A decision support system for rule discovery in social networks Nicholas V. Findler *, Sudheer Dhulipalla **

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1 A decision support system for rule discovery in social networks Nicholas V. Findler *, Sudheer Dhulipalla ** Department of Computer Science and the Artificial Intelligence Lab Arizona State University, Tempe, AZ , USA Abstract Automatic rule discovery of membership in and relations between classes or categories, from given examples and counter-examples, is an important objective in many areas of computing. We have established a fairly general purpose programming environment for inductive rule discovery. It can be used, for example, as a high-level decision support system for social and cultural anthropologists. The program hypothesizes and then asserts rules that govern (permit or prohibit) social interactions and relations in human societies. We also describe the domain-independent facilities of the decision support system offered to the user and how the program works. 1. Introduction The psychological term concept formation or concept learning refers to the discovery by humans or computers of (possibly) unique rules that define membership in categories of objects (the word object is used in the generic sense). These rules are gradually generated (hypothesized), tested, and subsequently accepted, refined or rejected in experimental settings, on the basis of a sequence of examples and counter-examples of membership. A rule represents a complete and consistent description of the concept Ñ if it characterizes all objects given as examples and none of the objects given as counter-examples. Researchers in Artificial Intelligence have produced programs from early times, which modeled different aspects of the cognitive activity involved in concept formation or aimed at reproducing this capability in computers (see, e.g., Hunt and Hovland, 1960; Hunt, 1962; Hunt et al., 1966; Winston, 1975; Mitchell, 1977; Michalski et al., 1983 & 1986; Kodratoff and Michalski, 1990; Findler, 1990). Several journals, particularly Machine Learning, contain relevant work (see, for example, Vol. 12, Nos. 1/2/3). Good surveys can be found on Machine Learning by J. Carbonell and P. Langley, and on Concept Learning by R. S. Michalski in (Shapiro, 1987), and on Learning and Inductive Inference by T. D. Dietterich (1982). 2. An Area of Application It is necessary first to outline a specific application of our multi-purpose decision support system, for the benefit of explanations to follow. An article by Benfer and FurbŽe (1989) describe the difficulties knowledge engineers have experienced in trying to capture indigenous knowledge from pre-literate people in the Peruvian Andes. The authors argued that anthropologists and * Corresponding author. Tel: (480) ; fax: (480) ; nicholas.findler@asu.edu ** Currently: Microsoft Corporation, Seattle, WA

2 2 knowledge engineers sometimes share quite a few problems and, consequently, some of the methodologies can be usefully transplanted across the disciplinary boundaries Ñ Artificial Intelligence may be able to provide help with problem is in Social and Cultural Anthropology. Kinship, the basic human relation derived from descent and marriage 1, was the primary factor in regulating behavior and attitudes in early societies. It still has a major role in contributing to the organization and structure of the modern industrial society. (The other obvious factors are based on age, sex, allegiance, association, class, authority, power, obligation, ordination, etc.) Our prevailing legal systems are normally based on cultural norms and values. Legal systems proscribe disallowed and unacceptable human interaction, and indirectly encourage "desirable" social contracts. Preliteral societies cannot rely on such codification of rules. However, they are known to have some sets of guidelines which control patterned and recurrent selection processes in social interactions, such as inheritance, succession, marriage, and injunction against incest and exogamy. Genealogy, whose form and contents have great social significance and consequence in primitive societies, is usually not verbalized and often cannot be stated explicitly by the members of the societies. Data collection by field workers in anthropology is difficult because often there is no one-to-one linguistic equivalence between kinship terms used in primitive and developed societies. In several Australian aboriginal languages, for example, "father" applies to a person's biological progenitor as well as all older male members of the community. Since descriptive and classificatory categories are culture-dependent 2, abstract kinship categories have little definitional value. As a result, the rules of human interaction must be characterized via exemplary relations between given individuals. We note that the intellectual origins of our ideas date back to 1910 when W. H. R. Rivers published his classical paper, ÒThe Genealogical Method of Anthropological InquiryÓ, reprinted in (Rivers 1968). Further, J. A. Barnes (1979) discussed the role genealogical charts and diagrams that show logical interconnections within a set of rules of marriage. Many researchers have tried to establish various mathematical structures (Balanoff 1974a, 1974b, 1974c, 1974d; Read 1984) that should help in classifying and systematizing the complex social patterns found all over the world (LŽvi-Strauss 1969). It seems obvious that there is a need for a tool much more accessible to the less mathematically-inclined anthropologist. 1 In this paper, we use the term kinship to denote both consanguineal and affinal relations. 2 In many non-indo-european languages, often there is a clear distinction between different structural and age relations within a kinship category that is denoted by one single English term, such as sibling, cousin, uncle, aunt, etc. Also, they may have a special name for a kinship relation that is difficult to formulate and considered irrelevant in our society, such as the linkage between the two mother-in-laws of a couple. It appears that modern Western social forms often use a less complete mapping onto the general genealogical grid than some primitive societies.

