| { | |
| "paper_id": "C86-1013", | |
| "header": { | |
| "generated_with": "S2ORC 1.0.0", | |
| "date_generated": "2023-01-19T13:15:02.193678Z" | |
| }, | |
| "title": "Plurals, Cardinal/ties, and Structures of Determination", | |
| "authors": [ | |
| { | |
| "first": "Christopher", | |
| "middle": [ | |
| "U" | |
| ], | |
| "last": "Habel", | |
| "suffix": "", | |
| "affiliation": { | |
| "laboratory": "", | |
| "institution": "Universiti~t Hamburg", | |
| "location": { | |
| "addrLine": "Fachbereich Informatik 8chliJterstr. 70", | |
| "postCode": "D-1000", | |
| "settlement": "Hamburg 13" | |
| } | |
| }, | |
| "email": "" | |
| } | |
| ], | |
| "year": "", | |
| "venue": null, | |
| "identifiers": {}, | |
| "abstract": "This paper presents an approach for processing incomplete and inconsistent knowledge. Beais for atteoking these prob]ems are 'structures of determination', which are extensions of Scott's approximation ]atticea taking into consideration some reguirements from natural language processing and representation of knowledge. The theory developed is exemplified with processing plural noun phrases referring to objects which have to be understood as classes or cots. Referential processes are hand]ed by processes on 'Referential Nets', which ere a specific knowledge structure developed for the representation of object-oriented know]edge. Problems of determination with respect to cardinaIity assumptions are emphasized.", | |
| "pdf_parse": { | |
| "paper_id": "C86-1013", | |
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| "abstract": [ | |
| { | |
| "text": "This paper presents an approach for processing incomplete and inconsistent knowledge. Beais for atteoking these prob]ems are 'structures of determination', which are extensions of Scott's approximation ]atticea taking into consideration some reguirements from natural language processing and representation of knowledge. The theory developed is exemplified with processing plural noun phrases referring to objects which have to be understood as classes or cots. Referential processes are hand]ed by processes on 'Referential Nets', which ere a specific knowledge structure developed for the representation of object-oriented know]edge. Problems of determination with respect to cardinaIity assumptions are emphasized.", | |
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| "section": "Abstract", | |
| "sec_num": null | |
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| "text": "Most approaches to 'proceesing reference' are concerned with the case of singular NPs and deal with the complications of plurals on]y periphericolly by remarks af the kind \"The plural case can be considered analogously.\" But such hopes are only partially justified: the plural case is worse and therefore more interesting. In the present paper I wlll discuss some spsclflc prob]ems of (in)definiteness with respect to plurals from an AI point of view. The heart of any knowledge-based system (KB$) -man or machine -is his/ her/Its knowledge base (KB), containing different types af knowledge (cp. sect. 2). The KB reflects the KB5' view af the world; in other (e.g. dackendoff 's, 1983) words: a projected world. (O/ring emphasis to projected worlds and thus to mental models leads to a psychological foundation of semantics.) The case easiest ta manage is that of a complete and consistent KB. But in normal life -of man es well as machine -thia almost never occurs; the knowledge is incomplete or inconsistent (or both). There are some reasons (cp. sect 3, ,t) to see both types of problem as clase]y connected, as twin problems, abbreviated by I&l. It is important to extend the KBS' faculties with regard to the maintenance af I&l. This includes:", | |
| "cite_spans": [ | |
| { | |
| "start": 677, | |
| "end": 686, | |
| "text": "'s, 1983)", | |
| "ref_id": null | |
| } | |
| ], | |
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| "section": "I. Introductory remarks", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "-Recognition and detection of I&l -Correction of I&l, i.e. forcing completeness and consistency -Dealing, i.e. arguing ar 'thinking', with Incomplete or inconsistent knowledge. These tasks for maintaining I&l is of specific importance in processing reference.", | |
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| "section": "I. Introductory remarks", | |
