Language Family Tree

On Friday evening September 30, 2005, soon after finishing his lectures, Professor Sergei Anatol'evic# Starostin passed away at the Russian State University of the Humanities in Moscow, at the age of 52. It was a sudden death, caused by coronary thrombosis. With due respect for the outstanding scholar he was, his ashes were interred on October 4, on Donskoe Kladbis# c# e, Moscow's most graceful cemetry. He is survived by his widow, Dr. Natalja Starostina, née C‹ alisova, and his sons Dr.

Brief history of the issue The apparent self-evident location of the ancestral homeland of the Turkшc people in Altai logically led to the idea of the genetic relationship of the Mongolian and Turkic languages, which found expression in the so-called Altai theory. Based on the analysis of words of the main lexical core of the Turkic and Mongolian languages, lexical parallels between Chuvash, on the one hand, and Greek, Latin, and German, on the other, as well as taking into account other data, the genetic relationship of the Turkic and Mongolian languages ​​is decisively rejected.

A central morphological feature of Semitic languages is the so-called 't-stems' associated with the G, D and C stems. These forms attach a /t/ to the verbal root and often convey reflexive, reciprocal, or mediopassive action. The Semitic languages attest a puzzling mix of prefixed and infixed t-stem forms, and thus it has been challenging to reconstruct the original Proto-Semitic (PS) structure. The general consensus is that PS prefixed the /t/ to the root and the daughter languages underwent a series of complex phonological changes. This study argues that the /t/ was infixed in the G-stem and prefixed in the D-stem in PS. This reconstruction easily accounts for the variety of forms attested in the Semitic languages and only requires paradigm levelling in one stem to account for the attested variety. I argue this by raising problems with the consensus view and presenting inscriptional evidence of systemwide levelling in Northwest Semitic.

In this paper, we define the set of all n-ary C-formulas on the partial algebraic system of type and define the operation on the set. After this definition we have a unitary Menger algebra of rank. Finally, we show that the set of all C-hypersubstitutions for an algebraic system of the type with a binary operation on this set and the identity element forms a monoid.

Historical linguistics studies the relationships between languages as they change over time. Occasionally, speakers of a language will split into separate groups for any number of reasons and become isolated from each other. When this happens, the language they ...

This paper examines visual formalisms in comparative-historical linguistics from the perspective of the history of science. It shows that visual aids representing key understandings of language relationship have followed on pre-existing visual metaphors. Using this observation to pry open canonical metaphors of language relationship, it traces the ways in which these ``visualizations'' have both consolidated existing research programs and opened up new lines of inquiry for students and recent advocates of phylogenetic methods.

A hypersubstitution maps an algebra to an algebra of the same type, by replacing the operations by term operations. A hypersubstitution is called proper with respect to a variety if it is a mapping on this variety and it is called inner if it is an identity mapping on this variety. Proper as well as inner hypersubstitutions characterize a variety. Each inner hypersubstitution is a proper one but not conversely. In the present paper, we characterize the relationship between proper and inner hypersubstitutions for varieties of rings satisfying x n+1 ≈ x, in particular for n = 6.

A hypersubstitution of a fixed type τ maps n-ary operation symbols of the type to n-ary terms of the type. Such a mapping induces a unique mapping defined on the set of all terms of type τ. The kernel of this induced mapping is called the kernel of the hypersubstitution, and it is a fully invariant congruence relation on the (absolutely free) term algebra F τ (X) of the considered type ([2]). If V is a variety of type τ, we consider the composition of the natural homomorphism with the mapping induced by a hypersubstitution. The kernel of this mapping is called the semantical kernel of the hypersubstitution with respect to the given variety. If the pair (s, t) of terms belongs to the semantical kernel of a hypersubstitution, then this hypersubstitution equalizes s and t with respect to the variety. Generalizing the concept of a unifier, we define a semantical hyperunifier for a pair of terms with respect to a variety. The problem of finding a semantical hyperunifier with respect to a given variety for any two terms is then called the semantical hyperunification problem. We prove that the semantical kernel of a hypersubstitution is a fully invariant congruence relation on the absolutely free algebra of * Research supported by NSERC of Canada.

