Network of Binary Relations in Natural Language

Adrian Birb~eeu 4./NTaOOO~-/'/ ON. It is an esmontl~, cha~acteristic of nat~al languages that one uox~l oan be concatenated mt~h certain others to form a et~Ing tha~ enters in correct phrases of the language, whale it cannot be eo~atamated ui~h othe~s. The same holds true for e~rlng~ of words. Such eoncatenable elements axe also "mutually eompatible elements" in the sense used b 7 KVAL in a paper dos-o~ib~n8 an aleori~ for formi~K naxlnum classes of such elements~ Mathematically, a set of ordered pa~s of such "s~tvall~ ¢ompa-t£ble elements" forms a x~lat£~. Ever 7 string Of ~ords belonging to a langua~ can be ~esax~d as being obtained by euoceesive oo~oatenatton of ordered pair8 of mttuall~ oompat£ble elements, i.e. as formed by eueoessive oonoatenation of elements of binary relations be~ to the languase, Some of these string e~e the phrases of the la~ua6e. It is thu possible to define a ~a~ mar of ~elation-and 6ene~ate by it all phrases of the lan~m~. If ue tx~ to describe by a ~ this gene~atlon~ the ~aph will be a network desc~Iblz~ the mhole system of lan~uaKe under oonsi-dex~t ion, The equivalence between a g~am~a~ of relations and an lO-~a~ma~ and the equivalence between a g£~m~r of ~ela~ions and a oategortal 8x~mmu~ ~ a]~mst self-evident. B~ usi~ the notations for union, interseotion and Oarte-siam prod~ct it is imssible to urite one single formula~ however