Diyanet İşleri Başkanlığı 2013-2014 eğitim yılıyla birlikte kendine yeni bir hizmet alanı açmış ve Cumhuriyet tarihinde ilk olarak resmi okul öncesi din eğitimini 4-6 yaş Kur’an Kursları ile başlatmıştır. Bu alanda her geçen yıl tecrübe kazanılmış olsa da çeşitli noktalarda bazı sorunların devam ettiği görülmektedir. Araştırmanın konusu 4-6 yaş Kur’an Kursları etkinlik kitaplarında yer alan hikâyelerin içerik ve resimlendirme bakımından okul öncesi çağındaki çocuklar için uygunluğunun incelenmesidir. Araştırmamızın amacı, okul öncesi dönemde okuma yazma bilmeyen çocuklar için hikâyelerin ve özellikle de (...) hikâyelerde yer alan resimlerin ve görsellerin öğrenmede çok önemli bir paya sahip olduğunun altını çizerek etkinlik ve ders kitaplarının düzenlenmesine ve zenginleştirilmesine katkı sağlamaktır. Nitel bir araştırma olan çalışmada mevcut etkinlik kitapları incelenmiştir. Araştırma, var olan durumu, var olduğu şekilde betimlemeyi amaçlayan tarama modelidir ve etkinlik kitaplarındaki hikâyeler ve resimler betimsel analiz yoluyla incelenmiştir. Ulaşılan sonuçlara göre; 4-6 yaş Kur’an Kurslarındaki etkinlik kitaplarındaki hikâyelerin içeriklerinin okul öncesi çocukların seviyesine göre, bilgilendirme işlevini gören ancak etkileme ve çocukta merak uyandırma noktasında yetersiz olduğu, resimlerinin ise bazı hikâyelerde metne uygun olmadığı ve çocuğun hayal dünyasına hitap etmediği tespit edilmiştir. Bu konuda daha hareketli ve renkli resimlerle hazırlanmış ders ve etkinlik kitaplarının gerekliliği ortaya konmuş ve önerilerde bulunulmuştur. The Presidency of Religious Affairs initiated a new service area in the 2013-2014 Academic Year. The Presidency, which previously provided educational activities for young and middle-aged groups and primary school children during summer courses, started official preschool religious education for the 4-6 year-old age group in Quran Courses for the first time in 2013-2014. Although the experience has been acquired in this field with each passing year, some problems are still noticeable at various points. The present study examines the contents and aesthetic aspects of the stories included in Quran Courses activity books for 4-6 year-old children. The purpose of the study is to underline that stories and especially the illustrations and visuals in stories, have very important roles in learning for children who are illiterate in the preschool period, and the study aims to contribute to the organization and enrichment of the activities and textbooks by drawing attention to this field. In this study, which has a qualitative design, the existing activity books are examined. The study also has a screening model, which aims to explain the present situation in the way it is. The stories and illustrations in the activity books were examined in this study via descriptive analysis based on the criteria that should exist in children’s literature books. In this respect, we tried to summarize and interpret the data obtained in the study according to the pre-determined criteria. This study, which draws attention to the importance of books with illustrations, which have an important function in the development of preschool children, and their effects on children, examined the contents of the stories and the pictures used in the narration of the stories in the activity books used in the Qur'an Courses for 4-6 year-old children. Before making an assessment on the subject, the author tried to find an answer to the question of what stories and pictures mean for preschool children and what is the function and importance of pictures and stories in their education. According to the criteria, the author examined and evaluated nine stories in the activity books prepared for the Qur'an Courses for the ages of 4-6, in which especially pictures are used in the narration. (shrink)

Background and aim: Surgical intensive care nurses should have ethical sensitivity allowing them to identify ethical issues in order that they can recognize them and make the right decisions. This descriptive study was conducted with the aim of evaluating the ethical sensitivity of surgical intensive care nurses. Materials and methods: The research was carried out with the participation of 160 nurses in six Turkish hospitals, four state, one university, and one private. The data were collected using the “Nurse Description Form” (...) developed by the researcher and the “Ethical Sensitivity Questionnaire.” The percent, mean, standard deviation, median, minimum and maximum values, significance test for the difference between two means, variance analysis, Mann–Whitney U test, and Kruskal–Wallis Variance Analysis test were used to evaluate the data. Ethical considerations: Ethical commission permission and the corporate permission of the hospitals were received before conducting the research. Results: It was determined that the ethical sensitivities of surgical intensive care nurses were moderate based on the Ethical Sensitivity Questionnaire total score and subdimension score averages. A statistical difference was determined between the Ethical Sensitivity Questionnaire total score of surgical intensive care nurses and the institution where they worked, the period of working in the occupation, and the period of working in the intensive care unit. Conclusion: Based on the results of the research, the organization of training and studies devoted to the elimination of ethical sensitivity differences between institutions and workers is suggested. (shrink)