Hypersubstitutions are mappings which map operation symbols to terms. Terms can be visualized by trees. Hypersubstitutions can be extended to mappings defined on sets of trees. The nodes of the trees, describing terms, are labelled by operation symbols and by colors, i.e. certain positive integers. We are interested in mappings which map differently-colored operation symbols to different terms. In this paper we extend the theory of hypersubstitutions and solid varieties to multi-hypersubstitutions and colored solid varieties. We develop the interconnections between such colored terms and multi-hypersubstitutions and the equational theory of Universal Algebra. The collection of all varieties of a given type forms a complete lattice which is very complex and difficult to study; multi-hypersubstitutions and colored solid varieties offer a new method to study complete sublattices of this lattice.

Defining an (n + 1)-ary superposition operation S n on the set W τ (X n) of all n-ary terms of type τ , one obtains an algebra n − clone τ := (W τ (X n); S n , x 1 ,. .. , x n) of type (n + 1, 0,. .. , 0). The algebra n − clone τ is free in the variety of all Menger algebras ([9]). Using the operation S n there are different possibilities to define binary associative operations on the set W τ (X n) and on the cartesian power W τ (X n) n. In this paper we study idempotent and regular elements as well as Green's relations in semigroups of terms with these binary associative operations as fundamental operations.

There are five equivalence relations known as Green's relations definable on any semigroup or monoid, that is, on any algebra with a binary operation which is associative. In this paper, we examine whether Green's relations can be defined on algebras of any typeτ. Some sort of (super-)associativity is needed for such definitions to work, and we consider algebras which are clones of terms of typeτ, where the clone axioms including superassociativity hold. This allows us to define for any varietyVof typeτtwo Green's-like relationsℒVandℛVon the term clone of typeτ. We prove a number of properties of these two relations, and describe their behaviour whenVis a variety of semigroups.

There is a well-known connection between hyperidentities of an algebra and identities satisfied by the clone of the algebra. The clone of an algebra is a heterogeneous algebra, and the correspondence between hyperidentities and clone identities is rather complicated to work with. It is also of interest to study this correspondence in a restricted setting, that of hyperidentities of unary algebras (of arbitrary unary type) and identities in the unary clone of unary term operations. This unary clone is just a monoid, usually called the transition monoid of the unary algebra. This correspondence is an important one in automata theory, since any finite unary algebra A can be regarded as an automaton: the set A is regarded as a set of states, with one state chosen as an initial state and a subset of A chosen as the set of final states, and the operations of the algebra regarded as inputs. Then terms and identities over the unary algebra A correspond to monoid words from the free monoid generated by the operations of A. In this paper we study the correspondence between hyperidentities and clone identities in this special case of unary algebras and transition monoids. We also look at generalizations of this approach to algebras of type (n, n,. . .), and the corresponding n-clones, which correspond to tree automata of type (n, n,. . .). 1 Preliminaries There is a well-known connection, described by Taylor in [Tay;81], between hyperidentities of an algebra and identities satisfied by the clone of the algebra. The clone of an algebra is a heterogeneous algebra, and the correspondence between hyperidentities and clone identities is rather complicated to work with. In this paper we study this correspondence in a restricted setting, that of hyperidentities of unary algebras (of arbitrary unary type) and identities in the unary clone of unary term operations. This unary clone is just a monoid, usually called the transition monoid of the unary algebra. Since unary algebras correspond to finite automata, this correspondence is an important one in automata theory. In 1965 Schützenberger ([Sch;65]) found an interesting connection between star-free languages and aperiodic monoids. The precise formulation of the correspondence between certain sets of formal languages and sets of finite semigroups is due to Eilenberg (see [Eil;74]) and uses the concept of a pseudovariety. The connection between finite deterministic automata and regular languages is given by Kleene's famous theorem ((Kle;50]). In this paper we consider the third side, the connection between finite deterministic automata and their transition monoids. This connection allows for instance to apply the decomposition methods of finite semigroups using a wreath product in which the factors are, alternately, finite groups and finite aperiodic semigroups in automata theory ([Kro-R;65]). If s ≈ t is an identity in a finite unary algebra, then the word t A is recognized by the automaton corresponding to the unary algebra iff the word s A is recognized. If s ≈ t

