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Metalogicon (2004) XVII, 2 Hausa Grammar and Classical Logic: Transculturality of Sentential Calculus Nunzia D’Aniello ABBREVIATIONS AC.P. = ACTUALISATION PARTICLE ADJ. = ADJECTIVE ADV. = ADVERB AO. = AORIST A.P. = ATTACHMENT PARTICLE ART. = ARTICLE C.A. = COMPLETED ASPECT CONJ. = CONJUNCTION F.N. = FEMININE NOUN F.V. = FUTURE VERB IMP.V. = IMPERATIVE VERB IND.ADJ. = INDEFINITE ADJECTIVE INF.V. = INFINITIVE VERB M.N. = MASCULINE NOUN N.P. = NEGATIVE PARTICLE P.A. = PARTITIVE ADJECTIVE P.C. = PERSONAL CONTINUATIVE P.N. = PERSONAL NOUN P.P. = PRESENT PARTICIPLE P.PRON. = PERSONAL PRONOU PL. = PLURAL PREP. = PREPOSITION PRE.SUBJ. = PRESENT SUBJUNCTIVE PRE.IND. = PRESENT INDICATIVE P.T. = PAST SIMPLE TENSE R.P. = RELATIVE PRONOUN S. = SUBSTANTIVE U.A. = UNCOMPLETED ASPECT V. = VERB 1. Hausa grammatical characteristics The Hausa language, which is spoken in centre-west 49 Metalogicon (2004) XVII, 2 Africa, presents many grammatical aspects which make it very different from the Indo-European languages. First of all, in Hausa, the verb «to be» does not exist, so it is expressed by the enclitic actualization particles: ne , ce . The first one is used after a singular or plural masculine noun, the second one after a singular or plural feminine noun. See the example below: It is a city P.PRON. PRE.IND. ART. S. In Hausa: gari ne M.N. AC.P. Literally: City is In Hausa the genitive is expressed by three suffixes called «attachment particles», which take place of the English «of». They are –n for masculine, -r for feminine, -n for plural. See the following instance: The horse of the chief ART. S. PREP. ART. S. In Hausa Doki–n sarki M.N. – A.P. M.N. Literally: Horse–belonging to chief. (‘–n’ is an attachment particle concerning the following noun). In the western languages, like Italian, German, French, verb is inflected in moods and tenses, which means that there is a temporal system. In Hausa, on the contrary, tense is something secondary, because verb expresses time but only to determine the expression it is referred to. In fact, the verbal system is figurative and what is important is the kind of action expressed by the verb. Consequently, action can be completed or uncompleted, as 50 Metalogicon (2004) XVII, 2 we notice in the following examples: I ate some meat P.PRON. P.T. P.A. S. In Hausa: Na ci nama P.PRON. C.A.V. F.N. Literally: I to eat (verb in the completed aspect) meat. This language, therefore, presents some features which make it different from the western ones, but it is no wonder if we think that in the whole world there is a large variety of different languages with regard to their structures and syntaxes. So the question is: does the formal logic have an exclusive relation with a particular language or a group of languages, or has it something to do with language itself? The classical logic is characterised by bivalence, no temporality, inter-definable connectives, acceptation of the third excluded law, etc. Hence the question arises: does it innervate all the languages or just the Indo-European shackle which has conceived it? As there is an inseparable relation between mind and language, the question now is: does the learning of a language go together with the learning of a new logic? On this subject, it is interesting to compare the main points of the classical logic to the Hausa, a tonal language, whose syntax and phonetics are very different from that of the Indo-European languages which elaborated the formal logic. The Hausa language belongs to the Chadic group of the Afro-Asiatic family of languages, and it is spoken in a large area of sub-Saharan Africa, which includes the countries of Niger, Nigeria and Chad. It has been classified as a Semitic language (like Arabic, Hebrew, Aramaic, etc.), and it is closely related with Berber, ancient Egyptian and the Cushitic languages. This is 51 Metalogicon (2004) XVII, 2 Greenberg’s classification [GREENBERG (1963)]. It has gained general acceptance. Till first decades of the last century, Hausa was written in Arabic characters, the Ajami. In 1911, Hans Visher, a Swiss scholar, English by adoption, made the first