The Crusades are a period of struggle between the East and the West, or between Muslims and Christians, covering nearly two centuries. However, much of the academic research on the Crusades is European-centered and written by experts of the Middle Ages of the West. Changing this viewpoint whose impressions about the Muslim perspective are incomplete and distorted is possible by reconsidering the History of the Crusades from an East / Muslim point of view. In this study, the first reaction of (...) the Muslims against Crusades, the situation of the Seljuk State, the struggles between Frenk and Turks after the seizure of Seljuqan capital İznik by the Crusaders and the collapse of Urfa and Antakya cities will be discussed in the axis of the first Crusade. The sources of the research constitute the chronicles, biographies and geographical studies related to the subject. (shrink)

Hicrî birinci yüzyılın sonu ile ikinci yüzyılın ortalarında yaşamış bulunan Ca‘fer-i Sâdık ve Ebû Hanîfe, akran iki âlimdir. Kûfe’de yetişen ve Ehl-i sünnet mezheplerinden birinin imamı olan Ebû Hanîfe’nin, Medine’de yetişen ve İsnâaşeriyye’nin altıncı imamı kabul edilen Ca‘fer ile bir araya geldiği ve onun talebesi olduğu hem sünnî hem Şiî kaynaklarda rivayet edilmektedir. Mukaddem kaynaklarda Ebû Hanîfe’nin Ca‘fer-i Sâdık’ın öğrencisi olduğu yönündeki ifadelerin, muahhar kaynaklarda abartılı bir şekilde yorumlandığı görülmüştür. Bu çalışmada Ebû Hanîfe ile Ca‘fer-i Sâdık arasındaki hoca-talebe ilişkisi netleştirilmeye (...) çalışılmıştır. Bu sebeple öncelikle kısaca her iki imamın hayatı ele alınarak onların ilmî birikimi tespit edilmiştir. Akabinde Ebû Hanîfe ile Ca‘fer’in ne zaman ve ne kadar süre birlikte oldukları, Ebû Hanîfe’nin Ehl-i beyt’e yönelik tutumunun Ca‘fer’den ilim almasında ne gibi bir etkisinin bulunduğu ve çeşitli ilim dallarında Ebû Hanîfe- Ca‘fer ilişkisi tespit edilmeye çalışılmıştır. (shrink)

Background:The development of a profession’s autonomy closely relates to that profession’s level of autonomy in performing its specific role. For the nursing profession, this key role is nursing care.Objectives:This study was undertaken to evaluate the professional autonomy of nurses in care provision, from an ethical perspective.Research design:A mixed methods approach is employed in this research, which makes use of both quantitative and qualitative methods. The quantitative dimension of this research covers sociodemographic aspects and makes use of the Sociotropy–Autonomy Scale. The (...) qualitative dimension of the research relates to the factors that affect professional autonomy in nursing care.Participants and research context:The sample consisted of 30 nurses working in the orthopedics, neurology, or intensive care units of three hospitals.Ethical considerations:Before conducting this research, we received permission from the ethical committee, as well as written permits from all the institutions in which the research was carried out. Informed consent was obtained from all participants.Findings:According to the findings of this study, only 6.7% of the nurses surveyed stated that nurses had professional autonomy; they also stated that professional autonomy in nursing was mostly restricted by the need to be “dependent upon the physician in nursing implementations” and that autonomy in nursing care was mostly limited by a “high number of patients per nurse.”Discussion:This study determined that delays in resolving problems with regard to professional autonomy in nursing care in Turkey could be creating many of the professional and ethical problems that nurses face there.Conclusion:It is recommended that: individuals choose the nursing profession conscientiously; nurses need to be given professional awareness; their professional organizations need to be strengthened; and plans need to be made to increase research and to accumulate both knowledge and expertise. (shrink)