Introduction. This article is an attempt to extract information about the interactions of
dialects of the Indo-European dialect continuum with each other using a comparative
analysis of the basic vocabularies of some Indo-European (IE) descendant languages.
The search for external borrowings and influence of a common substrate would help to
clarify the ethno-linguistic surrounding of the area where the IE proto-dialects developed.
In turn, these data are actual being pro and contra arguments of the well-known hypotheses
about the IE ancestral home.
Methodology and sources. The number of mutually understandable basic lexemes taken
in relation to the number of lexemes in the compared lists was chosen as a measure of the
interaction of IE dialects, indicators of their commonality.
207-word Swadesh lists of 12 languages in their possibly more ancient states were analysed.
For geographical binding of the IE language areal we have selected cross-borrowings
from/to neighboring / substrate non-IE languages, the ancient settlement areas of native
speakers of which are considered well-known.
Results and discussion. The results of the comparison of the basic vocabularies of 12 IE
languages have been interpreted in the form of a graph demonstrating the relative location
of areas of the corresponding IE dialects. Lexemes meaning 'predator (bear, lion, etc.)', 'cattle
(bull, ox)' determined the ethno-linguistic surrounding of the IE areal.
Conclusion. The relevant linguistic data permitted to identify in the IE dialect continuum the
core of proto-dialects: Baltic, Slavic, Aryan and Italic – and partially superimposed dialect
subcontinua:
– Balto-Greco-Aryo-Tocharo-Anatolian subcontinuum in the northern part of the IE areal;
– Tocharo-Celto-Germanic subcontinuum in the eastern part;
– Germano-Celto-Italo-Greco-Armeno-Baltic subcontinuum in the southern part;
– Balto-Slavo-Italo-Aryan subcontinuum in the western part.
The representation of the Proto-IE areal as a dialect continuum solves a number of
difficulties inherent in the most common model of a single IE proto-language.

MultiTree is an NFS-funded project collecting scholarly hypotheses about language relationships, and visualizing them on a web site in the form of trees or graphs. Two open online interfaces allow scholars, students, and the general public an easy access to search for language information or comparisons of competing hypotheses. One objective of the project was to facilitate research in historical linguistics. MultiTree has evolved to a much more powerful tool, it is not just a simple repository of scholarly information. In this paper we present the MultiTree interfaces and the impact of the project beyond the field of historical linguistics, including, among others, the use of standardized ISO language codes, and creating an interconnected database of language and dialect names, codes, publications, and authors. Further, we offer the dissemination of linguistic findings world-wide to both scholars and the general public, thus boosting the collaboration and accelerating the scientifi...

A country that, according to the famous historian 'Vincent Smith', possess the "unity in the midst of diversity", India is a huge land whose big part is inhabited by aboriginal people thought to have been living here from many ages back and who are of many types such as-'Kol', 'Bhil', 'Santal', 'Ho', 'Munda', 'Toto' 'Garo' and many others like these. In accordance with our course study, I, along with the members of the group I have been assigned to, have visited a small village named 'Keshiari' of 'Paschim Medinipur District' and made a survey on 'Munda' tribes living there and thus, have made a type of short documentation on "their geographical background", "historical background", "mythological background", "history of their race", "vocabulary", "their literature and language. I cordially thank Madam Arpita Raj (hon'ble HOD, English Department of our college) along with the other hon'ble faculty members of our English Department for guiding us cordially and thus, helping us do it and I thank Mr Ramsing Munda for guiding us in that field work. Santanu Chaudhuri PG (Semester-I) Roll Number-73 Department of English Detail of the guide and the place Geographical background Historical background Mythological background Brief detail of Munda race Munda vocabulary Munda language and literature Photographs captured in the field work Conclusion ITEM DETAIL Detail of the guide Name Mr Ramsing Munda Community Munda Occupation Employee of Indian Railway Detail of the place Village Hirdaa Locality Hasim Pur Mouza PO Keshiari District Paschim Medinipur PIN Code 721133 'Jharkhand' state. In 'West Bengal', the majority of this race is seen in 'Purulia' district. They are of the sister group of other tribal groups belonging to this 'Austroasiatic family' like 'Santal', 'Kol', Bhil', 'Toto'. A linguistic map indicating a ratio among the Munda groups in India.

