Sequent Calculi for Semi-De Morgan and De Morgan Algebras

A contraction-free and cut-free sequent calculus \(\mathsf {G3SDM}\) for semi-De Morgan algebras, and a structural-rule-free and single-succedent sequent calculus \(\mathsf {G3DM}\) for De Morgan algebras are developed. The cut rule is admissible in both sequent calculi. Both calculi enjoy the decidability and Craig interpolation. The sequent calculi are applied to prove some embedding theorems: \(\mathsf {G3DM}\) is embedded into \(\mathsf {G3SDM}\) via Gödel–Gentzen translation. \(\mathsf {G3DM}\) is embedded into a sequent calculus for classical propositional logic. \(\mathsf {G3SDM}\) is embedded into the sequent calculus \(\mathsf {G3ip}\) for intuitionistic propositional logic.     

Natural Deduction Calculi and Sequent Calculi for Counterfactual Logics

In this paper we present labelled sequent calculi and labelled natural deduction calculi for the counterfactual logics CK + {ID, MP}. As for the sequent calculi we prove, in a semantic manner, that the cut-rule is admissible. As for the natural deduction calculi we prove, in a purely syntactic way, the normalization theorem. Finally, we demonstrate that both calculi are sound and complete with respect to Nute semantics [12] and that the natural deduction calculi can be effectively transformed into the sequent calculi.     

LE^{t}_{ \to } , LR^{ \circ }_{{\widehat{ \sim }}}, LK and Cutfree Proofs

Two consecution calculi are introduced: one for the implicational fragment of the logic of entailment with truth and another one for the disjunction free logic of nondistributive relevant implication. The proof technique—attributable to Gentzen—that uses a double induction on the degree and on the rank of the cut formula is shown to be insufficient to prove admissible various forms of cut and mix in these calculi. The elimination theorem is proven, however, by augmenting the earlier double inductive proof with additional inductions. We also give a new purely inductive proof of the cut theorem for the original single cut rule in Gentzen’s sequent calculus $ LK $ without any use of mix.     

Book reviews

Muhammad: a short biography.Martin Forward, 1997. Oxford, Oneworld. 131 pp., pb. £8.99, ISBN 1 85168 131 0

Image of the Prophet Muhammad in the West: a study of Muir, Margoliouth and Watt. Jabal Muhammad Buaben, 1996. Leicester, The Islamic Foundation. 394 pp., hb. n.p., ISBN 0 86037 260 X, pb. n.p., ISBN 0 86037 261 8

Seven Doors to Islam: spirituality and the religious life of Muslims. John Renard, 1996. Berkeley, Los Angeles, London, University of California Press. xv + 333 pp., pb. £13.95, ISBN 0 520 20417 4

Global Communication in Transition: the end of diversity?. Hamid Mowlana, 1996. Thousand Oaks, Sage Publications. 233 pp., pb. n.p., ISBN 0 8039 4319 9

Islamic Fundamentalism. Abdel Salam Sidahmed & Anoushiravan Ehteshami (Eds), 1996. Boulder, Oxford, Westview Press. 284 pp. hb. £43.95, ISBN 0 8133 2429 7; pb. £14.95. ISBN 0 8133 2430 0

Political Participation and Identities of Muslims in Non‐Muslim States. W. A. R. Shadid & P. S. van Koningsveld, 1996. Kampen, KOK, Pharos. 239 pp., hb. FF69,50, ISBN 90 390 0611 3

Islams d'Europe: intégration ou insertion communitaire?. Robert Bistolfi & François Zabbal (Eds), 1995. Paris: L'Aube. 382 pp., pb. FF160, ISBN 2 87678 201 4

Sectarian Influences Within Islam in Britain: with reference to the concept of ’ummah’ and ‘community‘. Ron Geaves, 1996. Leeds, Department of Theology and Religious Studies, University of Leeds. 319 pp., £8.00 ISBN 1871 363 047

Political Islam: essays from the Middle East report. Joel Beinin & Joe Stork (Eds), 1997 Berkeley, University of California Press 395 pp. pb.. Make a Shield from Wisdom: selected verses from Nasir‐i Khusraw's Divan. Annemarie Schimmel (Ed. and tr.), 1993. London and New York, Kegan Paul International. vii + 103 pp., n.p., ISBN 0 7103 0455 2

The Shape of the Holy: early Islamic Jerusalem. Oleg Grabar, 1996. Princeton, Princeton University Press. xiv + 232 pp. with 84 illustrations in color and black‐and‐white, hb. $65, ISBN 0 691036535     

Book reviews

The Oxford Encyclopedia of the Modern Islamic World. John L. Esposito (Ed.), 1995. New York, Oxford, Oxford University Press. 4 vols, £295.00, ISBN 0 19 506613 8.

