We introduce -algebras and -algebras as semantic domains for data re nement of imperative programming languages. The functorial semantics of -calculus is given by using the adjunction between the category of -algebras and the category of small locally ordered categories. We de ne the notion of upward and downward simulation between the interpretations of atomic commands, and re nements between ...

In this paper we investigate the weak generative capacity of minimalist grammars with late adjunction. We show that by viewing the Specifier Island Condition as the union of three separate constraints, we obtain a more nuanced perspective on previous results on constraint interaction in minimalist grammars, as well as the beginning of a map of the interaction between late adjunction and movemen...

Sufficient conditions are provided for quantifier elimination to hold in a first-order theory. The conditions have two main purposes: (1) to ensure that satisfaction of existential formulas is reflected by an embedding; and (2) to guarantee the existence of a “minimal" model of the theory extending a model of the universal formulas entailed by the theory. The first goal is obtained by requiring...

This paper shows how to introduce predicative adjunction in a dependency grammar inspired from TAG, MTT and RG. The addition of predicative adjunction allows us to obtain a modular surface syntactic grammar, the derivation structures of which can be interpreted as semantic representations.

We introduce, comment and develop the Scott adjunction, mostly from point of view a category theorist. Besides its technical conceptual aspects, in nutshell we provide categorification topology over posets with directed suprema. From establish an adjunction between accessible categories colimits Grothendieck topoi. show that bicategory topoi is enriched $2$-category it has tensors respect to th...