A functional Menger ∩-algebra is a set of n-place functions containing n projections and closed under the so-called Menger's compositions of n-place functions and the set-theoretic intersection of functions. We give the abstract characterization for these subsets of functional Menger ∩-algebras which contain functions with fixed points.

A hypersubstitution maps the operation symbols of a type τ to terms of the same arity and can be uniquely extended to a mapping defined on the set of all terms of this type. In this paper we prove that the group of all clone automorphisms of an algebra A is isomorphic to a certain group of hypersubstitutions supposed the variety V (A) generated by A is solid.

Sets of terms of type τ are called tree languages (see [5]). On sets of tree languages superposition operations can be defined in such a way that the collection of all tree languages of type τ forms an abstract clone. Considering only sets of n-ary terms one obtains a Menger algebra (see e.g.[3]). From the superposition operations binary operations on tree languages can be derived. For the corresponding semigroups of tree languages we study idempotent and regular elements as well as Green's relations L and R.

A hypersubstitution maps the operation symbols of a type τ to terms of the same arity and can be uniquely extended to a mapping defined on the set of all terms of this type. In this paper we prove that the group of all clone automorphisms of an algebra A is isomorphic to a certain group of hypersubstitutions supposed the variety V (A) generated by A is solid. AMS Mathematics Subject Classification (2000):08B15, 08B25

Clones are sets of operations on a given base set which are closed under superposition of operations and which contain all the projection operations. A clone can be regarded as a heterogeneous or multi-based algebra, consisting of universe sets of n-ary operations, for n > 1, with the superposition operations for n,m > 1. Such an algebra is called a Menger system. For a fixed n, a set of n-ary operations with the (n 4-l)-ary superposition operation S n forms a homogeneous algebra called a Menger algebra of rank n. These structures can also be defined on sets of term operations of a fixed type r. The set of all terms of type r which contain at least one operation symbol forms such a clone-like structure which we call the pre-clone of type r. We determine a generating system for this pre-clone. A similar structure can be formed using the terms with respect to a variety, giving the pre-clone of a variety. The normalization of a variety is the model class of all identities a « i of the variety for which both s and t contain at least one operation symbol. We show that identities in the pre-clone of the normalization of a variety correspond to normal hyperidentities in the normalization. We use the well-known Galois connection Id-Mod between sets of identities and classes of algebras of a given type: for any set £ of identities we Research of the second author supported by NSERC of Canada.

Two elements a;b of a monoid M are related with respect to Green's relation L if there are elements c;d 2 M such that a = cb and b = da. The flrst equation a = cb deflnes Green's quasiorderL on M. This quasiorder and Green's relations can also be deflned for Menger algebras. After this deflnition we formulate some elementary propositions for Green's quasiorderL and then we considerL in several concrete Menger algebras: n-ary operations, terms and tree languages. In any case we give a characterization of L and ofL.

We consider four useful measures of the complexity of a term: the maximum depth (usually called the depth), the minimum depth, the variable count, and the operation count. For each of these, we produce a formula for the complexity of the composition S n m (s, t 1 ,...,t n) in terms of the complexity of the inputs s, t 1 ,..., t n. As a corollary, we also obtain formulas for the complexity ofσ [t] in terms of the complexity of t when t is a compound term and σ is a hypersubstitution. We then apply these formulas to the theory of M-solid varieties, examining the k-normalization chains of a variety with respect to the four complexity measures.

