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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)
Model-theoretic syntax deals with the logical characterization of complexity classes. The first results in this area were obtained in the early and late Sixties of the last century. In these results it was established that languages recognised by finite string and tree automata are defin-able by means of monadic second-order logic (MSO). To be slightly more(More)
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 [16] 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)
The definitions of propositional modal logic are traditionally formulated in the following way. 1 First, a formal language is defined, usually with atomic formulas p, q,. .. and complex formulas involving the connec-tives ¬, → and the 2 operator. Models M for this language are then defined as triples W, R, V in which W is a nonempty set of worlds, R is an(More)