3 3 Australian anthropologists experienced the above noted difficulties among Australian aborigines and with certain tribes in Papua-New Guinea some years ago (C. R. Pearson, personal communication). It was suggested that the anthropologists' inability to understand the rules governing acceptable social relations was not due to problems in communication 3. Rather, problems arose because the definition of the rules could not be obtained in terms of abstract concepts. Only the use of examples and counter-examples of participants' names could effectively convey the operational meaning of the rules. For example, the extremely forceful injunction against a male person having sexual relation with his mother-in-law or with his son's wife can be expressed only by naming the people who could and who could not engage in such act. This approach appeared to work well when the description of the kinship relations were unambiguous and in strict correspondence with our terminology. However, this certainly is not the usual case. The complexity of the problem suggested a computer-based solution. We have tried to satisfy the need for a computer-based rule discovery tool in anthropology, which turned out to be a fairly domainindependent decision support system. 3. The "Base Programs" as a Starting Point Two existing programs with modifications and extensions suggested a potential solution (Findler & McKinzie, 1969; Findler, 1973). It is necessary to describe these briefly before the final system is discussed. The following terminology will be used: a member is an element of a given set of individuals; a central member is the focal point of a kinship definition or query; a related member is the secondary participant in a kinship definition or query; a member symbol is a unique computer-generated symbol associated with one and only one member; a relationship is a consanguineal and/or affinal kinship tie between a central member and a related member; a primary relationship is one of the basic (biological) kinship ties: father, mother, son, daughter, brother, sister, husband, wife; a non-unique relationship is one that is not expressed exclusively in terms of primary relationships, such as the mother-in-law's cousin; a general relationship is a single or an ordered sequence of primary and/or non-unique relationships, between any two of which the symbol " " represents Teutonic genitive ('s in current 3 Anthropologists do acquire a working knowledge of the vernacular. Also, the subjects of such studies usually also command a modicum of some Western language or a language like pidgin English.

4 4 English). The string son mother spouse daughter represents the son's mother's spouse's daughter (who is not necessarily a full or even a half sister, say, in California); a kinship structure is a network (in fact, a directed graph) in which the nodes represent distinct members and the connecting arcs are labeled by a primary relationship; traversing is the process of advancing through the kinship structure starting from a central member either to a specified related member or following a traversal pattern; a traversal pattern is a string of a single or an ordered sequence of primary and/or non-unique relationships each of which may itself be a Boolean AND combination of such entities. For example, the pathways from a central member to all paternal granduncles and grandaunts is represented by the string father (father AND mother) (brother AND sister). Here, the parentheses are not necessary because of the strong ordering of the operators, and are used only for the sake of clarity in specifying the routing from the central member to his/her father, then to the father's father and mother (the two paternal grandparents), then to the brothers and sisters of the latter. The first program (Findler and McKinzie, 1969) was originally designed to generate, modify and query arbitrarily complex kinship structures. The user was to provide only "birth information" (a member's name, sex and parents' names) and "marriage information" (the participants' names). The user could leave out data that were not available at that time or at all. (This caused the system to flag such partially defined individuals as "deficient".) With complete input information, even incestuous, polygamous and polyandrous relations were treated appropriately. There were five types of inquiries possible: (1) The List Members inquiry prints the kinship definitions specified. (2) The Traversal Map inquiry yields the members visited in the course of traversing along the pattern provided. For an unconventional example, if the central member's mother is also his father's sister, requesting the central member's cousins would produce a response set that contains also the central member and his siblings. (3) The Related Members inquiry gives all individuals at the end of the traversing operations defined by the pattern. (4) The Verify Relations inquiry checks whether a given traversal pattern connects the central and related members specified. (5) The All Relations inquiry generates all possible relations between the central and related members specified. It was also possible to intersperse inquiries between partial data specifications. The system was tested with data on Greek mythology (Graves, 1955) where the divine participants are known not to adhere to our Judeo-Christian moral principles. Only two interesting facts are noted here (both worthy topics for an ancient soap opera): Zeus and Aphrodite had an exclusively Platonic