important study about the way Hausa could be written in Latin characters [VISHER (1911)] and his essay was supported by the English monarchy, which improved the diffusion of this new writing system. This involved the necessity, for the Europeans, of an understandable graphic system relating to a standard language which had to be chosen among the great variety of the Hausa dialects. The Kano dialect seemed to be the most appropriate, unless when it was completely different from the other ones. In Hausa, as we said before, one of the most pregnant grammatical feature is the fact that the verb «to be» does not exist, therefore it is expressed by the actualisation particle. See the examples below: 1st instance: It is a horse P.PRON. PRE.IND. ART. S. In Hausa: Doki ne M.N. AC.P. Literally: Horse is. 2nd instance It is a road P.PRON. PRE.IND. ART. S. In Hausa: kanya ce F.N. AC.P. Literally: Road is. 3rd instance 52 Metalogicon (2004) XVII, 2 They are some goats P.PRON PRE.IND. P.A. S.PL. In Hausa: Awaki ne M.N.PL. AC.P. Literally: Goats are In Hausa, the verb «to have» does not exist, so it is expressed by the person of the uncompleted aspect construction plus «da», as in the following example: I have money P.PRON. PRE.IND. S. Ina da kudi P.PRON. V. M.N. In Hausa: Literally: I to have money. ‘Ina’ is the first personal continuative person-aspect construction. The verbal system, as we said before, is one of the most complex aspects of the Hausa grammar because it depends on the action, which can be completed or uncompleted [See KRAFT, KIRK-GREENE (1973) p. 145]; besides, it presents a very typical verbal tense, the Aorist, or subjunctive, which is used to express a not indefinite action [See BALDI (1992) p. 25]. These verbal aspects have their equivalence in the classical terminology: COMPLETED ASPECT PERFECT, PAST, PERFECTIVE. UNCOMPLETED ASPECT IMPERFECTIVE, PRESENT, PROGRESSIVE CONTINUOUS. AORIST SUBJUNCTIVE See the examples below: 53 Metalogicon (2004) XVII, 2 1st instance You ate some meat P.PRON. P.T. P.A. S. In Hausa: Ka ci nama P.PRON. C.A. M.N. Literally: You to eat meat. ‘Ka’is the second singular masculine completive person- aspect pronoun. 2nd instance I am coming P.PRON. PRE.IND. P.P. In Hausa: Ina P.PRON. zuwa U.A. Literally: I to come (uncompleted aspect) 3rd instance Let me come IMP.V. P.PRON. INF.V. In Hausa: In P.PRON. zo V. Literally: (That) I come (Aorist. form). ‘In’ is the first singular subjunctive person-aspect pronoun. In Hausa, there are two future aspects. The Future I expresses an action which has already started, by employing the specialized verbal za plus the subjunctive aspect person-aspect pronouns. The Future II expresses an uncertain and indefinite action [ See GOUFFÉ (1965) pp. 191-210]. 54 Metalogicon (2004) XVII, 2 See the examples below: Future I 1st instance Men will leave S.PL. F.V. In Hausa: Mutane za PL.N. su tafi P.PRON. V. Literally: “Men they leave”. Note that ‘za’ is used with personal pronoun to express the Future I. 2nd instance I will come P.PRON. F.V. In Hausa: Na zo V. Literally: “I to come” (Future II aspect). ‘Na’ is the first singular Future II person-aspect pronoun. As we have noticed, while in the Indo-European languages, time is expressed by changes in the verb itself, in Hausa it is expressed by changes in the personal pronoun. For example, the sentence «I’m coming», in Hausa will be «ina zuwa», where the pronoun «ina» introduces the continuative or uncompleted construction. This means that in Hausa, temporality is expressed by the variation of the pronoun. A question arises: Given such different grammatical frames are we allowed to speak of transculturality of classical sentential logic? 