Ḥājj, the ancient religious symbol in the Sami’s, is not only a religious duty for the Muslim individual, but also an important worship that creates a social awareness of the ummah and at the same time creates a serious population mobility in the Islamic geography. With the message of the Prophet, the pilgrimage was restored to its original form, and in the next process, those who were in charge of this region made an effort to enable all Muslims of the (...) world to carry out their duties comfortably and to carry their religious, scientific and social experiences to their own regions. The Maghreb (today’s Morocco) and Andalusia bonded and strengthened with the eastern Islamic world through pilgrimage, science and trade journeys. The Marīnid State started the pilgrimage journeys again with official convoys, which were partially interrupted due to the conquest of Andalusia. They gave great importance to these journeys in order to express their longing for the Prophet and to show their political and social power. In this study, the arduous pilgrimages Marīnid Sultan Abū’l-Ḥasan’s (d. 752/1351) mother Maryam and his sister Maryam bint Saʿīd- lasting at least one year in the 14th century are discussed in the context of diplomatic, social and cultural dimensions the pilgrimage. As a matter of fact, Muslims living in the distant lands of Morocco and Andalusia, where Islam was lived, made their material and spiritual ties with the lands where Islam was born and developed by means of pilgrimage, knowledge and trade. The pilgrimages of these two Maghribi noble women, who succeeded in the Maghrib-Hijaz pilgrimage, have become epic as even the noble men of the Maghrib and Mashriqi noble women rarely dare it. These pilgrimages, which took place during the reign of sultan of Abū l-Ḥasan should be evaluated in terms of the political developments and socio-cultural characteristics of the period. The Sultan has progressed considerably in his aim of becoming the sultan of the western Islamic world with the conquest of the places outside the Maghrib Aqṣā and the jihad he participated in Andalusia. It was during this period that he established multifaceted relations with the holy lands and their sultans. In these relations, the women of the Marīnid sultans, the pilgrimages made almost competing with the lady sultans of the Mamlūks, diplomatic correspondence and Exchange of gifts between the sultans, gifts and al-Masjid an-Nabawi letter expressing longing of those who could not go on the pilgrimage are included. With this subject, the effect of the fact that the pilgrimage is an exciting journey even in the most distant lands, the sultans of the period supported these journeys, as well as the help of the Ṣūfī connoisseurs to the state with their ribāṭ (hospice) for road safety. In the study, first of all, the women's pilgrimage stories were given, and then the pilgrimages of the dynastic women of the Marīnid period were discussed. The gifts sent to the Mamlūk sultans, who were the sultans of the holy lands, and the Qurʾān sent to Mecca, Medina and Jerusalem, which are considered sacred by Muslims, have become important symbols of these pilgrimage journeys. It is remarkable how pilgrimage journeys united all Muslims materially and spiritually during the periods when Muslim state administrators were powerful. Especially the fact that these two Maghribi ladies were carried out easily should be expressed as another important aspect of the issue. (shrink)

Hajj is both an obligation on Muslims and a source of communication that allows unity among them. In the realization of this worship, in addition to the financial power of the individual, the distance of the place from Harameyn and the safety of the road route, etc. are also important. Except for the rulers of nearby regions, many state administrators made great efforts to maket he pilgrimage comfortable, which they could not fulfill and which they saw as a matter of (...) legitimacy on behalf of their administration. In particular, they gave importance to diplomatic meetings and gifts with the rulers of Haramayn in order to ensure that their pilgrims fulfill this obligation and reunite with their country and their families safely. Pilgrimage was much more difficult for Andalusia and African lands.Those who could not go to the holy land made it a tradition to send gifts, letters and odes.However, the African Sultans were an exception in this regard and made pilgrimages that would go down in history.They have also given importance to these journeys in order to have the necessary scientific knowledge so that they and their people can lead a life in harmony with the Islamic mentality.In this study, the pilgrimage that led to the recognition of Mansā Musā, the Sultan of Western Sudan/Mali of Africa which is ignored in terms of its material-spiritualwealth in its pre-colonial life, and the impact of his pilgrimage on his country will be discussedfrom various aspects. (shrink)

Vidal intertwines fond recollections of films savored in the movie palaces of his Washington, D.C., boyhood with strands of autobiography and trenchant observations about American politics. Never before has the renowned author revealed so much about his own life or written with such immediacy about the forces shaping America. 26 halftones.

