Two notions of compactness in Gödel logics

Compactness is an important property of classical propositional logic. It can be defined in two equivalent ways. The first one states that simultaneous satisfiability of an infinite set of formulae is equivalent to the satisfiability of all its finite subsets. The second one states that if a set of formulae entails a formula, then there is a finite subset entailing this formula as well.In propositional many-valued logic, we have different degrees of satisfiability and different possible definitions of entailment, hence the questions of compactness is more complex. In this paper we will deal with compactness of Gödel, Gödel_Δ, and Gödel_～ logics.There are several results (all for the countable set of propositional variables) concerning the compactness (based on satisfiability) of these logic by Cintula and Navara, and the question of compactness (based on entailment) for Gödel logic was fully answered by Baaz and Zach (see papers [3] and [2]).In this paper we give a nearly complete answer to the problem of compactness based on both concepts for all three logics and for an arbitrary cardinality of the set of propositional variables. Finally, we show a tight correspondence between these two concepts     

The ecological validity of the “who said what?” technique: An examination of the role of self‐involvement,cognitive interference and acquaintanceship

Questions are raised about the possible ecological invalidity of the traditional “who said what?” (WSW) procedure. Three studies are reported which use a modified, quasi‐naturalistic version of the WSW technique, in which rather than being passive recipients of presented information, participants instead play an active role in the production of such information in an interactive context. Data are presented that demonstrate that the social categorization effect typically obtained through the traditional WSW procedure generalizes beyond the circumstances in which it was initially demonstrated. Thus, in Study 1 it was established that social categories (gender, in this case) are cognitively used in real interactions between participants in order to organize information. Moreover, Study 2 demonstrated that the use of categories is accentuated when, as is typical in real world situations, recollections are not made immediately after the perception of the relevant stimuli but following a period of intervening cognitive activity. The findings of Study 3, however, suggest that the WSW technique may not inevitably lead to social categorization effects: typical effects did not appear when participants knew each other well, and therefore saw one another as unique, idiosyncratic individuals, rather than as category members.     

Finding the space between east and west: the emotional impact of teaching in St Petersburg

The paper describes our experience of teaching analytical psychology to a group of graduates of the East European Institute of Psychoanalysis in St Petersburg, our developing partnership as we struggled to teach and learn, each with our own assumptions, preconceptions and projections about the other, and the emotional impact of our radically different social, intellectual and political histories. We had to be affected to become effective. It draws on contemporary Jungian ideas to unpack the interpersonal dynamics involved when there are culturally different styles of learning, which created a complicated transference/countertransference matrix. We believe we have by now witnessed a process of individuation among our students and at the same time they too have witnessed some change and growth in us.     

On Łukasiewicz's Four-Valued Modal Logic

ukasiewicz's four-valued modal logic is surveyed and analyzed, together with ukasiewicz's motivations to develop it. A faithful interpretation of it in classical (non-modal) two-valued logic is presented, and some consequences are drawn concerning its classification and its algebraic behaviour. Some counter-intuitive aspects of this logic are discussed in the light of the presented results, ukasiewicz's own texts, and related literature.     

The ʿUlamāʾ, Fatāwā and Challenges to Democracy in Contemporary Indonesia

This article examines the fatāwā issued by the Council of Indonesian ?ulamā? (Majelis Ulama Indonesia; MUI) regarding democracy, pluralism and religious minorities and explores their socio-historical contexts. The MUI emerges as having an ambiguous attitude towards democracy. The 1998 reform in Indonesia offered a backdrop that encouraged the MUI to be more independent from the state. This enabled the MUI to produce Islamic religious discourses that intersect with democracy, civil society, law enforcement, human rights, public security and elections. The MUI has accepted several principles that are prerequisites for a democratic society and state, such as equality before the law, good governance, protection of human rights, maintenance of public peace and security, and participation in fair elections. However, the Council is very conservative when comes to safeguarding Islamic faith and theology. It rejects pluralism, religious freedom and Muslim minorities such as the Ahmadiyya. The MUI's strict interpretation of Islam and support for Islamist ideology and conservatism prevent it from accepting democracy fully.     

The Prophet’s Letter to al-ʿAlāʾ b. Al-Ḥaḍramī: An Assessment of Its Authenticity in Light of the Covenants and the Correspondence with the People of Yemen

The letter to al-?Alā? b. al-?a?ramī embodies a number of parallels to the covenants and to the Prophet Mu?ammad's correspondence with the people of Yemen. This study examines the different versions of the letter that have come down to us from the Musnad of al-?ārith b. Abī Usāma and from a recension from al-?abarānī's Al-mu?jam al-kabīr to reconstruct a critical edition. Having translated the critical edition and analysed its contents, the study then concludes that the letter is in all likelihood authentic and that it is, generally speaking, textually accurate. The implication of this is that the letter and the covenants represent mutual attestations of one another and that the religion of Islam was well-established, having attained a great level of maturity in the Prophet's lifetime.     

A non-commutative generalization of Łukasiewicz rings

The goal of the present article is to extend the study of commutative rings whose ideals form an MV-algebra as carried out by Belluce and Di Nola [1] to non-commutative rings. We study and characterize all rings whose ideals form a pseudo MV-algebra, which shall be called here generalized Łukasiewicz rings. We obtain that these are (up to isomorphism) exactly the direct sums of unitary special primary rings.     

Between daʿwa and Dialogue: Religious Engagement in Muslim-minority Environments

ABSTRACT

Muslim engagement in interfaith and intercultural dialogue began in earnest after the turn of the twenty-first century in response to the rise of global jihad. Both dialogue and jihad are outgrowths of da?wa, the call or mission of Islam, the principal mode of modern Islamic activism. The foundations were laid in the later part of the twentieth century by Muslim intellectual-activists living in non-Muslim environments, who played a special role in conceptualizing the new notion of dialogue and its relation to da?wa. This essay focuses on four pioneering figures, two from the indigenous context of India – the modernist Asghar Ali Engineer and the reformist ?ālim Wahiduddin Khan, and two from the diaspora milieu of the West – the Palestinian-American academic activist Ismail Raji al-Faruqi and the European Muslim spokesman Tariq Ramadan. Each represents a distinct religious orientation that also reflects a different phase in the evolution of modern Islamic discourse. Taken together, these intellectual-activists chart the trajectory of modern Islam from the early pre-Islamist liberal hopes to the present post- and neo-Islamist efforts to navigate between Western-dominated globalization and Islamist jihadism.