A new formal tool: functorial variables representing assertions and presuppositions

The language of classical propositional iog-Ic is extended by functorial variables as a new syntactical category. Functorial variables render to be a possible integrating representation of both assertion and presup-position in one and the same logical formula different from such using classical conjunction. O~ Introduction From a computational point of vlew there is an important difficulty of an adequate formalization of both assertion and presup-position, It rests on dividing utterances into an explicit part (assertion) and an implicit one (presupposition). Frege 118921 refused any explication of this implicit part, because of hls ideallza= t/on that logic deals only with correct ~tatemerlts. At least in regard of definite descriptions Russell /1905/ pleaded for such an explication. But classical conjunction was one of its essential formal tools. To a certain extent assertion and presuppoeltion were represented at one and the same level. Strawson /1950/ claimed that presuppositions have to be explicated, but not at the same level like the implicit part. Many linguists = e, g. Klefer 11973/-believe that logical means can be used to represent both parts of utterances aeparately~ but these representations cannot be put together in one and the same logical expreeslon~ because Russell's solution Is unsatisfactory. My intention is to show that functorlal variables render to be possible tools for integrating representation of both assertion and presupposition in one and the same logical formula, Moreover-unlike Bergmann i1981/, OunglKOstner /19861-this representation Is a svntactlcal one and different from that given by means of classical conJunction (cp, Max l1986/i /forthcoming/). 1. The logical apparatus 1,1~ Functors as classical functions n Let ~t be the form of n-placed propositional 2n functors; 1 ~ t ~ 2 ~ I will use 1-and 2-placed functors only, These functors are interpreted as classical (i. e, 2-valued end extensional) functions, The value-tables are= 0 0 0 0 1.2, Functorlal variables I introduce functorial variables as e ne~ pyntactlcal category, and take the classical functors as values of these variables. Introducing such variables we get a whole class of syntactical extensions of the classical pro-positional logic. Only functorlal varlablee of the following form are considered= G~=gi_ I ~ f,g ~ 16. The f's and g's are called components. The f-component (g-component) is called first (second) component. are values of 2 Semantically, ~ and ~gG2 the functorial variables f,g. Therefore these functorlal variables (abbreviation= FV's) represent eats of functors wlth exact two (not necessarily different) elements. Wlth …