Mühendishâne-i Berrî-i Hümâyûn hocalarından Masdariyecizâde Hüseyin Efendi 1238/1822’de doksan dereceden küçük bir açının Eukleides geometrisi yöntemleriyle üç eşit parçaya bölünmesine dair antik prob- lem hakkında bir risale kaleme alır. Risale, köklerini Antik Yunan’da bulan bu meşhur problemin Eukleides geometrisinin araçları olan çizgilik (işaretsiz cetvel) ve pergel kullanılarak ulaşıldığı düşünülen çözümünü içerir. Ayrıca, sunulan ispat Mühendishâne eğitim kadrosunun her birinin onayını gösteren imzalarla kayıt altına alınmıştır. Akademik literatürde bu risaleye dair yapılan değerlendirmelere bakıldığında, çözümde kullanımı sınırlandırılmış araçlarla bir sonuca ulaşılamayacağının Hüseyin (...) Efendi’nin risalesini yayınladığı tarihte çoktan ispatlanmış olduğu iddiasına dayanarak eser, müellif ve dönemin ilim çevresi ile seviyesi hak- kında tahkir eden genelleştirilmiş yorumlar görülür. Tüm bu güncel yayınlar, tek bir kaynaktan, Salih Zeki Bey’in konuya dair yaklaşık bir asır önce kaleme aldığı ve içerik itibariyle doğruluğu tartışılır makalelerinden neşet etmiştir. Bu çalışma bu güncel yayınların ortak kaynağının iddialarını inceler ve problemin çözümü- nün tarihine odaklanır. Böylece verilen hatalı bilgilerin tashihini sunar. (shrink)

Thomas Hill Green, _ Prolegomena to Ethics_, ed. David O. Brink (Oxford: Clarendon Press, 2004), 632 pp. _ _.

Muharrem Hafız, Platon Felsefesinde Khora [Khôra in Plato’s Philosophy], 304 pp.

The article focuses on the concept of active power as an ability that activates the agent, who is the implementer of common sense principles in Thomas Reid's philosophy. Reid argues that the use of active power in the process of realizing the principles of common sense in action is very important for the morality of the agent. While the correct use of active power ensures the emergence of honorable and moral actions, the wrong use of this power causes the emergence (...) of evil and immorality. For this reason, Reid defines the concept of active power as a distinctive feature of humans, such as the ability to think. In addition, Reid argues that people are conscious of the existence of their active power. Thus, people are also aware of their own limits. By being aware of other people's active powers, they can regulate their moral relationships. After briefly summarizing Reid's philosophical method in the article, the relationship between common sense principles and active power, which are presented as two important components of action, is discussed. (shrink)

We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without resorting to embeddings, (...) semantic arguments, or interpreted connectives external to the underlying logical language. A novel feature of our proof includes an orthogonality condition for defining duality between interpolants. (shrink)

