|Mereology: deals with the relationship between parts and the whole and systematizes the relations that can exist between them. A characteristic of mereology versus set theory is the same ontological status of parts and whole in mereology as opposed to the unequal status of set and element in the set theory. Thus, paradoxes can be avoided, such as those known e.g. with the universal-class or universal-set. See also part-of-relation, Russellian paradox, transitivity, extensibility, sum._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
Peter Norvig on Mereology - Dictionary of Arguments
Norvig I 470
Mereology/programming/knowledge representation/Norvig/Russell: [in this book] the proposition is adopted, in which in which substances are categories of objects; [it] was championed
by Richard Montague (1973)(1). It has also been adopted in the CYC project.
VsMontague: Copeland (1993)(2) mounts a serious, but not invincible, attack.
Mereology: The alternative approach mentioned in the chapter, in which butter is one object consisting of all buttery objects in the universe, was proposed originally by the Polish logician Lesniewski (1916)(3). His mereology (the name is derived from the Greek word for “part”) used the part–whole relation as a substitute for mathematical set theory, with the aim of eliminating abstract entities such as sets. A more readable exposition of these ideas is given by Leonard and Goodman (1940(4), and Goodman’s The Structure of Appearance (1977)(5) applies the ideas to various problems in knowledge representation.
While some aspects of the mereological approach are awkward - for example, the need for a separate inheritance mechanism based on part–whole relations - the approach gained the support of Quine (1960)(6). Harry Bunt (1985)(7) has provided an extensive analysis of its use in knowledge representation. Casati and Varzi (1999)(8) cover parts, wholes, and the spatial locations.
1. Montague, R. (1970). English as a formal language. In Linguaggi nella Societ`a e nella Tecnica, pp. 189-224. Edizioni di Comunit`a.
2. Copeland, J. (1993). Artificial Intelligence: A Philosophical Introduction. Blackwell.
3. Lesniewski, S. (1916). Podstawy og´olnej teorii mnogo´sci. Moscow
4. Leonard, H. S. and Goodman, N. (1940). The calculus of individuals and its uses. JSL, 5(2), 45–55.
5. Goodman, N. (1977). The Structure of Appearance (3rd edition). D. Reidel
6. Quine, W. V. (1960). Word and Object. MIT Press.
7. Bunt, H. C. (1985). The formal representation of (quasi-) continuous concepts. In Hobbs, J. R. and
Moore, R. C. (Eds.), Formal Theories of the Commonsense World, chap. 2, pp. 37–70. Ablex.
8. Casati, R. and Varzi, A. (1999). Parts and places: the structures of spatial representation. MIT Press_____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Stuart J. Russell
Artificial Intelligence: A Modern Approach Upper Saddle River, NJ 2010