Deciphering the Signs of God: a phenomenological approach to Islam. Annemarie Schimmel, 1994. Edinburgh, Edinburgh University Press. 302 pp., hb. £39.50, ISBN 0 7486 0460 X.

The Rainbow of Faiths. John Hick, 1995. London, SCM Press. 160 pp., pb. £9.95, ISBN 0 334 02608 3.

Scholarly Approaches to Religion, Interreligious Perceptions, and Islam. Jacques Waahdenburg, (Ed.), 1995. Bern, Berlin, Frankfurt a. M., New York, Paris, Vienna, Peter Lang. 464 pp., hb. Sf76. (= £38), ISBN 3 906752 93 3.

Tariqat al‐Tahin al‐Balaghi wa al‐Tafsir. Roland Meynet, Louis Pouzet, Naila Farouki & Ahyaf Sinno, 1993. Beirut, Lebanon, Dar al‐Mashriq. 306 pp., pb. n.p., ISBN 2 7214 5003 4.

Religious Polemic and the Intellectual History of the Mozarabs, c. 1050–1200. T. Burman, 1994. Leiden, E. J. Brill. 407 pp., hb. np., ISBN 90 04 09910 7.

Justice, Courtesy and Love: theologians and missionaries encountering world religions, 1846–1914. Kenneth Cracknell, 1995. London, Epworth Press. 459 pp, pb. £20, ISBN 0 7162 0501 7.

Mission and Dialogue. Michael Nazir‐Ali, 1995. London, SPCK Press. 152 pp, pb., £8.99, ISBN 0 281 04810 X.

Early Mamluk Diplomacy (1260–1290): treaties of Baybars and Qalawun with Christian rulers. P. M. Holt, 1995. Leiden, E. J. Brill. 161 pp., hb. NLG 100, ISBN 90 04 10246 9.

The Search for Fundamentals: the process of modernization and the quest for meaning. Lieteke Van Vucht Tljssen, Jan Berting & Frank Lechner (Eds), 1995. Dordrecht, The Netherlands, Kluwer Academic Publishers. 293 pp., £80.00, 0 7923 3542 2.

Religion und prosoziales Verhalten Ein Symposion. Walter Kerber, (Ed.), 1995. Munchen, Kindt Verlag. 224 pp., hb. DM.36.00, ISBN 3 925412 18 2.

Nationalism, Ethnicity and Cultural Identity in Europe. (Comparative Studies in Migration and Ethnic Relations 1). Keebat von Benda‐Beckman & Maykel Verkuyten (Eds), 1995. Utrecht, European Research Centre on Migration and Ethnic Relations (ERCOMER). 199 pp., £11.95, ISBN 90 75719 01 9.

‘Das Projekt Weltethos’ in der Erziehung: Referate und Ergebnisse des Nurnberger Forums 1994. Johannes Lahnemann (Ed.), 1995. Hamburg, E.B. Verlag. 410 pp., pb. n.p., ISBN 3 923002 86 6.

Fundamentalism and Intellectuals in Egypt, 1973–1993. David Sagiv, 1995. London, Frank Cass. 188 pp., hb. £35, ISBN 0 7146 4581 8.

Being Human in Africa: toward an African Christian anthropology. Augustine C. Musopole, 1994. New York, Peter Lang. 261 pp., pb. n.p., ISBN 0 8204 2304 1.

Russians in the Former Soviet Republics. Paul Kolstoe with a contribution by Andrei Edemsky, 1995. London, Hurst & Company. 340 pp., hb. £35.00, ISBN 1 8065 206     

Book reviews

One Thousand Roads to Mecca. Michael Wolfe (Ed.), 1997. New York, Grove Press. 620 pp., hb. $32.50, ISBN 0 8021 1611 6

Early Mamluk Syrian Historiography: Al‐Yunini's Dhayl Mir'at al‐zaman. Li Guo, 1998. Leiden, E.J. Brill. 2 vols, 241 pp. and xv + 338 pp. Arabic, hb. n.p., ISBN 90 04 11028 3 and 90 04 11029 1

Defenders of Reason in Islam: Mu'tazilism from medieval school to modern symbol. Richard C. Martin & Mark R. Woodward with Dwi S. Atmaja, 1997. Oxford, Oneworld Publications. xv+ 251 pp., pb. £14.99/$22.95, ISBN 1 85168 147 7

Rethinking Tradition in Modern Islamic Thought. Daniel Brown, 1996. Cambridge Middle East Studies 5. Cambridge, Cambridge University Press. x+ 185 pp., hb. n.p., ISBN 0 521 57077 8