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| "text": "In representing the knowledge about the world (not linguistic knowledge) of a KBS I distinguish three types, hnawledge of facts, knowledge ofru/~ and knaw/ed]e af objects, which is represented by 'Referential Nets' (ReiN). The formal objects, which can be underatood as internal (ar mental) proxies for entities of the real (or other possible) world(s) are called 'Referential Objects' (RafO). RefOB can be seen as underdetermlned formal objects (UFCO) in case of incompleteness, or as overdetermined (OFOs) in case of inconsistency. For representing the knowledge of a KB$ and the meaning of utterances I use a propositional 'eamanttc representation language' $RL. Far processing, e.g. storing and retrieving, referential relations SRL contains apectfic 'descriptian operators', which are from a formal point of view variable-binding, term-making operators. Here I will neglect the details of 5RL and exemplify only those 8RL-concopta which are involved in knowledge about objects (cp. Habel, 1986) . The tatellty of RafOs and their properties (see below) form a net-like knowledge structure: the Ref~rentialNet(ReiN). ReINs are based on three types of formal entities: referentialebj~ts(RafOs) as system-internal proxies of the abjecte of the world, designMionsaf RefOs, i.e. terms [as opposed to formulas) of 8RL and attribute~ to RafOs and dssignationa. From a formal point of view (Habel, 1985 (Habel, , 1986 ( 1 ) John's children will travel abroad during their summer vacation. leads to the following entries in a ReIN (only the most relevant parts are formulated; attributes are omitted in the present sect.):", | |
| "cite_spans": [ | |
| { | |
| "start": 982, | |
| "end": 999, | |
| "text": "(cp. Habel, 1986)", | |
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| }, | |
| { | |
| "start": 1386, | |
| "end": 1398, | |
| "text": "(Habel, 1985", | |
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| { | |
| "start": 1399, | |
| "end": 1413, | |
| "text": "(Habel, , 1986", | |
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| "section": "]he frame of representation", | |
| "sec_num": "2." | |
| }, | |
| { | |
| "text": "(I') r. I -- 'John' r.2 --ALL x : child_of (r. 1, x)", | |
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| "section": "]he frame of representation", | |
| "sec_num": "2." | |
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| { | |
| "text": "\"\"-SOHE x :trave] (x, r.3, r.4) r. 3 --\"abroad\" r.4 --\"during r.2'a summer vacation\" Remarks:", | |
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| "section": "]he frame of representation", | |
| "sec_num": "2." | |
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| "text": "I. There are proxies for objects in a narrow sense as waI] as for some in a wider sense, e.g.w.r.t, locations (r.3) or time (r.4). Their SRL-designaticos will nat be formalized here. 2. \"ALL\" is the intenstonal class-building operator, which differs from the formula-making universal quantifier. \"SOME\" is the indefinite pluro] term-maklng analogy to the definite \"ALL\". (On \"SOtIE\", tlle definite descriptor \"IOTA\" and the indefinite \"ETA\", which are used in (5'), cp. Hahel 1982 Hahel , 1986 ).", | |
| "cite_spans": [ | |
| { | |
| "start": 470, | |
| "end": 480, | |
| "text": "Hahel 1982", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 481, | |
| "end": 493, | |
| "text": "Hahel , 1986", | |
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| } | |
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| "section": "]he frame of representation", | |
| "sec_num": "2." | |
| }, | |
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| "text": "In the following I will mainly deal with proxies for concrete objects, especially persons. A first analysis of the situation in question shows that a hearer of ( I ) possesses a RefO representing \"John's children\" without the abligation to knew more details about them. e.g., though s/he does not have to know how many they are it is passible to refer to them definitely. With the introduction of the additional concept 'attribute of e RefO' it is possible to deal with the I&l problem, 1.e. the problems af under-and overdetermination of formal objects. (Furthermore, the use of attributes leads to knowledge representations which allow easy and quick access to the objects in question, e.g. in anaphora resolution and generation). A more adequate analysis of ( I ) should lead to a representation, which represents the plural explicitly (and not only implicitly via \"ALL\"):", | |
