Lambek categorial grammars is a class of formal grammars based on the Lambek calculus. Pentus proved in 1993 that they generate exactly the class of context-free languages without the empty word. In this paper, we study categorial grammars based on the Lambek calculus with the permutation rule LP. Of particular interest is the product-free fragment of LP called the Lambek-van Benthem calculus LBC. Buszkowski in his 1984 paper conjectured that grammars based on the Lambek-van Benthem calculus (LBC-grammars for short) generate (...) exactly permutation closures of context-free languages. In this paper, we disprove this conjecture by presenting a language generated by an LBC-grammar that is not a permutation closure of any context-free language. Firstly, we introduce an ad-hoc modification of vector addition systems called linearly-restricted branching vector addition systems with states and additional memory (LRBVASSAMs for short) and prove that the latter are equivalent to LBC-grammars. Then we construct an LRBVASSAM that generates a non-semilinear set and thus disprove Buszkowski’s conjecture. Since Buszkowski’s conjecture is false, not so much is known about the languages generated by LBC-grammars or by LP-grammars. The equivalence of LRBVASSAMs and LBC-grammars allows us to establish a number of their properties. We show that LP-grammars generate the same class of languages as LBC-grammars; that is, removing product from LP does not decrease expressive power of corresponding categorial grammars. We also prove that this class of languages is closed under union, intersection, concatenation, and Kleene plus. (shrink)

This paper focuses on what can be said to be the definitive features of the approach to theology by three Russian theologians: Fathers Sergii Bulgakov and Georges Florovsky as well as the Venerable Father Sophrony Sakharov. The article argues that the following common themes characterize the nature of their theology. First, personalism, in other words, the use of the term “person”, which they extensively applied to both God and human and angelic beings. The concept of person is indispensable in the (...) thought of all three theologians. The second common theme is how the authors understood the relationship between theology and experience and what is the significance of religious experience for philosophical theology. Finally, all three theologians agree that when theological truths are expressed in human language the problem of interpretation consequently arises. However, they answer in different ways the question of the number and status of possible theological languages. I conclude that it is St. Sophrony Sakharov who in his life and theology realized Florovsky’s famous call for a neo-patristic synthesis. (shrink)

"Proceedings of an international workshop held in memory of Professor Shlomo Pines at the Institute for Advanced Studies, The Hebrew University of Jerusalem, 28 February - 2 March 2005".

This paper examines the relationship between the generation and suspension of meaning in Dostoevsky’s Demons with reference to Bakhtin’s thesis that one’s meaning is defined by someone else’s answer. By generation I mean both the generational conflict between fathers and children and the generative power of language. It is the division between what one says and what one means that troubles Stavrogin. He has his authorship usurped by others and is not in control of his own discourse. Although the document (...) headed “From Stavrogin” in the unpublished chapter “At Tikhon’s” has traditionally been called a confession by critics, that is misleading, for, as the narrator points, the pages look very much like a political tract, and what is at stake in his dialogue with Tikhon is the very question: is it a confession or not? This document also raises questions about the authenticity of signatures, as does Prince Myshkin’s counterfeiting of someone else’s signature in The Idiot. (shrink)