Ebu's su'ud, the Islamic Legal Tradition. Colin Imber, 1997. Edinburgh, Edinburgh University Press. 288 pp., hb. £40.00, ISBN 07486 0767 6

Islam and the West: the making of an Image. Norman Daniel, 1997 (1993). Oxford, Oneworld. 467 pp., pb. $25.95/£16.99, ISBN I 85168 129 8

Exegesis as Polemical Discourse: Ibn Hazm on Jewish and Christian Scriptures. Theodore Pulcini, 1998. Atlanta, GA, Scholars Press. 216 pp., hb. $44.95, ISBN 0 7885 0396 0; pb. $19.95, ISBN 0 7885 0395 2

Christians and Jews under Islam. Youssef Courbage & Philippe Fargues, trans. Judy Mabro, 1997. London and New York, I.B. Tauris. xii + 242 pp., hb. £39.50, ISBN 1 86064 013 3

The Construction of Nationhood: ethnicity, religion and nationhood. Adrian Hastings, 1997. Cambridge, Cambridge University Press. 235 pp., pb. £12.95, ISBN 0 521 62544 0

Muslim Identity and Balkan State. Hugh Poulton & Suha Taji‐Farouki (Eds), 1997. London, Hurst & Co.. 250 pp., hb. n.p., ISBN 1 85065 276 7; pb. n.p., ISBN 1 85065 348 8

Turkish and Other Muslim Minorities of Bulgaria. Ali Eminov, 1997. London, Hurst & Co.. 218 pp., hb. £25, ISBN 1 85065 319 4

Al‐yahūd fi misr min al‐fath al‐'uthmani hatta awa'il al‐qarn al‐tas’ ‘ashar. [History of the Jewish Community in Egypt from the Ottoman Invasion to the. Beginning of the Nineteenth Century] (Arabic). Mohsen Shouman, 1996. Cairo, privately printed (available from the author, Department of History, College of. Arts, University of Zaqaziq, Egypt). 492 pp., n.p., no ISBN

The Society of the Muslim Brothers in Egypt: the rise of an Islamic mass movement 1928–1942. Brynjar Lia, 1998. Reading, Ithaca. 272 pp., hb, £30.00, ISBN 0 86372 220 2

African Islam and Islam in Africa: encounters between Sufis and Islamists. David Westerlund & Eva Evers Rosander (Eds), 1997. London, Hurst & Co.. 347 pp., hb. £40, ISBN 85065 282 1; pb. £15.95, ISBN 1 85065 281 3

Transforming Female Identities: women's organizational forms in West Africa/Transformation des identités feminines: formes d'organisations feminines en Afrique de l'Ouest. Eva Evers Rosander (Ed.), 1997. Uppsala, Nordiska Afrikainstitutet 243 pp., pb. £18.95, ISBN 91 7106 403 6

The Pure and the Powerful. Nadia Abu‐Zahra, 1977. Reading, Ithaca, NY. xx+ 320 pp., hb. £35.00, ISBN 0 86372 179 6     

Book reviews

Gott ist schön und Er liebt die Schönheit: God is Beautiful and He Loves Beauty. Alma Giese and J. Christoph Bürgel, 1994. Bern, Peter Lang. 474 pp., hb. n.p., ISBN 3–906750–90–6.

The Concept of Islamic International Criminal Law. Farhad Malekian, 1994. London, Graham & Trotman. 213 pp., £55.00, $92, ISBN 1859660851.

Religion in Europe: contemporary perspectives. S. Gill, G. D'Costa, and U. King (Eds), 1994. Kampen, Kok Pharos. 213 pp., pb., Fl 49.90, ISBN 90–390–0508–7.

Religious Freedom and the Position of Islam in Western Europe. W. A. R. Shadid and P. S. van Koningsveld, 1995. Kampen, Kok Pharos. 229 pp., pb., Fl 64.90, ISBN 90–390–0065–4.

Christianity in the Arab World. HRH Crown Prince El Hassan Bin Talal, 1994. Amman, Arabesque. 120pp., hb.

Holymen of the Blue Nile: the making of an Arab‐Islamic community in the Nilotic Sudan 1500–1850. Neil MHugh. Evanston Illinois, Northwestern University Press. 280pp., hb., $54.95, ISBN 0–8101–1069–5.     

