In the tradition of Model Theoretic Syntax, we propose a logical approach to the description of grammars. We combine in one formalism several tools that are used throughout computer science for their power of abstraction: logic and lambda calculus. We propose then a high-level formalism for describing mildly context sensitive grammars and their semantic interpretation. As we rely on the correspondence between logic and finite state automata, our method combines conciseness with effectivity. We illustrate our approach with a simple linguistic model of several interleaved linguistic phenomena involving extraction. The level of abstraction provided by logic and lambda calculus allows us not only to use this linguistic model for several languages, namely English, German, and Dutch, but also for semantic interpretation.
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The notion of a meander of an ideal in lattices is generalized in two directions: to ideals in orthoposets and to ideals in QMV-algebras, and used to a characterization of subclasses of the above structures, namely Boolean orthoposets and QMV-algebras m which every ideal is closed under perspectivity, and to a characterization of Riesz ideals in orthoposets and perspectivity closed ideals in QMV algebras.
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