the use of spatial relati ons in representa- tion systems. 1 Diagrammatic representation systems Diagrammatic representation systems are of increasing interest for at least two reasons. Philoso phically, diagram sys- tems interest those concerned with the nature of representa tion itself—in particular, those who argue that too much attention has been given to sequential symbol sys- tems. These writers claim that diagrams represent by analogyor surrogacy—in virtue of sharing structure with the domains that they represent (s ee Barwise and Shimo- jima (2), Cummins (4), and Swoyer (20)). Practically, diagrammatic representations are frequently used in visual interfaces to databases, prog ramming languages, and in logic teaching. Each of these domains demands careful consideration of the formal properties of the diagrammatic systems in question. For bot h of these reasons we pro- pose to investigate the expressive power of one proposed diagram system and to de- termine its utility in reasoning tasks. |
Year | DOI | Venue |
|---|---|---|
1998 | 10.1305/ndjfl/1039118871 | Notre Dame Journal of Formal Logic |
Keywords | Field | DocType |
formal logic,expressive power | Syllogism,Spatial relation,Discrete mathematics,Diagrammatic reasoning,Symbol,Logical possibility,Algorithm,Diagram,Counterexample,Analogy,Mathematics | Journal |
Volume | Issue | Citations |
39 | 4 | 13 |
PageRank | References | Authors |
0.99 | 3 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Oliver Lemon | 1 | 13 | 0.99 |
| Ian Pratt | 2 | 5420 | 506.92 |