Book reviews

Wertewandel und Religiose Umbruche [Religionen im Gesprach, 4]. Reinhard Kirste, Paul Schwarzenau, Udo Tworuschka (Eds), 1996. Balve, Zimmermann Druck und Verlag 671 pp., ISBN 3 89053 061 3

Jesus and the Other Names: Christian mission and global responsibility. Paul F. Knitter, 1996. Oxford, Oneworld. 193 pp., pb. £14.99, ISBN 1 85168 125 6

Marcion, Muhammad and the Mahatma. Heikki RAis Anen, 1997. London, SCM Press. xi + 293 pp., pb. £14.95, ISBN 0 334 02693

Medieval Christian Perceptions of Islam. John Victor Tolan (Ed.), 1996. New York and London, Garland Publishing. xxi + 414pp., hb., ISBN 0 8153 1426 4

Islamic Legal Interpretation: Muftis and their fatwas. Muhammad K. Masud, Brinkley Messick & David S. Powers (Eds), 1996. Cambridge, M, and London, Harvard University Press. 431 pp., hb. £29.95, ISBN 0 674 46870 8

The Fatimids and their Traditions of Learning. Heinz Halm, 1997. London, I.B. Tauris. xv + 112 pp., hb. £25.00, ISBN 1 85043 920 6.

Dreams of Trespass: Tales of a Harem Girlhood. Fatima Mernissi, 1994. Reading, MA, Addison‐Wesley. 242 pp., pb. ISBN 0 201 62649 7

Intellectual Origins of Islamic Resurgence in the Modern Arab World. Ibrahim M. Abu‐Rabi, 1996. Albany, NY, State University of New York Press. 370 pp., pb. $19.95, ISBN 0 7914 2664 5

The Islamic Middle East: an historical anthropology. Charles Lindholm, 1996. Oxford, Blackwell. 324 pp. pb. £14.99, ISBN 1 55786 421 7

Hizb'Allah in Lebanon: the politics of the Western hostage crisis. Magnus Ranstorp, 1997. London, Macmillan. xvi + 257pp., pb. £15.99, ISBN 0 333 68401 X

Hezbollah: born with a vengeance. Hala Jaber, 1997. London, Fourth Estate. xvi + 240pp., hb. £16.99, ISBN 1 85702 381 1.

Lebanon on Hold: implications for Middle East peace. Rosemary Hoixis & Nadim Shehadi (Eds), 1996. London, The Royal Institute of International Affairs. 94 pp. pb, ISBN 1 86203 020 0

African Muslims in Antebellum America: transatlantic stories and spiritual struggles.. Aixan D. Austin, 1997. New York/London, Routledge. 194 pp., pb. £13.99, ISBN 0 415 91270 9

The Crown and the Turban: Muslims and West African pluralism. Lamin Sanneh, 1997. Boulder, CO, Westview Press. 290 pp., pb. np, ISBN 0 8133 3059 9

Legacy of a Divided Nation: India's Muslims since Independence. Mushirul Hasan, 1997. London, C. Hurst. xv+ 383 pp., hb, £35, ISBN 1 85065 234 1; pb. £14.95, ISBN 1 85065 304 6

A Dictionary of Indonesian Islam. Howard M. Federspiel, 1995. Athens, OH, Ohio University. 297 pp. pb. $25.00, ISBN 0 89680 182 9     

Book reviews

E1 Evangelio de San Bernabé: un evangelio islámico español. Luis F. Bernabé Pons, 1995 Alicante, University Press 260 pp., hb. n.p. ISBN 84 7908 223 2

Muhammad and Jesus. William. E. Phipps, 1996 300 pp., pb. £14.95, ISBN 0 334 02630 X

Arabic Grammar and Qur'anic Exegesis in Early Islam.. C. H. M. Versteegh, 1993 Leiden, E. J. Brill xi + 230 pp., hb. ISBN 9004098453.

Religious Truth for Our Time. William Montgomery Watt, 1995 Oxford, Oneworld 109 pp., pb. £5.95, ISBN 1 85168 102 7

Dialogue of Life: a Christian among Allah's poor. Bob McCahill, 1996 Maryknoll, New York, Orbis Books 109 pp., pb. $13, ISBN 1 57075 066 1

Questioning the Secular State: the worldwide resurgence of religion in politics. David Westerlund (Ed.), 1996 London, Hurst & Company xii + 428 pp., pb. £14.95, ISBN 1 85065 241 4

Religion and Globalization. Peter Beyer, 1994 London, Sage Publications vi + 250 pp., pb. $21.95

A Critique of the Origins of Islamic Economic Thought. Yassine Essid, 1995 Leiden, E. J. Brill 257 pp., hb. n.p., ISBN 90 04 10079 2

Muslims in the Margin: political responses to the presence of Islam in Western Europe. W. A. R. Shadid & P. S. van Koningsveld, 1996 Kampen, KOK Pharos 288 pp., hb. F169.90, ISBN 90 390 0520 6

Muslim Eurasia: conflicting legacies. Yaacov Ro'i (Ed.), 1995 London, Frank Cass xii + 330 pp., hb. and pb., $47.50, ISBN 0714646156     