2. Logical connectives 55 Metalogicon (2004) XVII, 2 We will examine the presence and use of the logical connectives in Hausa starting from the negative sentence. This is a molecular utterance born by negation of an atomic sentence. The negative, in Hausa, is formed by placing two particles: «ba.......ba», which delimit what is denied. In this respect, it is interesting to see how negative in Hausa is similar to the French negative «ne… pas». Let the following atomic sentence be: It is him P.PRON. PRE.IND. P.PRON. In Hausa: Shi ne P.PRON. AC.P. Literally: “He is”. The negation of the above sentence is: It is not him P.PRON. PRE.IND. ADV. P.PRON. In Hausa: ba shi ne ba N.P. P.PRON. AC.P. N.P. Literally: Not he is not. Starting from these examples, we can sketch the below table, where GASKIYA and KARYA translate English TRUE and FALSE respectively : 56 Metalogicon (2004) XVII, 2 Shi ne GASKIYA KARYA Ba shi ne ba KARYA GASKIYA Let symbolise “Shi ne” by ‘p’ and “Ba shi ne ba” by ‘Np’ we obtain the following table of classical logic negation where ‘N’ is the negation function in Polish symbolic language. We have p 1 0 Np 0 1 Now, we will go on analysing the logical product, or copulative. As we know, the classical logic has only two truth values: true and false, hence, when we have two atomic sentences, the corresponding possibilities or dispositions are four: both are true; the first is true and the second is false; the first is false an the second is true; both are false. The truth values of molecular sentences generated by the logical functions are therefore four. Let us begin with the logical product. In Hausa, the conjunction «and» is expressed by the particle «da». Let us consider two atomic sentences, for example «it is raining» and «the wind is blowing». The Hausa corresponding ones are “ana yin ruwa” (literally: it makes rain) and “ana yin iska” (literally: it makes wind). To the English molecular sentence “it is raining and the wind is blowing” corresponds the Hausa “ana yin ruwa da iska” (literally: it makes rain and wind), simplified expression for “ana yin ruwa da ana yin iska” (literally: it makes rain and it makes wind). Now let us sketch the truth table of logical product: ana yin ruwa GASKIYA GASKIYA KARYA KARYA ana yin iska GASKIYA KARYA GASKIYA KARYA 57 ana yin ruwa da iska GASKIYA KARYA KARYA KARYA Metalogicon (2004) XVII, 2 Now if we symbolise “ana yin ruwa” by ‘p’, “ana yin iska” by ‘q’, “ana yin ruwa da iska” by ‘Kpq’ like in Polish symbolism, we obtain the classical truth table of logical product p 1 1 0 0 q 1 0 1 0 Kpq 1 0 0 0 As we can notice, the truth table is the same of the Indo-European languages. The examples given till now have shown the use of some connectives in the Hausa language, so now we will consider the use of the connective «or», one of the few words of everyday life which has so much linguistic ambiguity. In Hausa it is expressed by the word «ko». See the example below: It is raining or the wind is blowing In Hausa we have: Ana yin ruwa ko iska Literally: It makes rain and wind. In this example, «Ana yin ruwa ko iska» is a molecular utterance composed by two atomic utterances: «Ana yin ruwa» and «Ana yin iska». The verb «yin», which means «to do», takes both the nouns «rain», «ruwa», and «wind», «iska». The two atomic utterances are linked by the connective «ko». In the above example the connective «ko» has an inclusive meaning because both utterances are compatible and they might also take place together. In this case, the connective «ko» can be compared to the Latin «vel». [On this interesting topic see MALATESTA (2003)]. 58 Metalogicon (2004) XVII, 2 Now, we will calculate the logical sum by using Hausa both as language and metalanguage , we obtain the following table: ana yin ruwa GASKIYA GASKIYA KARYA KARYA ana yin iska GASKIYA KARYA GASKIYA KARYA ana yin ruwa ko iska GASKIYA GASKIYA GASKIYA KARYA Symbolising «ana yin ruwa» by ‘p’, «ana yin iska» by ‘q’ and «Ana yin ruwa ko iska» by ‘Apq’like in Polish symbolism, we obtain the following truth table which proves the transculturality of logical function of inclusive disjunction. p 1 1 0 0 q 1 0 1 0 Apq 1 1 1 0 In logic, the Hausa connective «ko» («or») can be also used except when the two utterances are both possible but they can’t take place together. See the example below: . Is it day or night In Hausa: Rama ne ko dare Literally: Day is or night. As you can see such a molecular sentence is a contracted form of the following expression «rama ne ko dare ne», which is made up two atomic sentences «rama ne» and «dare ne». In this case, the connective «ko» expresses the meaning of the Latin «aut». Now we will