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| "section": "ItefNs: Under-and overdeterminetion", | |
| "sec_num": "3." | |
| }, | |
| { | |
| "text": "(1\") card~2-- r.2-- ALLx:child_of(r.l,x) human -J", | |
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| "section": "ItefNs: Under-and overdeterminetion", | |
| "sec_num": "3." | |
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| "text": "using a cardlnality attr/Dute to the RefO r.2 which represents the essential property that r.2's real-world counterpart is assumed to consist of more than one human being; the sertal attribute \"human\", which will be, used here only, exemplifies another type of attribute, namely ~rtalattribut~ By this attribute mechanism I represent the meaning of numerals, e.g. \"dahn's two cars\" leads to card= 2-r.9 ~ ALL x:cor (x) &ewn(r.l,x) In text generation the communicative goals determine which designation(s) and R-ATTs are used to form the content of the message. What counts as determinate depends an the type of attribute in question. Each type of attribute possesses its own cot af completeness and consistency conditions. In the case of cardlnallty, the determinacy condition is given by Each set has exactly one cerdinolity. This eondition defines the idaal-state of the cardinality attribute which a system aspires to. The actual knowledge with respect to cardine]ity concerns a 'rarlge of pesslble cordlna]lttes'. From this follows what under-and overdeterminotion (I&l) are:", | |
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| "sec_num": "3." | |
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| "text": "in the case of underdotarmination some cerdinalities are pessible, eg. the cardtnallty Is greater or ague1 2, but the exact value is unknown, in the determinate ~ only one cardinolity is possible, i.e. the exact cardinality is known, -In the case of overdetermination more than one cerdinality is assumed, which violates the cerdinality condition. I wlll go on with dohn's children:", | |
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| "section": "ItefNs: Under-and overdeterminetion", | |
| "sec_num": "3." | |
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| "text": "(3) The boys will visit France. Hory and Sue will go to Italy. Analogously to ( 1 ) the ReiN has to be extended to:", | |
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| "text": "(3') cord;~'t ~ r.2---ALLx :chllr.L_of (r.l,x) cord ~ 2 --r.5 ~ ALL x : child_of (r. 1, x) & boy(x) SOME x :visit (x, 'France') cord ~. 2 ~ r.6 --ALL x : child_of (r. I, x) & girl (x) CONTAINS (r.7) CLASS ('Mary', 'Sue') card --, 2 ~", | |
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| { | |
| "text": "r.7 ~ SOME x : visit (x, 'Italy') Remarks:", | |
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| "sec_num": "3." | |
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| "text": "1. \"cord(r.6) ~ 2\" because tt ls pesslble that there ere further daughters of John. Note, that o]l bays -\"cord(r.5) ~. 2\" -visit France but only some girls, namely those represented by r.7, visit Italy. 2. I assume that the competence of calculating attributes is used in the maintenance of ReiNs. By this \"cord(r.2) ~. 4\" is calculated from cord(r.5) and cord(r.6).", | |
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| "sec_num": "3." | |
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| "text": "3. There exists an operator \"IS_CONTAINED\" duo] to \"CONTAINS\", which I neglect in this paper (ep. Habel, 1986) . r.7 con be seen as determined wlth respect to cordinoilty since an exact value is assumed, whereas r.2, r.5 end r.6 are underdetermined. As a ]est example for cordinality computations, let us take the input (~r) John has four or five children. Three of them are girls. That leads to the following changes in the ReiN:", | |
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| "text": "(ep. Habel, 1986)", | |
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| "text": "(4') cord :", | |
