Representing Numbers in Semantic Networks: Prolegomena

Introduction

We are study~ng var~ous metnods of representing numbers in semantic networks. 'l'nere ar~ two reasons for this. First, semantic networks have .been proposed since tne late sixties as formalisms for the general representation of knowleage. Late­ ly, tneir popularity has increased. Yet proolem areas persist for which tne repre­ sentations have not yet been carefully workeu out. Some of tnese are discussed in Woods, 19 7 !:i. l~umeric information is anoth­ er of the issues tnat "need to be address­ eo ana solutions integrated into a con­ sistent wnole in order to proauce a logi­ cally adequate semantic network formalism" (Woods, 1975, p. 80).

'l'ne seconu r<=ason for tne interest in representing numeric information is that reflection on tuis pro.olem, and experimen­ tat~on witn various alternatives have lea to tue conclusion tnat numeric information is uasically syntactic ratner tnan seman­ tic. 'nlis conclusion suggests tnat tne way to proviue numeric infontlation to a seman­ tic network is to proviue it witn a gracious interface to a syntactic repre­ sentation - say a syntactic network. Hare­ over, sucn a uual network representation seems generally useful for natural lan­ guage unaerstanaing systems.

'.l'uis note sets tile stage for an explica­ tiou of semantic and syntactic networks, tueir aifferenc~s, ana possiole interfaces oetween tnem. A more complete aiscussion is in preparation. ~~umeric information proviues an example uomain for tne study.

Semantic Networks

1~oues of semant~c networks generally represent unique concepts. An arc of a semantic network represents a relationship oetween two concepts that itself is not a concept. For many examples of such rela­ tions see ~ruce, 1975.

In .l?ictorial representations of semantic uetwor.res it is common to uraw a node as a lcwelleu circle. '.l'h~ lauel is a token of a turee-way dnwiguous sym.t>ol: a mnemonic de­ vice to nelp tue urawer of the picture conuuunicate witn tne reauer of tne pic­ ture; an iaentifier in tne programmed im­ plem~ntation of tne network that accesses tne uata structure representing the same noue as tu~ circle represents; an identi­ fier of a node of tne network considered as au austract data structure (a kina of grapn). we will refer to tnese tnree-way arnoiguou~ syml?o~s as fdentij'iers. We mignt use tn~ ~uent~f~er )Ll for tne noae representing tne number variously written as "521", "JJXXI", "five nundrea twenty-one", etc. In an implementation of a semantic network, we might be able to convert the iaentifiers 5Ll and 26, to integer data types and compute the fact that 521 is numerically greater than 26, but informa­ tion derived in such a manner is not be­ ing derived from the semantic network and is based on knowledge not represented in the semantic network.

Sucn knowledge can be represented in a semantic network by representing the .con­ cept of greater-than as a node, storing some greater-than facts explicitly, and storing rules for recursively deriving implicit greater-than facts from explicit ones using formalisms such as those de­ scribed in Shapiro, 1977.

Syntactic Networks

A syntactic network nas nodes repre­ senting sucu tr1ings as lexemes, clauses, and syntactic classes and arcs represent­ ing such relations as linear order in the surface string, membership in a constitu­ ent phrase, and dependency of a constitu­ ent on its governor. An example of a syn­ tactic network is the chart of Kay, 1973.

We mignt uetermine that 521 is greater tnan 26 by noting that the numeral 521 has more digits than the numeral 26. 'l'hat tnis is a syntactic tecnnique may be noted oy realizing that it does not work for DXXI vs. XXVI. A syntactic network coulu be used to represent a numeral as a kind of clause consisting of a linear string of its digits.

Interface

An inter-network arc could be introducea between a semantic node and the highest level syntactic node representing the ex­ pression of the concept in some natural language. 'I'lle LeA arc of Snapiro, 1975 serves such a purpose.