5 5 relationship, and Rhea was Kronos' sister, wife, grand-aunt and daughter-in-law's mother at the same time 4. The second program (Findler, 1973) rectified some shortcomings of the previous one. It did not restrict data and traversal patterns to primary relationship terms. In addition to the two connecting operators of the first program, Boolean AND and the Teutonic genitive, the second program made use of many more operators (see Table 1) and of the powerful definitional capabilities of the computer language AMPPL-II (Findler, Pfaltz and Bernstein, 1972). Symbolic Notation Type Representing Boolean NOT Reverse (only with REL) < Less then Less then or equal to = unary Equal to Greater then or equal to > Greater then max Maximum min Minimum Equivalent Boolean AND binary Boolean OR Teutonic genitive Table 1 Ñ Various operators for defined entities The relational triple (or relational descriptor), REL(OBJ) = VAL, defines a relation (REL) between an object (OBJ) and its value (VAL). While REL is always symbolic, OBJ and VAL can be either symbolic or numerical, simultaneously or separately 5. Any of the three can be a single item or (various types of) lists. The reverse relation can be expressed as REVREL(VAL) = OBJ and may be defined by the user in terms of the reverse operator and the original relation. There are also other types of defined entities which are constructed in terms of primitive, 'atomic' entities or other defined entities and connecting operators, (see Table 1). The entity, SELF is used to exclude unwanted self-referencing. 4 Spreading such information was enough to get the gossiper into jail under the Greek junta some years ago. 5 For example, SON-OF (JOE) = {BOB, JOHN} and NUMBER-OF-SONS (JOE) = 2.

6 6 A few simple examples of definitions of Western (biological) kinship relations (as well as some currently irrelevant properties) follow, where ":=" means "defined as". PARENT := FATHER MOTHER; CHILD := PARENT; GRANDFATHER := (FATHER MOTHER) FATHER; WIFE := SPOUSE FEMALE; HUSBAND := SPOUSE WIFE or SPOUSE MALE; BROTHER := ((MOTHER FATHER) SON) SELF; BROTHER := ((MOTHER FATHER) SON) SELF; [incl. half-brothers] GRANDFATHER := GRANDPA GRANDDAD; [for the explanation's sake] OLDERSISTER := AGE(SISTER1) > AGE(SISTER2); GOOD(ITEM) := V(ITEM) > V1; [V being a quality measure of items] BAD(ITEM) := V(ITEM) < V2; BEST(ITEM) := max (V); WORST(ITEM) := min (V). The following basic tasks can be performed: ascertain whether a particular relation is true; retrieve all valid values of one of the three entities of the relational triple when the other two are given; retrieve all valid values of two of the three entities of the relational triple when the third is given; retrieve all values of X from the symbolic proportionality equation, explained below. Let A : B = C : X where the operator ":" is interpreted as "is related to". Assume that there are at least two relational descriptors in the Simulated Associative Memory 6 (SAM) in one of the following three forms: QA ( ) = B QC ( ) = X AQ ( ) = B CQ ( ) = X AB ( ) = Q CX ( ) = Q Here, Q is an entity common to two or more relational descriptors both in contents and in position. For example, if SAM contains two relational triples UNCLES (JACK) = {JOE, BILL, PETER} AUNTS (JACK) = {MARY, CAROL}, 6 Associative memories are "content-addressable"; i.e. an item's name and all its properties can be recalled if the query references only some of its properties. Several items are recalled, in which case each shares the referenced properties.