MultiTree is an NFS-funded project collecting scholarly hypotheses about language relationships, and visualizing them on a web site in the form of trees or graphs. Two open online interfaces allow scholars, students, and the general public an easy access to search for language information or comparisons of competing hypotheses. One objective of the project was to facilitate research in historical linguistics. MultiTree has evolved to a much more powerful tool, it is not just a simple repository of scholarly information. In this paper we present the MultiTree interfaces and the impact of the project beyond the field of historical linguistics, including, among others, the use of standardized ISO language codes, and creating an interconnected database of language and dialect names, codes, publications, and authors. Further, we offer the dissemination of linguistic findings world-wide to both scholars and the general public, thus boosting the collaboration and accelerating the scientifi...

This thesis aims to examine the lexical and typological change found in the Western European language families of Germanic, Romance and Celtic over the last two millennia. The method used was to create one lexical and one typological database and the data was analysed according to etic grids. Tree models were generated from the results of the databases and the groups found in the tree models were mapped out on a map over Western Europe. The lexical results were similar to traditional classifications. The lexical results also showed that the changes appeared according to a pattern that could be described by the wave theory where lexical changes spread from the centre to the periphery. The results of the typological data were different from traditional classifications as it did not follow the boundaries of the three language families. In general the wave theory was applicable to a lesser extent to the typological data but it was relevant for the verbal morphology. Contrary to the lexi...

This thesis aims to examine the lexical and typological change found in the Western European language families of Germanic, Romance and Celtic over the last two millennia. The method used was to create one lexical and one typological database and the data was analysed according to etic grids. Tree models were generated from the results of the databases and the groups found in the tree models were mapped out on a map over Western Europe. The lexical results were similar to traditional classifications. The lexical results also showed that the changes appeared according to a pattern that could be described by the wave theory where lexical changes spread from the centre to the periphery. The results of the typological data were different from traditional classifications as it did not follow the boundaries of the three language families. In general the wave theory was applicable to a lesser extent to the typological data but it was relevant for the verbal morphology. Contrary to the lexical results the typological results indicated the existence of conservative centres with the peripheral languages being more typologically innovative. The conclusions drawn were that lexical change and typological change are two diametrically different and independent processes.

We describe the reconstruction of a phylogeny for a set of taxa, with a character-based cladistics approach, in a declarative knowledge representation formalism, and show how to use computational methods of answer set programming to generate conjectures about the evolution of the given taxa. We have applied this computational method in two domains: to historical analysis of languages, and to historical analysis of parasite-host systems. In particular, using this method, we have computed some plausible phylogenies for Chinese dialects, for Indo-European language groups, and for Alcataenia species. Some of these plausible phylogenies are different from the ones computed by other software. Using this method, we can easily describe domain specific information (e.g. temporal and geographical constraints), and thus prevent the reconstruction of some phylogenies that are not plausible.

This thesis aims to examine the lexical and typological change found in the Western European language families of Germanic, Romance and Celtic over the last two millennia. The method used was to create one lexical and one typological database and the data was analysed according to etic grids. Tree models were generated from the results of the databases and the groups found in the tree models were mapped out on a map over Western Europe. The lexical results were similar to traditional classifications. The lexical results also showed that the changes appeared according to a pattern that could be described by the wave theory where lexical changes spread from the centre to the periphery. The results of the typological data were different from traditional classifications as it did not follow the boundaries of the three language families. In general the wave theory was applicable to a lesser extent to the typological data but it was relevant for the verbal morphology. Contrary to the lexical results the typological results indicated the existence of conservative centres with the peripheral languages being more typologically innovative. The conclusions drawn were that lexical change and typological change are two diametrically different and independent processes.

This paper, written as a term paper for the course History of Linguistics at Leiden, reviews the historical origins and theoretical underpinnings of two competing models for representing linguistic genealogy: the tree model and the wave model. I make the argument that the wave model is a more powerful tool than the tree model for understanding linguistic genealogy.