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| "text": "= 5 ---r.2 ALL x : chlld__of (r. 1, x) ~ CONTAINS (r.5) CONTAINS (r.6) ALL x : child_of (r.i, x) & hay(x) cord == 2- r.5 ~ SOME x : visit (x, 'France') ALL x : child_of (r. l, x) & girl (x) card,= 3 .--r.6 ~ CONTAINS (r.7)", | |
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| { | |
| "text": "Bemark:", | |
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| "text": "In a first step (corresponding to the first part of the input) cord(r.2) is sat to ,1 or ,5, In a ,second (inferential) step card(r.2) is computed to `5 based on the cerdinalities of r.5 (>_2) and r.6 (=3). In a third step card(r.5) can t)e computed to exactly 2. New we turn to overdoterminotton, i.e. inconsistencies. Suppose someone tells the KBS (or\" you):", | |
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| "text": "(5) The oldest, Peter, travels to Spain. What is there to do now? Where are the problems, hew are they noticed, and how can they be solved? Before rejecting (5) wlth \"That ls impossible!\" let us discuss the changes in the REIN:", | |
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| "text": "(5') cord=5~ r. The newly created RefO r.8 is integrated in the ReiN by two links: on the one hand via CONTAINS from r.5 \"the bays\"; this link is inferred by use of knowledgo about Christian names in English. On the other hand via the oldost-eonnectlon to r.2. Thus the cordlnalltles of r.2 and r.5 (In 4') have to be changed, which is rcolized by assigning o second cardinolity attribute. (This reading of the sentence end interpretation of the net assumes a third son, \"Peter\", which vlslts Spain only. Note, that the inheritance about visiting France can be blocked via the 3rd designation of r.8. The points of inconsistency or everdetermination can be ]coated at the cardinality of r.2 (\"card=5\" vs. \"eard>5\") and of r.5 (\"card=2\" vs. \"card,~ 3\"). What is reasonable to do now? There are several poselbiltties:", | |
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| "text": "-Reject the newest input. But why should \"card=5\" be preferable to \"cord>5\" (or \"card=2\" to \"cerd~3\")? -Try to eo]va the inconsistencies. Ask other people or undo inferences.", | |
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| "text": "-Try to live with inconsistencies. Be aware that reasoning con be dangerous. Why is it convenient and pessible to fol]ow the third strategy? On the one hand, though there are inconsistencies with respect to the cerdineHty of r.2 and r.5, these inconsistenclaa ore localized and do not infect the whole KB. (This strategy of marking inconsistencies and thus avoiding infections of the KB, i.e. putting inconsistencies in quarantine, follows 8elnap (1976)). Therefore the system is justified In answering questions with regard to other ports of the ReiN. On the other hand, locating paints/cress of inconsistency and waiting for future information con ]Pad -by means of inferences -to the solution of the inconsistency in question. One possible correction of the inconsistencies in (5') cou]d be ~chieved by detecting that the informants u~d different concepts of 'daughter', e.g. 'daughter', 'sdepted daughter', 'stepdaughter'. In the pre~.~nt example the \"updating of the boys\", i.e. the new \"cord(r.5) ~ 3\", was not given explicitly but was inferred from the male Christian names 'Peter'. It is possible that the inference in question, which uses common knowledge about Christian names, was misleading, because John's oldest daughter is nicknamed, she is \"a girl named Peter\" (as Russoll's wife, who was known as Peter Spence). B.e~ac_k~ 1. Another way of analysis, namely concerning designations but not cerdinalities, leads to a different solution with respect to r.8. Peter can be seen as a person visiting both France and Spain. Note, that this reading would also be baaed on a careful analysis of card(r.5).", | |
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| "text": "2. The parallel example in Carman would lesd either not to an inconsistency at all or to another type of inconsistency since gender-informatiea of the article would distinguish between two cases: \"Der ~lteste, Peter...\" ('dor' ~ 'masc.') leads also to (5'), but the possibilities for the solution of the overdotermination mentioned above are not usable in this case. \"Die ~lteste, Peter...\" ('die' ~ 'fern.') leads to linkage of r.8 to r.6, \"the girls\", and no inconsistency of cardinality would appear. But, most hearers would be suprised with the strange Christian name of the girl. The similarities and differences of under-and overdetermination, i.e. the justification of the twin-concept I&l, can be seen best by discussing the appropriate response to questions llke \"How many children does ,John have?\". On the one hand with respect to on undardatermined case, e.g.", | |