7 the system can answer the question, formulated in a simple way, "Who are the aunts of the person whose uncles are Joe, Bill and Peter (or any subset of these people)?" However, the system shows its real strength when also defined entities appear in various relational descriptors. Every possible path, established by the associations in the definitions, is followed in retrieving the answers. The definitions are stored in a canonical form, which means that on the right hand side only primary kinship terms may appear. A "window" is slid along the definitions and every time its contents can be (temporarily) replaced by a higher-level term (a defined kinship relation), it is used in matching part of the query. (The retrieval process also recognizes the fact that equivalence relations are both symmetric and transitive, and reverse relations are symmetric.) Suppose the user has given the following definitions: PARENT := FATHER MOTHER UNCLE := PARENT BROTHER AUNT := PARENT SISTER COUSIN := (UNCLE AUNT) CHILD CHILD := SON DAUGHTER PARENT := CHILD NEPHEW := (MALE SEX) (UNCLE AUNT) 7 NIECE := (FEMALE SEX) (UNCLE AUNT) BROTHER := PARENT SON SELF SISTER := PARENT DAUGHTER SELF Note that the input of data can have redundancies and missing information. Let the user now ask for the COUSINs of a certain individual. The system will form a list whose members are the union of the members of the following lists: (1) the individual's cousins directly recorded in relational triples, (2) the children of the individual's uncles and aunts, (3) the nephews and nieces of the individual's parents, (4) the children of the individual's brothers and sisters (see Figure 1). Of course, the Central Member, SELF, has to be excluded from the members of the answer set. All the basic tasks listed as the capabilities of the first program can be performed by the second program as well but, importantly, both the queries and the answers can reference also defined entities now. This facility has enabled us to make further steps. 4. The Program CLAUDE To Discover Rules for Social Interaction The program CLAUDE can form concepts by generating and testing hypotheses of various properties (such as non-western type kinship relations between individuals), by processing 7 7 A little explanation may be useful here; nephew references a person whose sex is male and, as a kinship relation, it is the reverse of that of uncle or aunt.

8 8 examples and counter-examples of patterns of social interaction. The resulting hypothesis of a rule is essentially the simplest relation 8 applicable between each pair of individuals who are instances of allowed social interactions and relations. For example, A could marry B, C, D,... but could not marry U, V, W,... A possible derived rule may for example be that a male can marry an unrelated unmarried female of the same tribe, a patrilateral cousin or aunt but not a matrilateral cousin or aunt. Brothers and Sisters 1 Father Mother 1 Brothers and Sisters Uncles and Aunts Central Member Uncles and Aunts 2 Sons and Daughters Nephews and Nieces 4 Nephews and Nieces Sons and Daughters Cousins Figure 1 Ñ The different paths from the Central Member to all Cousins To accomplish this, the program has to be given some additional information about the already existing relation between the participants in the exemplary and counter-exemplary social interactions. These domain-specific relations become part of the rules in permitting and prohibiting, respectively, the interactions. We list them below, with an explanation when necessary: The minimum number of generations separating the members. This is usually a checking facility for the program; the data may not always be available (and meaningful without a consanguineal relation). The qualifier minimum is necessary because of possible multiple kinship relations. Is there another, prior relation between the individuals and, if so, is it by blood or marriage? Even in Western societies, in-laws are often spoken of as parents. In primitive societies, the difference in designation between actual relatives and tribal ones can often disappear. Is the prior relation lineal or collateral? In the Western kinship structure, father and father's brother distinguishes the above two types whereas a society, in which there is only a single term for cousin and brother, leaves such distinction inoperative. Age comparison within one generation. In English, we do not distinguish between, for example, older and younger brother. 8 The simplest kinship relation is the shortest common pathway type in the so-called kinship graph between each pair of individuals involved.

9 9 The sex of the central member 9. This is irrelevant in English but in many languages, the relations father, mother, brother, sister and even more distant relatives receive different designations from a man than from a woman. The sex of the related member. Unlike in the previous category, English carries out this distinction (grandmother vs. grandfather, brother-in-law vs. sister-in-law) with the exception of the truncated acquisition from French, cousin. The sex of the intermediate member. This is ignored by English unless special emphasis requires the distinction between the father's brother and the mother's brother, or between the paternal grandfather and the maternal grandfather. The status of the central and the related member. It can make a difference if one or the other or the intermediate member is dead, married or not married yet, or no longer married. Another important factor is whether the central and the related member belong to the same class (tribe, moiety, clan, etc.). In view of the above, one can see, for example, the multitude of possible, but operationally distinct, relations that the English word cousin groups together. We emphasize that there is no guarantee that the above distinctions suffice in characterizing all possible rules of prohibited/required/preferred social interaction but, according to the experts of the field, it is a fairly complete set. Let us look at the previous example of marriage rules: "a male can marry...a patrilateral cousin or aunt but not a matrilateral cousin or aunt". For the sake of terminology, let a pair of parallel cousins be first cousins and the sibling parents are of the same sex. In case of cross cousins, the sibling parents are of different sex. Each parent of a bilateral cousin is the sibling of one parent of the other bileteral cousin. The schema of both exemplary and counter-exemplary marriage rules are depicted in Figure 2. The links connecting two members and representing a hypothetical rule (in the above example and in general) can have the labels shown in Table 2. Similarly, possible member labels are given in Table 3. The type and the number of the labels and the possible label values are determined by the user/domain expert, and the workings of the program are independent of these choices. The program looks at the labels in the exemplary and counter-exemplary cases 10. It then discards from consideration those labels, i.e., rule components, that have "uninformative" values. (For example, if all marriage statuses Ñ married, not-yet-married, no-longer-married Ñ appear in the central male 9 As noted before, a central member is the focal point of a kinship definition or query whereas a related member is the secondary participant. 10 No noise is assumed in the data. Errors can, of course, occur in reporting or recording the data. There can also be accurate records of an unsanctioned social pattern. The user will eliminate or change a doubtful value of one or several labels and rerun the system.