This study investigates early employments of family trees in the modern sciences, in order to historicise their iconic status and now established uses, notably in evolutionary biology and linguistics. Moving beyond disciplinary accounts to consider the wider cultural background, it examines how early uses within the sciences transformed family trees as a format of visual representation, as well as the meanings invested in them.

Historical writing about trees in the modern sciences is heavily tilted towards evolutionary biology, especially the iconic diagrams associated with Darwinism. Trees of Knowledge shifts the focus to France in the wake of the Revolution, when family trees were first put to use in a number of disparate academic fields. Through three case studies drawn from across the disciplines, it investigates the simultaneous appearance of trees in natural history, language studies, and music theory. Augustin Augier’s tree of plant families, Félix Gallet’s family tree of dead and living languages, and Henri Montan Berton’s family tree of chords served diverse ends, yet all exploited the familiar shape of genealogy.

While outlining how genealogical trees once constituted a more general resource in scholarly knowledge production—employed primarily as pedagogical tools—this study argues that family trees entered the modern sciences independently of the evolutionary theories they were later made to illustrate. The trees from post-revolutionary France occasionally charted development over time, yet more often they served to visualise organic hierarchy and perfect order. In bringing this neglected history to light, Trees of Knowledge provides not only a rich account of the rise of tree thinking in the modern sciences, but also a pragmatic methodology for approaching the dynamic interplay of metaphor, visual representation, and knowledge production in the history of science.

Arm. ողջամբ ołǰamb 'safe and sound' is analyzed is the same thing (but with the opposite order of component) as ambołǰ 'whole, integral, intact, pure'.  One of the two words is found in Olsen 1999, the other in Martirosyan, which may be why this analysis has not been proposed before.

A családfamodell a nyelvek rokonsági viszonyait
ábrázolja. A családfamodell arra a megfigyelésre épül,
hogy a nyelvek generációról generációra változnak –
mivel azonban a változások a beszélők különböző
csoportjaiban különböző irányúak lehetnek, változatok
alakulnak ki, melyek egymástól egyre távolodva önálló
nyelvekké fejlődnek. A folyamat újra és újra lezajlik,
tehát a megszülető lánynyelvek maguk is alapnyelvként
osztódnak tovább.

This collection of short articles contains all my contributions in 2016 to the blog "The genealogical world of phylogenetic networks". The topics vary greatly in content, but most of them center around questions of how network methods can be used in historical linguistic research.

This collection of short articles contains all my contributions in 2017 to the blog "The genealogical world of phylogenetic networks". The topics vary greatly in content, but most of them center around questions of how network methods can be used in historical linguistic research.

Leibniz’s philosophical and philological interests overlapped at many points, and some of his fundamental philosophical notions shaped his views on language, particularly his thinking about language history, in decisive ways. Although he is better known for his work on universal language, his writings on natural language and language history are worth consideration both for their subtlety and for the insight they give into the complex history of thought on this topic. The principles of sufficient reason, praedicatum inest subjecto, and his doctrine of marks and traces are echoed in his work on natural languages and in his account of their histories. He attempted to reconcile philosophical investigations of the natural languages with the Biblical accounts of the confusion of languages at Babel, and in his approach to etymology he participated in a long tradition of thinking about language and its essence as hidden or secret, the truth of which remains scattered in signs and which etymology alone may occasionally reveal.

Specialization in linguistics vs. biological informatics leads to widespread misunderstandings and false results caused by poor knowledge of the essential conditions of the respective methods and data applied. These are analyzed and the insights used to assess the recent glut of attempts to employ methods from biological informatics in establishing new phylogenies of Indo-European languages.