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| "text": "(6) card ~ 5 r.2' ALLx:chiId_of(r.l,x) induced by \"John lies five or more children\". In the case of underdetermination (6) the KBS knows that it has incomplete knowledge and therefore it is justified in answering \"Five or more, but I don't know ex~ctly\". In the case of overdetormination (5)the KBS knows that it has inconsistent knowledge. Therefore it should warn the questioner, e.g. by responding wlth \"Presumably five or more, but I have contradictory information\". Note, that it would be reasonable far you to usa the concept of \"John's children\" in a similar way if you only have the information in question.", | |
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| "text": "From a formal point of view the cerdinelity attributes ore examples of approximation structures similar to the information lattices introduced by Scott ( 1970) ; cp. Belnep (1976) . The lower part of the structure of determination (see Fig. 1 ), \"UD-CARD\", represents the undardatermined end the upper one, \"OD-CARD\", the overdetermined cardinelities. The determined cases are represented by the \"D-CARD\" level, which is the symmetry axis of the structure. D-COrd is the set of singletons over the set N of natural numbers (including zero); UD-CARD consists of the not-singleton elements of the power-sat of N with the partial ordering induced by the set inclusion. OD-CARD is built up by introducing a 'dual to each UD-CARO' element, which Is symbolized by square brackets \"[_]\". The D-CARD elements stand for \"the cerdinality is exactly the n which forms the singleton in question\". UD-CARD represents e set of possible cardinelities. The minimal entity in the approximation structure, namely N, holds no relevant information, since \"Card=N\" stands for \"the RefO has a cardinolity\", and this ia true for ell RefOs. ('Cord' is o set of cardinalities 'cord'.) Oetting input from communication or inferential processes, leads to climbing up the structure, which reflects the enrichment of information with respect to cardinality, or to no change in knowledge about the attribute. The ideal-level is reached at the D-CARD-level: an exact cardinelity is assigned. Further input causes ( in the good case) no change end in the bad case of inconsistency climbing up into the OD-CARD-rogIOn. The structure of determination does not possess lattice properties; only the UD-CARD end the OO-cord parts are lattice-like. The sudden change at passing from UD-CARD or D-CARD to inconsistent OD-CARDs destroys the lattice properties (see below). The approach of structures of determination, which is exemplified here with the case of cordinality attributes, can be ussd analogously with respect to other types of attributes. The base of ell such structures ere lattices, e.g. those of eartal attributes, which con be interpreted as approximation lattices. This means that climbing up the lattice can be understood as increasing information. (Note.that the ALL-element in this Interpretation is the bottom-element). In e (half) formal way, a structure of determination is built up from e Scottien approximation ]etttco (AL) by the following method: 1. Delete NIL from the approximation latticeAL. 2. Devide the rest in the level of determination (LaD) which ia formed by the direct neighbors of the (now deleted) NIL end the undardatermined part of the lattice (UD-AL) which is given by those elements of AL which ere neither NIL nor in LaD.", | |
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| "start": 146, | |
| "end": 159, | |
| "text": "Scott ( 1970)", | |
| "ref_id": "BIBREF5" | |
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| "start": 166, | |
| "end": 179, | |
| "text": "Belnep (1976)", | |
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| } | |
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| "start": 236, | |
| "end": 242, | |
| "text": "Fig. 1", | |
| "ref_id": "FIGREF2" | |
| } | |
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| "sec_num": "4." | |