10 10 members' labels in the exemplary cases, marriage status is irrelevant for the rule.) On the other hand, if only two out of three values appear, these become a rule component as long as the counterexemplary cases have only complementary values. It also means that whenever both the exemplary and counter-exemplary cases show an identical value, that value becomes irrelevant. The whole label becomes irrelevant if all its values appear in both exemplary and counter-exemplary cases. It can, of course, happen that combinations of label values matter, which the user must flag as a special property, and the program will treat it accordingly. (For example, only tribal chiefs can have more than one wife.) This way, the hypothesis of the above marriage rule can be established. R:y; P:b,c,0; C:s Patrilateral parallel cousins R:y; P:b,c,0; C:s Patrilateral cross cousins Schema for exemplary (allowed) cases R:y; P:b,c,1; A:o; Patrilateral aunt R:n; P:b,c,0; C:s Matrilateral parallel cousins R:n; P:b,c,0; C:s Matrilateral cross cousins R:n; P:b,c,1; A:o; Matrilateral aunt R:n; P:b,c,0; C:s R:n; P:b,c,0; C:s Bilateral parallel cousins Bilateral cross cousins Schema for all non-exemplary (disallowed) cases : male central member : male member Legend: : female member : sibling relation : marriage : parent-child relation : relation considered for rule discovery Figure 2 Ñ Graphs representing allowed (exemplary) and disallowed (non-exemplary) marital rules for the case described in the text

11 11 Label Name Label Value Label Value Meaning Comment R y allowed exemplary case (rule) n disallowed non-exemplary case b by blood one or both may m by marriage appear together P l lineal one or both may (prior relation) c collateral appear together 0 - g minimum number of g can be any separating generations positive number A o older central member to (age t same age (twins) related member comparison) y younger C s same tribe, moiety, (class) d different clan, etc. D 0 - n number of years n can be any positive (age difference) or negative number Table 2 Ñ Labels and their possible values on links between central members and related members Label Name Label Value Label Value Meaning Comment V a alive (living) d dead m married M s not-yet-married (marital) w no-longer-married T designation specific e.g., tribal chief (class title) H n negative (inhibitory) personal or ancestral (characteristics) p positive (promotive) history or property Table 3 Ñ Labels and their possible values on members How can the program disambiguate kinship relations? Some Surinamese dialects are said not to distinguish between the following pairs of relations (from a male point of view Ñ equivalent drawings and computations can be made from a female perspective): R1: mother's brother's wife vs. mother-in-law R2: mother's brother's daughter vs. wife R3: mother's brother's son vs. brother-in-law Figure 3 shows the alternate graphs for the three pairs of relations as identified by the program. In general, the hypotheses are corroborated, modified or rejected by further examples and counter-examples. The usual fate of hypotheses is to become theories after a while...