Since its popularization by August Schleicher (1853, 1873), the most common way of representing a language family has been as a tree. Tree representations are highly amenable to computational methods (as in biology), and they are sufficiently restrictive that they allow one to deduce the features that characterize each clade. The tree model has well-recognised limitations (Saussure 1995 [1916], Gray et al. 2010, etc.); in particular, it assumes that the language family evolved primarily by successive demographic splits, and so is incapable of representing (former) dialect networks. However, while other ways of representing a language family have occasionally been proposed, starting from Schmidt’s (1872) “Wave Model”, few of these alternatives are as precisely-specified or as restrictive as the tree model. In this presentation, we describe a computational method that allows us to represent the structure of a language family without assuming that it evolved by successive splits, and in such a way that we can identify the exact features that characterize each subgroup (allowing that subgroups may overlap). This method is correspondence analysis.
Correspondence analysis (also known as optimal scaling, or dual scaling) allows one to take a binary matrix tabulating the presence or absence of m features in each of n items, and produce a solution in min(m – 1, n – 1) dimensions in which there are points that represent the items as well as points that represent the features. Crucially, the point representing each item is close to the points representing the features it exhibits; likewise, the point representing each feature is close to the points representing the items that exhibit it. Correspondence analysis has been successfully used in social network analysis as a representation of bipartite “affiliation” networks (Wasserman & Faust 1994: 334–342).
We applied correspondence analysis (using the FactoMineR package in R: Lé et al. 2008) to a database of “plausible cognacy” judgments for a selection of 26 Germanic languages. In our data, each column represents a language (e.g. English, German, etc.), and each row represents a word that looks similar across at least some of the languages (e.g. water, Wasser, etc.), whether due to shared inheritance or borrowing. We would expect the clusters in the correspondence analysis solution to correspond to genealogical subgroups or to contact zones.
Indeed, this is what we find. As seen in Figure 1, the languages divide neatly into the well-established North Germanic (Scandinavian), East Germanic (Gothic) and West Germanic subgroups, as well as a cluster consisting of English and Scots (i.e. languages of the British Isles). In addition, we can see that within each subgroup, there are “central” and “peripheral” members—e.g. Danish (a North Germanic language) approaches the West Germanic languages. Most importantly, these language clusters correspond directly to clusters of cognate sets, which means that (unlike with many other alternatives to the tree model), we have immediate access to the evidence that supports each cluster.

A functional Menger $\cap$-algebra is a set of n-place functions containing n projections and closed under the so-called Menger's compositions of n-place functions and the set-theoretic intersection of functions. We give the abstract characterization for these subsets of functional Menger $\cap$-algebras which contain functions with fixed points.

A functional Menger system is a set of n-place functions containing n projections and closed under the so-called Menger's composition of n-place functions. We give the abstract characterization for subsets of these functional systems which contain functions having one common fixed point.

A functional Menger ∩ -algebra is a set of n-place functions containing n projections and closed under the so-called Menger's composition of n-place functions and the set-theoretic intersection of functions. We give the abstract characterization for these subsets of functional Menger ∩ -algebras which contain functions with fixed points.

Dünya dillerinin kaynağını bulmak uzun zamandır dilbilimcilerin hayali olmuştur. Bunun için yapılmış olan girişimler 18. Yüzyılın sonlarında başlamış ve şu ana kadar da çok verimsiz olmuştur. Dilin süreç içerisinde değişkenliğini göz önüne aldığımızda, bir dili sınıflandırmak, o dilin birkaç yüzyıl öncesinde nasıl bir yapısı olduğunu gösteren bir kayıt olmadan, son derece zor gözükmektedir. Ne var ki sürekli yeni verilerin bulunması, çok farklı dil akrabalıkları üzerine ışık tutulmaktadır. Aksan’ın da ileri sürdüğü gibi, biçim ya da yapı bakımından dilleri öbeklere ayıran bugünkü sınıflamanın temelini-daha önce birtakım ilkeler konmuş olmakla birlikte-ünlü Alman dilcisi August Schleicher’e dayandırabiliriz. Bilginin ünlü soykütüğü kuramı (Stammbaumtheorie) Hint-Avrupa ailesindeki dilleri, tıpkı bir ağacın dallara ayrılması, dallanmasında olduğu gibi, bir kökten ayrılan dallarla göstermiştir.