An asymmetric effect of relational integration on recognition memory

Two experiments assessed whether conceptual relations (e.g., contains: cookie jar) facilitate the retrieval of concepts (e.g., cookie and jar) from long-term memory. The CARIN model of nominal combination asserts that conceptual relations are represented with and selected from the modifier noun (cookie). Thus, the model predicts that relational integration will facilitate memory for modifiers but not for head nouns (jar). In Experiment 1, concepts were studied in pairs and were then tested individually. Recognition accuracy was higher for modifiers than for head nouns. In Experiment 2, the studied concepts (e.g., cookie jar) were tested in the context of a new pair that instantiated either the same relation (e.g., cookie plate) or a different relation (e.g., cookie crumb). Recognition was again better for modifiers than for head nouns, but only when the same conceptual relation was instantiated at both study and test. Thus, results indicate that conceptual relations (a) facilitate recognition memory, and (b) are associated more strongly with the modifier than with the head noun.     

Book reviews

Islam: a challenge for Christianity (Concilium 1994/3). Hans Kung & Jurgen Moltmann (Eds), 1994. London, Concilium; Maryknoll, SCM Press; London, Orbis Books. 163 pp., pb. £8.95, ISBN 0–334–030269.

Cultures in Conflict: Christians, Muslims and Jews in the age of discovery. Bernard Lewis, 1995. New York, Oxford University Press. 101 pp., hb., $16.95, ISBN 0–19–509026–8.

Beyond Faith and Infidelity: the Sufi poetry and teachings of Mahmud Shabistari. L. Lewisohn, 1995. Richmond, Surrey, Curzon Press. 344 pp. pb. £14.99, 0–7007–0343–8.

The Prophet's Pulpit: Islamic preaching in contemporary Egypt. [Comparative Studies on Muslim Societies, 20]. Patrick Gaffney, 1994. Berkeley and Los Angeles, University of California Press. 367 pp., hb. £40.00, ISBN 0–520–08471–3, pb. £15.95, ISBN 0–520–08472–1.

Sufi and Scholar on the Desert Edge: Muhammad b. CA1i al‐Sanūsi and his Brotherhood. K. S. Vikor, 1995. London, Hurst & Co. 310 pp. hb. £37.50, ISBN 1 85065 218 X.

Children of Islam. Marie Parker‐Jenkins, 1995. Stoke‐on‐Trent, Trentham Books Ltd. 162 pp., £12.95, ISBN 1–85856 034 9.     

Gentzen-Style Sequent Calculus for Semi-intuitionistic Logic

The variety \({\mathcal{SH}}\) of semi-Heyting algebras was introduced by H. P. Sankappanavar (in: Proceedings of the 9th “Dr. Antonio A. R. Monteiro” Congress, Universidad Nacional del Sur, Bahía Blanca, 2008) [13] as an abstraction of the variety of Heyting algebras. Semi-Heyting algebras are the algebraic models for a logic HsH, known as semi-intuitionistic logic, which is equivalent to the one defined by a Hilbert style calculus in Cornejo (Studia Logica 98(1–2):9–25, 2011) [6]. In this article we introduce a Gentzen style sequent calculus GsH for the semi-intuitionistic logic whose associated logic GsH is the same as HsH. The advantage of this presentation of the logic is that we can prove a cut-elimination theorem for GsH that allows us to prove the decidability of the logic. As a direct consequence, we also obtain the decidability of the equational theory of semi-Heyting algebras.     

Book reviews

Déclarations Communes Islamo‐Chrétiennes 1954–1995: textes originaux et traductions françaises. Choix de textes présentés par: Juliette Nasri Haddad, sous la direction de: Augustin Dupré la Tour et Dr Hisham Nashabé, 1997. Beyrouth, Dar el‐Machreq, Distribution Librairie Orientale, B.P. 1986, Beyrouth, Liban. 376 pp. + 14 large charts, hb. np., ISBN 2 7214 5008 5

Ultimate Visions: reflections on the religions we choose. Martin Forward (Ed.), 1995. Oxford, One World Publications. 208 pp., pb. $14.95, ISBN 1 85168 100 0

Cross and Crescent: responding to the challenge of Islam. Colin Chapman, 1995. Leicester, Inter‐Varsity Press. 364 pp., pb. £9.99, ISBN 0 85110 992 6

Louis Massignon: the crucible of compassion. Mary Louise Gude, 1996. Notre Dame and London, University of Notre Dame Press. 283 pp., hb. np., ISBN 0 268 031308 X

The New Islamic Dynasties: a chronological and genealogical manual. C. E. Bosworth, 1996. Edinburgh, Edinburgh University Press. 389 pp., hb. £49.50, ISBN 0 7486 0684 X

