4 papers
Ultraposet, Distributive Lattice, and Coherent Locale
Lingyuan Ye
In this paper, we provide an alternative description of the duality result for distributive lattices and coherent locales using ultraposet. In particular, we show that there are fu…
Categorical structure in coherent theory of arithmetic
Lingyuan Ye
In this paper we provide a semantic and syntactic analysis of parametrised natural numbers object in coherent categories, or pr-coherent categories. Semantically, we show the defin…
Unification of Modal Logic via Topological Categories
Lingyuan Ye
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of…
Syntax and Consequence Relations -- A Categorical Perspective
Lingyuan Ye
In this paper, we use a categorical and functorial set up to model the syntax and inference of logics with algebraic signature, extending previous works on algebraisation of logics…