Psikolojik ve öznel iyi oluş, bireyin yaşamı hakkında nasıl hissettiğine ve yaşam olaylarına nasıl tepki verdiğine bağlıdır. Bireysel olarak kişi, kontrolü dışında gerçekleşen tüm dış olayları bilişsel şemalarında istemsizce hissedebilir. Özellikle ruh sağlığı göz önüne alındığında, son yıllarda dini inanç ve uygulamaların ruh sağlığının çeşitli bileşenleri üzerindeki etkisi, din psikolojisinde en çok çalışılan konulardan biri olarak ortaya çıkmaktadır. Çoğu çalışma, bireylerin anlam arayışları ve yaşam olaylarına tepkileri hakkında cevaplar ararken dinin rolüne odaklanmıştır. Hayatın zorluklarıyla karşılaşan ve strese maruz kalan bireylerin (...) yaşamlarında ibadetlerin onarıcı bir rol oynadığına dair yaygın bir kanı vardır. Bu nedenle, son birkaç yılda bilim adamları için, bilişsel davranışçı çerçevenin din psikolojisi içindeki olası uygulaması hem öznel hem de psikolojik iyi oluşun kilit bir unsuru haline gelmiştir. Dindarlık ve ruh sağlığı arasındaki ilişkiye ilişkin teorik uygulamalar kullanılarak, çeşitli dua biçimlerinin ağırlıklı olarak Hıristiyan dini norm ve inançlarından türetildiği ortaya çıkmaktadır. Ancak, bu tür araştırmalarda Hıristiyan olmayan dinler çoğunlukla göz ardı edilmiştir. Daha spesifik olarak, İslam'da inananların günlük yaşamlarında büyük önem taşıyan çeşitli dini davranış biçimleri olmasına rağmen, Müslüman bireyler arasında dindarlık ve ruh sağlığı arasındaki bağlantılar ihmal edilmiştir. Bu nedenle, mevcut araştırma, Müslüman bireyler arasında bilişsel-davranışçı mekanizmayı kullanarak farklı İslami dua türleri ile iyi oluş hali göstergeleri arasındaki bağlantıyı araştırmayı amaçlamaktadır. Bu çalışmada İngiltere'nin farklı şehirlerinde/bölgelerinde birçok İslami öğrenci topluluğundan ve çeşitli ibadet yerlerinden katılımcı toplamak için çevrimiçi bir anket linki kullanılmıştır. Online anket altı dua türünden (farz, vacip, sünnet, nafile, dua ve zikir formlarından), altı psikolojik iyi bileşenlerinden (özerklik, çevresel hakimiyet, başkalarıyla olumlu ilişkiler, kişisel gelişim, kendini kabul ve yaşamda amaç) ve iki öznel iyi oluş bileşeninden (hayat memnuniyeti ve olumlu ve olumsuz etkiler) oluşmaktadır. Temsili örneklem, yaşları 18 ile 66 arasında (Ort. = 27.01, SS = 8.80) olan 214 katılımcıdan (Kadın= 145, Erkek= 69) oluşmaktadır. Korelasyon analizi sonuçları, farz namaz, sünnet namaz, sözlü dua ve zikir/Allah'ı anmanın iyi oluş hali değişkenleri ile pozitif bir ilişkiye sahip olduğunu, ancak vacip ve nafile namazların iyi oluş hali değişkenleriyle herhangi bir korelasyon göstermediğini ortaya çıkarmıştır. Çoklu regresyon analizi sonuçları, farz, sünnet ve vacip namazların psikolojik veya öznel iyi oluş değişkenlerinin yordayıcıları olmadığını göstermiştir. Sadece nafile namazın türü yordayıcı bulunsa da bu ilişki tam tersi yöndedir. Ek olarak, dua ibadeti psikolojik iyi oluş puanlarını tahmin etmedeki benzersiz varyansı açıklarken, zikir ibadeti ise öznel iyi oluşu tahmin etmedeki benzersiz değişkenliği açıklamaktadır. James ve Wells'in bilişsel ve davranışçı modelleri ışığında, bu çalışma sadece dua ve zikir ibadetlerini, bireylere psikolojik destek sağlamada olumlu etkisi olan önemli faktörler olarak belirlemiştir. Dolayısıyla sunulan veriler, kişilerin ibadetleri, rehberlik ve destek için Tanrı'ya güvendikleri ve Tanrı'nın varlığını hissederek düşüncelerini tazeledikleri bir dua ve zikir modelini aldığında daha iyi psikolojik ve öznel iyi oluşa sahip olma olasılıklarının daha yüksek olduğunu göstermektedir. Mevcut bulgulardan görülebileceği gibi, inanç yapılarının belirli topluluk ortamlarında uygulanabilirliğini göz önünde bulundurmak önemlidir. Burada hem teorik çerçeve hem de pratik yön, Müslüman dua türleri ile zihinsel iyi oluş arasındaki ilişkiye ilişkin bir anlayışa katkıda bulunabilir ve sağlık uygulayıcılarına farklı dua modellerinin bireyleri daha iyi bir iyi oluşa nasıl yönlendirebileceği konusunda rehberlik edebilir. (shrink)

Ibn Kammūna (d. 1284) is one of the prominent names to have presented the new structuring that emerged after the classical period studies of Islamic philosophy following the 12th century. This article deals with his theory of the body, previously undiscussed in the academic community. The subject has been handled in connection with the philosophy of nature and metaphysics concerning questions such as how the body exists as a possible essence and how the principles guiding this process are reflected in (...) the field of nature, as well as what the body is and what its constituent elements, types, qualities, and additions are. Thus, Ibn Kammūna has been determined to consider the first body to be the first sphere, the later bodies to occur in the process of emanation, and the cause of the body to be the intellect. In addition, he established the body consisting of matter and form to be continuous, to point to itself, and to be an infinitely divisible substance. However, he is observed to have not evaluated matter and form, which are constituent elements of the body, under the category of substance. Moreover, this article also reviews Ibn Kammūna’s approach to the main claims of the Peripatetic and Illuminationist traditions about the body contained in his original works and commentaries. Through the proofs and reasoning made in the details of these claims, Ibn Kammūna is understood to have thought mostly in line with Ibn Sīnā about the definition and essence of the body. He occasionally agreed with Suhrawardī about the properties and additions of the body. This study investigates how Ibn Kammūna shaped Ibn Sīnā’s theory of the body, upon which Suhrawardī had expanded, and whether its content is original in this context. Thus, I aim to contribute to the field by following the processes of change, expansion, and transfer of philosophical accumulation in Islamic thought after these two philosophers who had founded of the Peripatetic and Illuminationist schools. (shrink)