A Short Introduction to Islamic Philosophy, Theology and Mysticism. Majid Fakhry, 1997. Oxford, Oneworld. 151 pp., pb. £8.99, $13.95, ISBN 1 85168 134 5

Religion and Politics under the Early ‘Abbasids: the emergence of the proto‐Sunni elite. Muhammad Qasim Zaman, 1997. Leiden, Brill. 232 pp., hb, Nlg 137.00, US$85.75, ISBN 90 04 10678 2

NichtMuslimische Untertanen im Islam: Grundlage, Ideologie und Praxis der Politik frühislamischer Herrscher gegenüber ihren nichtMuslimischen Untertanen mit besonderem Blick auf die Dynastie der Abbasiden (749–1248). (Studies in Oriental Religions, 34). Wolfgang Kallfelz, 1995. Wiesbaden, Harrassowitz Verlag. 180 pp., pb. np., ISBN 3 447 03720 2

Hierarchy and Egalitarianism in Islamic Thought. Louise Marlow, 1997. Cambridge, Cambridge University Press. 194 pp., hb. np., ISBN 0 521 56430 1

The Dual Nature of Islamic Fundamentalism. Johannes J. G. Jansen, 1997. Ithaca, Cornell University Press/London, Hurst & Co.. 197 pp., hb. £25.00, ISBN 1 85065 274 0

Islam and Democracy. John Esposito & John Voll, 1996. Oxford, Oxford University Press. 232 pp., pb. £16.99, ISBN 0 19 510816 7

New World Order: Western fundamentalism in action. S. M. KORESHI, 199?. Islamabad, Institute of Policy Studies and Islamabad Publications. 306 pp., hb. Rs.250.00, ISBN 969 448 039 6

Das Eigene als Fremdes: Chancen und Bedingungen des christlich‐islamischen Dialogs. Ralf Geisler, 1997. Hannover, Lutherisches Verlagshaus. 104 pp., hb. DM24.80, ISBN 3 7859 0741 9

Making Muslim Space in North America and Europe. Barbara D. Metcalf (Ed.), 1996. Berkeley and London, University of California Press. xix + 264 pp., hb. $50, £40, ISBN 0 520 20403 4; pb. $20, £15, ISBN 0 520 20404 2

Allah in the West: Islamic movements in America and Europe. GILLES KEPEL, 1997. Oxford, Polity Press. 273 pp., pb. £13.95, ISBN 0 7156 1558 9

An Occasion For War: civil conflict in Lebanon and Damascus in 1860. Leila Tarazi Fawaz, 1994. Berkeley, University of California Press. 302 pp., pb. $17.00, ISBN 0 520 20086 1

Master and Disciple: the cultural foundations of Moroccan authoritarianism. Abdellah Hammoudi, 1997. Chicago & London, Chicago University Press. 195 pp., hb. £30.50, ISBN 0 226 31527 4; pb. £11.92, ISBN 0 226 31528 2

Islam in South‐East Asia: a study for Christians. Robert A. Hunt, 1997. New York, General Board of Global Ministries of the United Methodist Church; Petaling Jaya [Malaysia], Methodist Church of Malaysia. vii+ 172 pp., pb. np., ISBN 1 890569 04 6     

Book reviews and books received

Paradox and Passion in Psychotherapy van Deurzen, E., 1998 Chichester: Wiley Isbn 0-471-97390-4 £14.95

Witness and Vision of the Therapists Feltham, C. (Ed.), 1998 London: Sage ISBN 0-7619-5158-X £13.99

Are You Sitting Uncomfortably?: Windy Dryden Live and Uncut Dryden, W., 1998 Ross-on-Wye: PCCS Books ISBN 1-898059-18-7 £10.50 (discounts for buying direct)

The Integrative Power of Cognitive Therapy Alford, B.A. & Beck, A.T., 1997 New York: Guilford Press ISBN 1-57230-171-6 £11.95

Psychotherapy Counselling and Mental Health Care: Assessment for Brief or Longer-Term Treatment Burton, M., 1998 Chichester: Wiley ISBN 0-471-98228-8 £17.99

Career Counselling: a Narrative Approach Cochran, L., 1997 London: Sage ISBN 0-7619-0442-5 £14.99

Telling Tales: Perspectives on Guidance and Counselling in Learning Edwards, R., Harrison, R. & Tait, A.I. (Eds), 1998 London: Routledge ISBN 0-415-19443-1 £14.99

Taking Issue: Debates in Guidance and Counselling in Learning Crawford, M., Edwards, R. & Kydd, L. (Eds), 1998 London: Routledge ISBN 0-415-19667-1 £14.99     