write the exclusive sentence using Hausa 59 Metalogicon (2004) XVII, 2 language both as language (in italic) and metalanguage (in capital letters). rama ne GASKIYA GASKIYA KARYA KARYA dare ne GASKIYA KARYA GASKIYA KARYA rama ne ko dare KARYA GASKIYA GASKIYA KARYA Now if we symbolise “rama ne” by ‘p’, “dare ne” by ‘q’, “rama ne ko dare” by ‘Jpq’ as in Polish symbolism, we obtain the truth table of exclusive disjunction: p 1 1 0 0 q 1 0 1 0 Jpq 0 1 1 0 In logic, another meaning of the connective «or» is that of the incompatibility, since either the first utterance or the second is possible or neither of them. See the example below: The team of Nigeria wins or loses contracted form of the molecular sentence «The team of Nigeria wins or the team of Nigeria loses», made up of two atomic sentences «The team of Nigeria wins» and «the team of Nigeria loses», connected by «or» in the meaning of «nand». [See MALATESTA (1997), pp. 86-93]. In Hausa: kungiya Nigeriya yaa ci ko an ci sa Literally: The team of Nigeria has won or has been won (or 60 Metalogicon (2004) XVII, 2 defeated). Also such a molecular sentence is a contracted form of the following expression «kungiya Nigeriya yaa ci ko kungiya Nigeriya an ci sa», which is made up two atomic sentences «kungiya Nigeriya yaa ci», and ««kungiya Nigeriya an ci sa». In this case, the connective «ko» expresses the meaning of «the first is true, or the second is true, or both are false». Therefore the case that both are true is excluded. Hence the name «nand» = «not and» given to such a logical function. In this example, it’s evident that there is no likelihood of the victory and defeat of the Nigerian team at the same time, but there are three possibilities: the Nigerian team could win, lose or draw. The meaning of the connective «or», in this example, is that of the incompatibility: one or another, or neither of them. See the informal Truth table below in Hausa language. kungiya Nigeriya yaa ci GASKIYA GASKIYA KARYA KARYA kungiya Nigeriya an ci sa GASKIYA KARYA GASKIYA KARYA kungiya Nigeriya yaa ci ko an ci sa KARYA GASKIYA GASKIYA GASKIYA Symbolising “kungiya Nigeriya yaa ci” by ‘p’, “kungiya Nigeriya an ci sa” by ‘q’, “kungiya Nigeriya yaa ci ko an ci sa” by ‘Dpq’ as in Polish symbolism, we obtain the truth table of exclusive disjunction of classical logic: p 1 1 0 0 q 1 0 1 0 Dpq 0 1 1 1 Now we will examine the material implication, which is the most basic logical function because it does not include an additional significance to the original one. Its meaning is: 61 Metalogicon (2004) XVII, 2 Cpq =df NKpNq In the Hausa language, the connective «if....then» is expressed by: « idan …sa’an». See the example below: if it raining then the wind is blowing In Hausa: idan ana yin ruwa sa’an iska Literally: If it makes rain, then (it makes) wind. See the following table where Hausa is used both as object language and metalanguage. As far as the material implication is concerned see the important experiment made in Zambia in MALATESTA (2003). ana yin ruwa ana yin iska GASKIYA GASKIYA KARYA KARYA GASKIYA KARYA GASKIYA KARYA idan ana yin ruwa sa’an iska GASKIYA KARYA GASKIYA GASKIYA Let ‘p’ stand for “ana yin ruwa”, ‘q’ for “ana yin iska” and ‘Cpq’ for “idan ana yin ruwa sa’an iska”, contracted form for “idan ana yin ruwa sa’ana ana yin iska”. The above table can be symbolised as follows: p 1 1 0 0 q 1 0 1 0 Cpq 1 0 1 1 62 Metalogicon (2004) XVII, 2 Once again we can note the transculturality of sentence classical logic. Now shall analyse the material equivalence, which can be derived from the material implication. Do not forget the classical standard definition Epq =df KCpqCqp The above connective, which in English is expressed by the phrase «if only if», in the Hausa language becomes «idan kadai idan». See the example below: if it raining if and only if the wind is blowing In Hausa: ana yin ruwa idan kadai idan iska Literally: If it makes rain if only if (it makes) wind. See the table below: ana yin ruwa ana yin iska GASKIYA GASKIYA KARYA KARYA GASKIYA KARYA GASKIYA KARYA ana yin ruwa idan kadai idan iska GASKIYA KARYA KARYA GASKIYA Now if we symbolise “ana yin ruwa” by ‘p’, “ana yin iska” by ‘q’ and ‘Epq’ for “idan ana yin ruwa sa’an iska”, contracted form for “ ana yin ruwa idan kadai idan ana yin iska”, the above table becomes p 1 1 0 q 1 0 1 Epq 1 0 0 63 Metalogicon (2004) XVII, 2 0 0 1 3. Conclusion Our study has showen that the grammatical structure of the Hausa language has some specific features which make it very different from the west languages, but it is possible to say that the formal logic does not favour an exclusive relation with a language or a group or languages, because it has something to do with language itself. It is common knowledge that there is an inseparable relation between mind and language, but the learning of a new language does not mean that we learn also a new logic. The fact that we talk about the logic of the Italian or Chinese language hides an ambiguity of language. In this case, the Chinese logic means the keeping of its grammar structures. In the Latin language, for example, when a text has three if clauses, we are in the presence of the Latin logic, actually the Latin logic is the keeping of its grammar rules. But logic means the science of the necessary inferences and of the conditions which make it possible. These conditions are given by the connectives and their respective True-False tables. Consequently, if the morphologic structures of a Chadic language of the Afro-Asiatic family like Hausa have the same logical functions of the west languages, it’s clear that we are in the presence of one and only one logic. Even though grammars are often different from one another, there are some elements which join together the languages of the whole world, and they are represented by the logical functions. Bibliography BALDI, S: 1992 Grammatica della lingua Hausa. Versione preliminare, N.P, Napoli. BOCHENSKI, J.M. 1961, A History of Formal Logic, Notre Dame Indiana, University of Notre Dame Press.; orig. titl. Formale Logic, FreiburgMuenich, Karl Alber, 1956. Transl by I. Thomas. 64 Metalogicon (2004) XVII, 2 GOUFFÉ, C. 1965: La lexicographie du Haussa et le préalable phonologique, in “Journal of Africa Languages” 4, 3, pp. 191-210. GREENBERG, J.M. 1963 Languages of Africa, Bloomington Indiana University. KRAFT, C.H., KIRK-GREENE, A.H.M. 1973. Hausa (Teach Yourself Books), London, Hodder and Stoughton. MALATESTA, M. 1997. The Primary Logic. Instruments for a Dialogue between the two Cultures, Leominster (Herefordshire), Gracewing Fowler Wright Books. MALATESTA, M.: 1999 Classic Logic as a Formal Transcultural System: the Case of Tonal Languages: Chinese, in Advances in System Research and Cybernetics, V.III, Partial proceedings of the XI International Conference on System Research, Informatics and Cybernetics, held Aug. 2-7, 1999 in Baden-Baden, Germany, IIAS, Windsor, Canada, 1999, pp. 81-85 MALATESTA, M. 2000, Classic Logic as a Formal Transcultural System: the Case Agglutinant Languages: Japanese, in Advances in System Research and Cybernetics, V.IV, Partial proceedings of the XII International Conference on Systems Research, Informatics and Cybernetics, held in Baden-Baden, Germany, July 31- Aug. 5, 2000, IIAS, Windsor, Canada, 2000, pp. 31-36. MALATESTA, M. 2002, Classic Logic as a Formal Transcultural System: the Case the Bantu Languages: Swahili, in Acta Systemica, II, 2, Address presented at the 14th International Conference on Systems Research, Informatics and Cybernetics, held in Baden-Baden, Germany, July 29Aug.3, in Acta Systemica, Vol. II, Num. 2, ed by G. E. Lasker, Windsor (Canada), IIAS, 2002, pp. 31-36, repr. in “Metalogicon” (2002) XV, pp. 107-116. MALATESTA, M. 2003, The Trans-Cultural Nature of Classical Logic System – A crucial Experiment in Zambia, presented at the 15th International Conference on Systems Research, Informatics and Cybernetics, held in Baden-Baden, Germany, July 28 - August 2, 2003, in IIAS–Transactions on Systems Research and Cybernetics, III, 2, IIAS, Windsor, Canada, 2003, pp. 31-37. NEWMAN, P. 1977, Modern Hausa - English Dictionary Idadan-Zazia: University Press Nigeria. 65 Metalogicon (2004) XVII, 2 VISHER, H. 1911 Rules for Hausa Spelling, Zungern: G.P.O. Reprinted in the “Journal of Royal African Society” XI, in 1912 43: 339-47. 66