… of the original poset and as a meet of joins of elements from the original poset. We show …
system of down-sets of the poset, a closure system of up-sets of the poset, and a binary relation …

… In general, the completions obtained through the construction described in this section are
Δ1-completions that satisfy a weaker “parametrized” notion of compactness. In the following …

In this paper, the Δ 1 -completions of an L-ordered set are introduced and characterized,
which generalizes the Δ 1 -completions of a crisp partial ordered set. Then the relationship …

… the canonical extension of a poset P is to take the sets of all … applied to construct canonical
extensions for posets in [3], … , we arrive at the generality of Δ1-completions [7]. This class …

… We thus add antisymmetry and work with posets. … powerset functor: Pc : Pos → Pos, sending
a poset to its set of convex subsets, where a subset U of a poset (X, ≤) is convex if x, z ∈ U …

This thesis is an analytical study of canonicity for logics with a language consisting of
constants and implications. More specifically, logics associated with certain distinguished sub-…

… Canonical extensions of posets and monotonic poset expansions were defined by Dunn,
Gehrke and Palmigiano [25] and studied further in [41,34,96,85]. They have been applied to …

… It is not hard to see that the poset Q we defined above is the pushout in Poset. This is an
instance of a general way to construct the pushout in Poset, that we do not discuss any further …

Canonical extensions of Boolean algebras with operators were introduced in the seminal
paper of Jónsson and Tarski. The two defining properties of canonical extensions are the …

School of Computer Science, University of Manchester, Manchester, UK. E-mail: uli. sattler@
manchester. ac. uk. Description logics (DL)[1, 2] form the logical basis of state-of-the-art …