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| "text": "NIL I x,,3] / / oo-o .o [1,2] [1,3] [2,3] [2,4] {0} {1}......_ {2} {3) {,'1.} {5) ... CARD \\ {1,2} { 1,3} {2,3} {2,4} {I ,2,3} {I ,2,4} \\ oo-CA.o {XEI } {x~3}", | |
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| }, | |
| { | |
| "text": "3. With respect to UD-AL construct a dual counterpart of overdetermined elements. This Is called OD-AL. '1. Olue OD-AL with UD-AL via the level of determination LaD. 5. The ordering relations can be defined in the canonical way. As mentioned for the case of cerdlnn]lty attributes such structur~ of determination do not possess lattice properties. This is proven in Hebel (1986). The same phenomenon is observed by Belnap (1976) with respect to his set of episternic stete~, E. The lattice properties ere violated at the passage to inconsistency (everdatorminetion). Nevertheless, the most relevant properties of Scott's approximation lattices else hold for structures of determination, especially the emplietivityby/nput( using Belnap's terminology). One very important difference between Scott's approach and determination structures concerns the NIL, which is the (!) failure element of ALs. In contrast, structures of determination contain many different failure elements, namely all beyond the level of determination. Thus a condensed history of informing end dtsinforming is abbreviated by the OD-ettribute. (A cherercterizetion of Scott's epprasch could be: \"All failures ere equal, namely disastrous. \") Repair processes, which e.g. can be triggered by Input from an especially competent or believable informant, e.g. with respect to my example by dohn himself, levi to climbing downward in the structure. Note, that repairing is informing of a specific type. In contrast to normal informing it leads downwards; this changing of the direction demands a specific prior decision based on the experience that something was going wrong. I conclude this section with e remark on overdetermination:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Structures of determinntlen", | |
| "sec_num": "4." | |
| }, | |
| { | |
| "text": "Overdstermined objects ere e specific type of /mpossl'ble objects (cp. Rapeport 1985) , which constitute e test case for every semantic theory. 'Impossibility' or 'non-existence' (as used in some approaches to this topic) refer to the real world and not to projected worlds, which are in the mind.", | |
| "cite_spans": [ | |
| { | |
| "start": 66, | |
| "end": 85, | |
| "text": "(cp. Rapeport 1985)", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Structures of determinntlen", | |
| "sec_num": "4." | |
| }, | |
| { | |
| "text": "In this paper I have only dealt with I&l problems concerning the subtype of referential knowledge. Obviously, e similar approach is appropriate for the other subtypes of knowledge, i.e. for other formal objects. (Notice that assentia] properties of RefOs, such as cerdinalfty, can also be seen as port of factual knowledge.) In the case of factual knowledge undardeterminetion or overdaterminetion concerns truth values. Belnep's (1976) four-valued logic with e lattice-theoretic semantics has influenced the concepts of the present paper from e logical point of view. Same types of ReiNs end of structures of determination ere implemented as parts of prototypicol text-understanding systems by the KIT-projects at the Technical University Berlin.", | |
| "cite_spans": [ | |
| { | |
| "start": 421, | |
| "end": 436, | |
| "text": "Belnep's (1976)", | |
| "ref_id": "BIBREF0" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Conclusion", | |
| "sec_num": "5." | |
| } | |
| ], | |
| "back_matter": [], | |
| "bib_entries": { | |
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| "ref_entries": { | |
| "FIGREF1": { | |
| "type_str": "figure", | |
| "num": null, | |
| "uris": null, | |
| "text": "5 ~-r.6 card = 2 --r.7 ~-card-1 ---r.8=---~ ALL x : child_of (r.1, x) & boy(x) SOME x : visit (x, 'France') CONTAINS (r.8) ALL x : clli]d_of (r. 1, x) & girl (x) CONTAINS (r.7) CLASS ( 'Hary', 'Sue') 'Peter\" IOTAx : oldest(x, r.2) ETA x: visit(x, '3pain')Remark:" | |
| }, | |
| "FIGREF2": { | |
| "type_str": "figure", | |
| "num": null, | |
| "uris": null, | |
| "text": "Approximation structure CARD of cordinelity attributes" | |
| } | |
| } | |
| } | |
| } |