Recently, proposals have been made to combine Tree Adjoining Grammar (TAG) with either Glue or Flat Semantic Representation Languages. In this paper, we additionally specify the combination of TAG with λ-based semantics and compare the three approaches. We observe several invariants and suggest that semantic construction in TAG is governed by a set of general principles that can be used to faci...

Our work over the past years shows that not only the collection of (for instance) all topological spaces gives rise to a category, but also each topological space can be seen individually as a category by interpreting the convergence relation x −→ x between ultrafilters and points of a topological space X as arrows in X. Naturally, this point of view opens the door to the use of concepts and id...

This paper proposes a combinatory algorithm of structure building within the bare phrase structure theory of the Minimalist program, which assumes operation Merge as the basic structure building device. The proposed algorithm enforces a particular timing of application of 'substitution' Merge and 'adjunction' Merge. In particular, I argue that XP adjuncts are Merged 'postcyclically' in overt sy...

We develop a general setting for the treatment of extensions of categories by means of freely adjoined morphisms. To this end, we study what we call composition graphs, i.e. large graphs with a partial binary operation on which we impose only rudimentary requirements. The quasicategory thus obtained contains the quasicategory of all categories as a full reflective subquasicategory; we character...

We exhibit an adjunction between a category of abstract algebras partial functions and set quotients. The are those atomic representable as collection closed under relative complement domain restriction; the morphisms complete homomorphisms. This generalises discrete Boolean sets. define compatible completion algebra, show that monad induced by our yields any algebra. As corollary, restricts to...

This paper sets two goals. The first is to present algebraists with a purely order-theoretic derivation of the adjunction between the category DCPO of DCPOs (directed complete posets) and the category Frm of frames. This adjunction restricts to several Stone-type dualities which are well-known and of considerable interest to computer scientists. The second goal is to describe the object classes...