Book Reviews and Books Received

Person-Centred Counselling: an Experiential Approach Rennie, D.L., 1998 London: Sage ISBN 07619-5345-0 £12.95

From Hearing to Healing: Working with the Aftermath of Child Sexual Abuse (2nd edn) Bannistkr, A. (Ed.), 1998 Chichester: Wiley ISBN 0-471-98298-9 £14.99

The Ethical Use of Touch in Psychotherapy Hunter, M. & Struve, J., 1998 London: Sage ISBN 0-7619-0361-5 £17.99

After the Death of a Child: Living with Loss through the Years Finkbeiner, A.K., 1996 Baltimore, MD: Johns Hopkins University Press ISBN 0-8018-5914-X £13

Remembering Trauma: a Psychotherapist's Guide to Memory and Illusion Mollon, P., 1998 Chichester: Wiley ISBN 0-471-98214-8 £16-99

Counselling and Communication Skills for Medical and Health Practitioners Bayne, R., Nicolson, P. & Horton, I., 1998 Leicester: BPS Books ISBN 1-85433-256-2 £14.50

Counselling in Healthcare Settings Bor, R., Miller, R., Latz, M. & Salt, H. 1998 London: Cassell ISBN 0-304-33986-5 £15.99     

On Gentzen Relations Associated with Finite-valued Logics Preserving Degrees of Truth

When considering m-sequents, it is always possible to obtain an m-sequent calculus VL for every m-valued logic (defined from an arbitrary finite algebra L of cardinality m) following for instance the works of the Vienna Group for Multiple-valued Logics. The Gentzen relations associated with the calculi VL are always finitely equivalential but might not be algebraizable. In this paper we associate an algebraizable 2-Gentzen relation with every sequent calculus VL in a uniform way, provided the original algebra L has a reduct that is a distributive lattice or a pseudocomplemented distributive lattice. We also show that the sentential logic naturally associated with the provable sequents of this algebraizable Gentzen relation is the logic that preserves degrees of truth with respect to the original algebra (in contrast with the more common logic that merely preserves truth). Finally, for some particular logics we obtain 2-sequent calculi that axiomatize the algebraizable Gentzen relations obtained so far.     

Book reviews

God, Reason, and Religions: new essays in the philosophy of religion. Eugene Thomas Long (Ed.), 1995. Dordrecht Kluwer Academic. 228 pp., hb. £67.50, ISBN 07 923333 810 3

Christians and Muslims: from double standards to mutual understanding. Hugh Goddard, 1995. London, Curzon Press. 200 pp., pb. £14.99, ISBN 0 7007 0364 0

Al‐Bayanat al‐Masihiyya al‐Islamiyya al‐Mushtaraka. Juliette Haddad (Ed.), 1995. Beirut, Dar al‐Mashriq. 207 pp., pb. n.p., ISBN 2 7214 5005 0

Muslim Writers on Judaism and the Hebrew Bible, from Ibn Rabban to Ibn Hazm. Camilla Adang, 1996. Leiden, E. J. Brill. 321 pp., hb. NLG140, ISBN 90 04 10034 2

Abū Ya qūb al‐Sijistani: intellectual missionary. Paul E. Walker, 1996. London, I. B. Tauris. 132 pp., rib. £35, ISBN 1 85043 921 4

The Cambridge Survey of World Migration. Robin Cohen (Ed.), 1995. Cambridge, Cambridge University Press. 570 pp., hb. n.p. ISBN 0 521 44405 5

Musulmans en Europe occidentals bibliographic commentée. Muslims in Western Europe: an annotated bibliography. Felice Dassetto & Yves Conrad (Eds), 1996. Paris, Editions L'Harmattan. 202 pp., pb., n.p., ISBN 2 7384 4126 2

Muslim Politics. Dale F. Eickelman & James Piscatori, 1996. Princeton, NJ, Princeton University Press. 235 pp., pb. n.p., ISBN 0 691 00870 1

Islam and the Myth of Confrontation: religion and politics in the Middle East. Fred Halliday, 1996. London, I. B. Tauris. 255 pp., £12.95, ISBN 1 85043 959 1

Nine Parts of Desire: the hidden world of Islamic women. Geraldine Brooks, 1995. New York, Doubleday. 255 pp. hb. £22.95, ISBN 0 385 47576 4

Aunt Safiyya and the Monastery. Bahaa’ Taher, 1996. Translated from the Arabic by Barbara Romaine. Berkeley, University of California Press. 124 pp., pb. n.p., ISBN 0 520 20075 6

Dreams of Trespass: tales of a harem girlhood. Fatima Mernissi, 1994. Reading, MA, Addison‐Wesley. 242 pp. pb., ISBN 0 201 62649 7

