This note presents a method of interpreting the tree adjoining languages as the natural third step in a hierarchy that starts with the regular and the context-free languages. The central notion in this account is that of a higher-order substitution. Whereas in traditional presentations of rule systems for abstract language families the emphasis has been on… (More)
Context-free tree grammars, originally introduced by Rounds (1970a), are powerful grammar devices for the definition of tree languages. The properties of the class of context-free tree languages have been studied for more than three decades now. Particularly important here is the work by Engelfriet and Schmidt (1977, 1978). In the present paper, we consider… (More)
The main result of this paper is a description of linguistically motivated non-context-free phenomena equivalently in terms of regular tree languages (to express the re-cursive properties) and both a logical and an operational perspective (to establish the intended linguistic relations). The result is exemplified with a particular non-context-free… (More)
Well-nested word languages have been advertised as adequate formalizations of the notion of mild context-sensitivity. The main result of this paper is a characterization of well-nested tree languages in terms of simple attributed tree transducers.
In this paper we show that non-context-free phenomena can be captured using only limited logical means. In particular, we show how to encode a Tree Adjoining Grammar  into a weakly equivalent monadic context-free tree grammar (MCFTG). By viewing MCFTG-rules as terms in a free Lawvere theory, we can translate a given MCFTG into a regular tree grammar.… (More)
To Rogers (1994) we owe the insight that monadic second order predicate logic with multiple successors (MSO) is well suited in many respects as a realistic formal base for syntactic theorizing. However, the agreeable formal properties of this logic come at a cost: MSO is equivalent with the class of regular tree automata/grammars, and, thereby, with the… (More)
This paper puts TAGs into an algebraic perspective. The operation of tree adjunction is shown to be a special case of function substitution within a derived theory. The underlying process of theory derivation is illustrated with the concrete example of free continuous tree algebras.
Context-free tree grammars, originally introduced by Rounds ((Rounds, 1970)), are powerful grammar devices for the definition of tree languages. In the present paper , we consider a subclass of the class of context-free tree languages, namely the class of monadic simple context-free tree languages. For this class of context-free tree languages, a faithful… (More)