This preface summarizes the wide-ranging claims about grammatical universals made by Greenberg (1966), a short book that is much less known by linguists than his 1963 article but that is equally important for understanding language systems.

Logic Journal of IGPL, 2005

This book provides an in-depth and advanced treatment of so-called non-monotonic logics, which were devised in order to represent defeasible inference (i.e., that kind of inference in which reasoners draw conclusions tentatively, reserving the right to retract them in the light of further information). Throughout this book the semantic side is stressed. Non-monotonic inference operations are studied within the framework of model theory. The main focus is on so-called preference-based semantics, the study of which was initiated by Shoham [20] among others. The book, which is based on a number of papers by the author, can be described as a research monograph. It brings the reader to the front line of current research in the field of non-monotonic logic and belief revision, by showing both recent achievements and directions of future investigations. The book is organized into nine chapters. Chapter 1 presents the basic concepts and results that are needed for what follows. Chapter 2 aims at clarifying the conceptual foundations of the different constructions of the author. Chapters 3 to 7 discuss representation results and problems for those constructions, and Chapter 8 is an attempt to integrate them into a single consistent whole. Chapter 9 summarizes the main points that have been made in the book, and ends with some suggestions as to useful ways forward. I shall here focus on the conceptual side of the book, outlining and commenting on some of its most noticeable aspects. In a review of this nature, one cannot enter into a detailed commentary. The reader must, thus, bear in mind that the material presented below represents only a thin sampling from a rather large volume. Chapter 2 considers various forms of common-sense reasoning, and argues that they can be based upon more basic semantical notions such as preference, size and distance, which (in some cases) are interdefinable. Much attention is paid to the core forms of common-sense reasoning that are traditionally discussed in the literature. These include: reasoning based on "what is normally the case"; default reasoning; counterfactual reasoning; revision. Here, in barest outline, is how the author analyzes them. The first kind of reasoning is studied within the tradition of the classic work by Kraus, Lehmann and Magidor − see [10]. Rules determining what is normal are written as conditional assertions having the form α |∼ β. This is read as "α normally entails β". Two evaluation rules for α |∼ β are introduced and compared. Both are formulated in terms of a preference relation ≺ (to be read as "is more normal than") on the set of possible worlds. One evaluation rule (referred to as the "minimal variant") is the standard one. It says that the relation α |∼ β holds whenever β holds in every world that is minimal under the relation ≺ in the set of all α-worlds. It is in general assumed that such minimal α-worlds exist − this is known as the Limit Assumption. One reason for ruling out the case where such minimal worlds do not exist, has to do with the fact that, in that specific scenario, the minimal account yields the somewhat counterintuitive result that α entails any proposition whatsoever. This observation leads the author * An enlightening discussion of the difference between representation and completeness theorems can be found in Makinson [14, p. 28-29].

Journal of Pure and Applied Algebra, 2001

Given a 2-category K admitting a calculus of bimodules, and a 2-monad T on it compatible with such calculus, we construct a 2-category L with a 2-monad S on it such that:

Given a 2-category K admitting a calculus of bimodules, and a 2-monad T on it compatible with such calculus, we construct a 2-category L with a 2-monad S on it such that: • S has the adjoint-pseudo-algebra property. • The 2-categories of pseudo-algebras of S and T are equivalent. Thus, coherent structures (pseudo-T-algebras) are transformed into universally characterised ones (adjoint-pseudo-S-algebras). The 2-category L consists of lax algebras for the pseudo-monad induced by T on the bicat-egory of bimodules of K. We give an intrinsic characterisation of pseudo-S-algebras in terms of representability. Two major consequences of the above transformation are the classifications of lax and strong morphisms, with the attendant coherence result for pseudo-algebras. We apply the theory in the context of internal categories and examine monoidal and monoidal globular categories (including their monoid classifiers) as well as pseudo-functors into Cat.

Bulletin of the South Ural State University. Ser. Computer Technologies, Automatic Control & Radioelectronics, 2018

Universals (from Latin "universalis"-general)-general concepts-are a subject matter of logicians since the ancient times. The question of universals represents the eternal issues. The nature of universals was thoroughly studied the philosophers of the Middle Ages. In IX-XIV centuries the scholastics continued the discussion about the essence of universals: do they really exist or are they certain names? The supporters of realism claimed that universals really existed and preceded the emergence of singular objects. Nominalists (from the Latin word 'nomen'-name) defended the contrary view point. In the article we emphasize the linguistic aspect. Mathematical linguistics develops methods of learning natural and formal languages. Linguistics, logic and mathematics are closely connected. Besides, there exists psycholinguistics as well. In our paper we consider current difficult sections: logic and linguistics of non-formalized and even non-formalizable concepts, the topic closely adjacent with the one discussed in the book by T.K. Kerimov of the same name. These sections broaden the opportunities of studying complex systems of logic and linguistics. As it was noted by the authors of "Mathematical linguistics" (R.G. Piotrovsky, K.B. Bektaev, A.A. Piotrovskaya) mathematics and a natural language represent semantic systems of information transfer. Moreover, there occurred a verbal analysis of mathematical problems solution. Language universal, a feature common for all the languages, is a kind of generalization of the language concept. The existential assertion of universals gives the opportunity to formulate a more grounded theory and practice of linguistics. The language universal determination is based both on extrapolation and empirical matter.

Philosophical Psychology, 2011

This is a book review of Language Universals by Morten H. Christiansen, Christopher Collins & Shimon Edelman (Eds.) New York: Oxford University Press, 2009

Language Universals, 2009

Erkenntnis, 1999

We prove that four theses commonly associated with coherentism are incompatible with the representation of a belief state as a logically closed set of sentences. The result is applied to the conventional coherence interpretation of the AGM theory of belief revision, which appears not to be tenable. Our argument also counts against the coherentistic acceptability of a certain form of propositional holism. We argue that the problems arise as an effect of ignoring the distinction between derived and non-derived beliefs, and we suggest that the kind of coherence relevant to epistemic justification is the coherence of non-derived beliefs.

Section 1 is an extended commentary on Edward Sapir's formulation nearly a century ago of what he considered two fundamental properties of human language, first that each one is a formally complete system of reference to experience and second that each one is formally distinct from every other. Section 2 considers some aspects of the development of these formulations, noting that they have been considered separately and not integrated as fully fleshed out systems of reference, as Sapir envisioned. Section 3 examines more closely what such an integration looks like in a case involving simple arithmetic. Section 4 begins with a brief review of the accomplishments of Greco-Roman logic and more recent developments in the theory of logic, leading to a consideration of what may be needed to fulfill Sapir's program. Section 5 summarizes some of my own recent research on extending first-order logic by replacing the unordered set of individuals with a specific ordering of a set of sets of individuals that is isomorphic to an ordering of a set of sets of numbers that contain no pairs of divisible numbers, which was investigated by Richard Dedekind shortly before the turn of the twentieth century.