Lettres et message d'Algérie. P. Claverie, 1996. Paris, Karthala. 222 pp., pb. 120FF, ISBN 2 86537 657 5

Islamic Resurgence and Islamization in Malaysia. S. Batumalai, 1996. Perak, Malaysia. 279 pp., pb. RM 25/‐, no ISBN

Christian‐Muslim Relations: a case study of Sarawak, East Malaysia. Theodore Gabriel, 1996. Aldershot, Avebury. xiv, 133 pp., n.p., ISBN 1 85972 325 X

Muslim Communities in the New Europe. Gerd Nonneman, T. Niblock & B. Sjajkowski (Eds), 1996. Reading, Ithaca Press. 356 pp., hb. £35.00, ISBN 0 86372 192 3

Al‐Mughtaribun: American law and the transformation of Muslim life in the United States. Kathleen M. Moore, 1995. Albany, State University of New York Press. 211 pp., pb. $16.95, ISBN 0 7914 2580 0

The Landscape of Belief: encountering the Holy Land in nineteenth‐century American art and culture. [The Princeton Series in Nineteenth‐Century Art, Culture, and Society]. John Davis, 1996. Princeton, Princeton University Press. 264 pp., hb. $65.00, ISBN 0 691 04373 6     

Book Reviews and Books Received

Integrative Stress Counselling: a Humanistic Problem-Solving Approach Milner, P. & Palmer, S., 1998 London: Cassell ISBN 0-304-33492-8 £16.99

Person-Centred Therapy: a Revolutionary Paradigm Bozarth, J., 1998 Ross-on-Wye: PCCS Books ISBN 1-898059-22-5 £15

The Presenting Past: the Core of Psycho-dynamic Counselling and Therapy (2nd edn) Jacobs, M., 1998 Buckingham: Open University Press ISBN 0-335-20196-2 £15.99

Sacred Science: Person-Centred Inquiry into the Spiritual and the Subtle Heron, J., 1998 Ross-on-Wye: PCCS Books ISBN 1-898059-21-7 £14

Person-Centred Therapy: a European Perspective Thorne, B. & Lambers, E. (Eds) London: Sage ISBN 0-7619-5155-5 £14.99

New Skills for New Futures: Higher Education Guidance and Counselling Services in the European Union Watts, A.G. & van Esbroeck, R., 1998 Brussels: VUB University Press ISBN 90-5487-199-7 £12     

On All Strong Kleene Generalizations of Classical Logic

By using the notions of exact truth (‘true and not false’) and exact falsity (‘false and not true’), one can give 16 distinct definitions of classical consequence. This paper studies the class of relations that results from these definitions in settings that are paracomplete, paraconsistent or both and that are governed by the (extended) Strong Kleene schema. Besides familiar logics such as Strong Kleene logic (K3), the Logic of Paradox (LP) and First Degree Entailment (FDE), the resulting class of all Strong Kleene generalizations of classical logic also contains a host of unfamiliar logics. We first study the members of our class semantically, after which we present a uniform sequent calculus (the SK calculus) that is sound and complete with respect to all of them. Two further sequent calculi (the \({{\bf SK}^\mathcal{P}}\) and \({\bf SK}^{\mathcal{N}}\) calculus) will be considered, which serve the same purpose and which are obtained by applying general methods (due to Baaz et al.) to construct sequent calculi for many-valued logics. Rules and proofs in the SK calculus are much simpler and shorter than those of the \({\bf SK}^{\mathcal{P}}\) and the \({\bf SK}^{\mathcal{N}}\) calculus, which is one of the reasons to prefer the SK calculus over the latter two. Besides favourably comparing the SK calculus to both the \({\bf SK}^{\mathcal{P}}\) and the \({\bf SK}^{\mathcal{N}}\) calculus, we also hint at its philosophical significance.     

Does the deduction theorem fail for modal logic?

Various sources in the literature claim that the deduction theorem does not hold for normal modal or epistemic logic, whereas others present versions of the deduction theorem for several normal modal systems. It is shown here that the apparent problem arises from an objectionable notion of derivability from assumptions in an axiomatic system. When a traditional Hilbert-type system of axiomatic logic is generalized into a system for derivations from assumptions, the necessitation rule has to be modified in a way that restricts its use to cases in which the premiss does not depend on assumptions. This restriction is entirely analogous to the restriction of the rule of universal generalization of first-order logic. A necessitation rule with this restriction permits a proof of the deduction theorem in its usual formulation. Other suggestions presented in the literature to deal with the problem are reviewed, and the present solution is argued to be preferable to the other alternatives. A contraction- and cut-free sequent calculus equivalent to the Hilbert system for basic modal logic shows the standard failure argument untenable by proving the underivability of ${\square\,A}$ from A.