12 12 R1/ a R1/ b Mother's brother's wife Mother-in-law R 2/ a Mother's brother's daughter R 2/ b Wife R 3/ a Mother's brother's daughter R 3/ b Brother-in-law Figue 3 Ñ Disambiguating graphs for three kinship relations referenced by the same term in Surinam We note that a different set of labels and ranges of label values are normally appropriate for every domain. The user specifies the totality of these when he/she deals with Schemata, Label Descriptions and Data Files (see Appendix 2). During the development of the programming system, we alternately constructed complex rules for different social interactions Ñ both allowed and disallowed Ñ as gleaned from reference books, and generated exemplary genealogical grids among the named participants. The program was then run to induce the rules. Initially, we had to extend the scope of the program a few times. Later on we found that the scope was sufficient but more examples and counter-examples had to be specified in order to produce unique rules. 5. Some Comments on the Structural-Functional Approach Although the arguments noted below do not affect the use of the program CLAUDE in constructing social networks in general, a few comments may be in order about some controversy concerning the usefulness of kinship terms in anthropological research. There was a debate on this issue between the mid-60s and early 80s (Conklin 1969; Goudenough 1969; LŽvi-Strauss 1969; Lounsbury 1969; Schneider 1969, 1972, 1980; Meggit 1972; Rejning 1972). Important questions were raised based on the fact that kinship terms are not transcultural, and there is no one-to-one correspondence between linguistically identical expressions as far as social relations and rules are concerned. Consequently, kinships terms in general are not so

13 13 correlated with genealogy as we think our own are. Words describing social roles, rights and obligations in one culture may appear to be polysemic and context-dependent from the point of view of another culture. Furthermore, genealogical research has traditionally dealt with explicit or implicit norms that may well be distinct from actual behavior. To support these points, several researchers have stated that various kinship terms in some linguistic communities have assumed the role of courtesies, modes of address and salutation. (Note that in Western societies, the term father can also refer to priests who are not supposed to be related to the speaker as his/her genitor.) Let us briefly examine the question as to whether the above concerns are relevant to the anthropological field worker using the program CLAUDE. How do we make sure that the empirical data obtained support a sufficient and parsimonious model of the rule structure sought? (No overprediction, underprediction or wrong prediction by the resulting rules.) There are two basic guidelines to be followed by the field worker: 1. Not to accept linguistic equivalents of Western compound kinship terms but only the names of the participants in primary relationships. These can be by blood or marriage (consanguinity or affinity), such as father, mother, son, daughter, brother, sister, husband and wife. The rest (establishing the genealogical grid, rule induction and interpretation) is done by the program. 2. If the informant is unable to provide the correct information because of some culture-based terminological ambiguity (cf., the English modifier of father: step-, -in-law and foster- being omitted), either the derived rule is still correct or else no rule can be induced because of conflicts in the data. In the latter case, further gathering and/or corroboration of data should help. 6. On the Domains of Applicability of the System Described As noted before, inductive rule discovery is an often-needed methodology in many disciplines. The decision support system described was developed in a relatively domain-independent manner but was tested in solving tasks facing social and cultural anthropologists. It should be pointed out that while the contents of Table 1 need not and cannot be changed, a reinterpretation of the label meanings (see Tables 2 and 3) can be done by the user for some network domains without any reprogramming whereas in some other domains, certain modifications to the program are necessary. Acknowledgment We express our gratitude to John Martin, Professor of Anthropology at Arizona State University for his comments and suggestions. APPENDICES 1. The Algorithm for Rule Induction --Process all positive and negative examples

14 14 Set positive result to NIL Set negative result to NIL Start from the central member --Repeat the following for each link (or relationship) WHILE (not DONE) DO Get next link (or relationship) and call it current link IF the current link ends in the central member THEN DONE = TRUE ENDIF FOR each example Get next example and call it current example IF the current example is positive example THEN FOR each label value of the current link of the current example IF the label value is present in the positive result and current example THEN do nothing ELSE add the label value to the positive result ENDIF ENDIF IF the current example is negative example THEN FOR each label value of the current link of the current example IF the label value is present in the negative result and current example THEN do nothing ELSE add the label value to the negative result ENDIF ENDIF Remove the label values from positive and negative results, if they are present in both positive and negative results ENDFOR ENDWHILE Repeat the above procedure for each member to find the permitted and unpermitted label values for members --Process the positive and negative results further Start from the central member