Functional Neurological Symptom Disorder or Conversion Disorder, is a fairly common diagnosis among mental health patients in Pakistan. Despite its prevalence there's a dearth of research on the phenomenon, particularly on the experience of FNSD. The study was conducted with the aim to ascertain the lived experiences of individuals with Functional Neurological Symptom Disorder around stressful situations in their families in Pakistan. For this purpose, a total sample of 10 participants were recruited from the psychiatry department of a tertiary care (...) hospital in Lahore, Pakistan. Semi-structured interviews were conducted and analyzed through Interpretative Phenomenological Analysis. The two main themes revealed in the analyses were quarrels and unexpressed emotions. The sub-themes of quarrels included quarrels with family members, quarrels within family, parental/marital discord, and quarrels with extended family members. The subthemes for unexpressed emotions were hurt, anger, sadness, and jealousy. In conclusion, this study revealed that in Pakistan, stressors related to family serve as significant contributing factors in the development of FNSD. (shrink)

Academic dishonesty that involves the use of any prohibited means for gaining unfair advantage academically has become a global problem in educational institutions. Limited studies have been conducted to explore the significance of personality with reference to academic misconduct. The present study was conducted to find out the different personality correlates as well as predictors of Academic Dishonesty. For this purpose 232 students of undergraduate and graduate courses from different faculties of University of Karachi, Pakistan, with ages ranging between 18-35 (...) years participated in the study. Big Five Inventory 1 was used to measure personality and English version of Academic Dishonesty Tendency Scale2 was used to measure academic dishonesty. Also five questions were developed to measure one more dimension of academic dishonesty which has been observed in local universities i.e., the tendency towards influencing teachers. For statistical analysis, correlation and regression analysis were conducted. Some personality types were found to be associated, and predictors of different dimensions of academic dishonesty. (shrink)

We define cut-free display calculi for knowledge logics wherean indiscernibility relation is associated to each set of agents, andwhere agents decide the membership of objects using thisindiscernibility relation. To do so, we first translate the knowledgelogics into polymodal logics axiomatised by primitive axioms and thenuse Kracht's results on properly displayable logics to define thedisplay calculi. Apart from these technical results, we argue thatDisplay Logic is a natural framework to define cut-free calculi for manyother logics with relative accessibility relations.

In 1983, Valentini presented a syntactic proof of cut elimination for a sequent calculus GLSV for the provability logic GL where we have added the subscript V for “Valentini”. The sequents in GLSV were built from sets, as opposed to multisets, thus avoiding an explicit contraction rule. From a syntactic point of view, it is more satisfying and formal to explicitly identify the applications of the contraction rule that are ‘hidden’ in these set based proofs of cut elimination. There is (...) often an underly ing assumption that the move to a proof of cut elimination for sequents built from multisets is easy. Recently, however, it has been claimed that Valentini’s arguments to eliminate cut do not terminate when applied to a multiset formulation of GLSV with an explicit rule of contraction. The claim has led to much confusion and various authors have sought new proofs of cut elimination for GL in a multiset setting. Here we refute this claim by placing Valentini’s arguments in a formal setting and proving cut elimination for sequents built from multisets. The formal setting is particularly important for sequents built from multisets, in order to accurately account for the interplay between the weakening and contraction rules. Furthermore, Valentini’s original proof relies on a novel induction parameter called “width” which is computed ‘globally’. It is diffi cult to verify the correctness of his induction argument based on “width”. In our formulation however, verification of the induction argument is straight forward. Finally, the multiset setting also introduces a new complication in the the case of contractions above cut when the cut formula is boxed. We deal with this using a new transformation based on Valentini’s original arguments. Finally, we show that the algorithm purporting to show the non termi nation of Valentini’s arguments is not a faithful representation of the original arguments, but is instead a transformation already known to be insufficient. (shrink)

Free-variable semantic tableaux are a well-established technique for first-order theorem proving where free variables act as a meta-linguistic device for tracking the eigenvariables used during proof search. We present the theoretical foundations to extend this technique to propositional modal logics, including non-trivial rigorous proofs of soundness and completeness, and also present various techniques that improve the efficiency of the basic naive method for such tableaux.