15 15 WHILE (not DONE) DO Get next link and call it current link IF the current link ends in central member THEN DONE = TRUE ENDIF FOR each label name of current link Print label name Print "label should have the following values" Read all the label values of the label from positive results and print each value if the value is not present in negative result Print "label should not have following values" Read all the label values of the label from negative result and print each value if the value is not present in positive result ENDFOR ENDWHILE Repeat the above procedure for each label name of all members 2. The Programming Environment of the Multi-Purpose Decision Support System We describe the two main components of the program, the User Interface (UIF) and the Rule Learning Program (RLP). The RLP requires a stream of data in the form of positive and negative examples, which are inputted in an interactive manner, through the high-level front-end UIF. The UIF consists of a main menu and submenus, text widgets, and file selection boxes that appear under each main menu button. All widgets (menus, text widgets, buttons, etc.) have been created using the DECÕs Visual User Interface Tool (VUIT). Sample menus and widgets are shown in Figures 4-6. Figures 4 and 5 depict the facilities for defining the Member Schema and the Link Schema, respectively. Figure 6 shows how data can be specified for the Member and Link Labels in one example. Using these menus, the user can enter data for the Schemata and the Data Files containing positive and negative examples 11. Most of the menu selections open up a set of text 11 A Label carries an attribute and its value for a member or a link. A Schema defines a set of all possible Label Descriptions for a member and a link. A Label Description consists of a label name, permitted values on that label and comments describing that label. A Data File consists of the names of positive or negative examples, and the labels of all members and links participating in the examples.

16 16 widgets to enable the user to enter data. A HELP button associated with each widget provides online, context-sensitive help for the user. An additional feature provided with the UIF is data validation. Each time the user tries to save data in the data widgets, the data entered is checked against the valid data ranges entered as part of the Schema. Invalid data is highlighted and the user is prompted to re-enter the data. Schema Data Positive examples Negative examples Run Help On-line help facility Run the learning program on the selected data files Select a negative example for the selected data file and create/ edit the data in it Select a positive example for the selected data file and create/ edit the data in it Create/ edit a data file and specify the names of all the examples for that data file Create a new schema or edit/select an existing schema (Selects the label names and the permitted values for that labels) Figure 4 Ñ The menu for defining the Member Schema Schema Data Positive examples Negative examples Run Help New Edit Member Link Member Link Create a new member schema or new link schema Edit an existing member schema or link schema Select Member Link Select a member schema and link schema. The selected schema will be used while entering data in examples Figure 5 Ñ The menu for defining the Link Schema

17 17 Schema Data Positive examples Negative examples Run Help New Create e new data file and name all the positive examples and negative examples for that data file Edit Edit an existing data file which contains the names of all the examples. Editing here means either adding new examples or deleting old examples Figure 6 Ñ Data specification for Member and Link labels Typically, the user selects a Schema, and creates a Data File defining the names of positive and negative examples. The user then enters data into these examples through the data widgets. All the data entered by the user in a session is stored in files and can be reloaded and modified later. The subsequent figures provide a concise description of the functionality of different options. Figure 7 shows the main menu of the top level screen, which defines the Member/Link Schema. Figure 8 and 9 contain the Data File widget and the Member Data widget, respectively. File Help Schema File Name Label Name Label Value Label Meaning Comment Figure 7 Ñ The Member/Link Schema widget Data File Name Positive Example Names Negative Example Names Save Cancel Figure 8 Ñ The Data File widget

18 18 Copy Save Cancel Clear Help Labels Defined In Schema Member1 (Link 1) Member2 (Link 2) Figure 9 Ñ The Member Data widget The RLP, written in Common LISP, implements the algorithm described in the Appendix. This algorithm assumes a consistent naming scheme for members and for links. The former requires that no two or more members in any given example have the same name and the latter requires that no two links in any given example have the same designating number. This consistency is checked for by the UIF program while accepting data from the user. The positive and negative examples are in the form of LISP data structures and they form the input to this program. The RLP and the UIF are integrated as follows. The RLP is activated as one of the callbacks attached to the RUN button of the main menu. When the user presses the RUN button, UIF reads all the positive and negative example Data Files and converts the data into LISP data structures. The LISP program is then activated automatically by the UIF and is made to run on the prepared LISP data structures. The output generated by the RLP is then put in a file to be read by the UIF, and is also displayed in an output window. If the user is not satisfied with the results, he/she can go back and modify the data in the examples and repeat the process again. References Ballonoff, P. A., 1974a. Mathematical Foundations of Social Anthropology (Mouton, The Hague, The Netherlands). Ballonoff, P. A. (Editor), 1974b. Genetics and Social Structure: Mathematical Structuralism in Population Genetics and Social Theory (Dowden, Hutchinson & Ross, Stroudsburg, PA). Ballonoff, P. A. (Editor), 1974c. Mathematical Models of Social and Cognitive Structures. Contributions to the Mathematical Development of Anthropology (University of Illinois Press, Urbana, IL). Ballonoff, P. A. (Editor), 1974d. Genealogical Mathematics (Mouton, The Hague, The Netherlands).

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