A structural semantics is developed for a first-order logic, with infinite disjunctions and conjunctions, that is characterised algebraically by quantales. The model structures involved combine the “covering systems” approach of Kripke-Joyal intuitionistic semantics from topos theory with the ordered groupoid structures used to model various connectives in substructural logics. The latter are u...

It is shown that a partial unital with more than q √ q+1−√q points in the Desarguesian plane of order q can be extended to a unital.

We study Ore extensions of non-unital associative rings. provide a characterization simple differential polynomial rings $R[x;\delta ]$, under the hypothesis that $R$ is $s$-unital and $\ker (\delta )$ contains non-zero idempotent. This

The ‘the’ in the title hides a subtlety. A metric space induces not one but four topologies - by means of open sets, closed closure, and interior they just so happen to coincide. agreement between these structures arising from function d:X×X→[0,∞] is due combination axioms lattice structure [0,∞]. Further motivation materializes Lawvere's observation 1973 effect that (slightly generalized) cate...

A Buekenhout-Tits unital is defined to be a unital in PG(2, q2) obtained by coning the Tits ovoid using Buekenhout’s parabolic method. The full linear collineation group stabilizing this unital is computed, and related design questions are also addressed. While the answers to the design questions are very similar to those obtained for Buekenhout-Metz unitals, the group theoretic results are qui...

Let U be the classical unital in PG(2, q2) secant to `∞. By deriving PG(2, q) with respect to a derivation set disjoint from U we obtain a new unital U ′ in the Hall plane of order q2. We show that this unital contains O’Nan configurations and is not isomorphic to the known unitals of the Hall plane, hence it forms a new class of unitals in the Hall plane.

We introduce and launch a study of compression bases in unital groups. The family of all compressions on a compressible group and the family of all direct compressions on a unital group are examples of compression bases. In this article we show that the properties of the compatibility relation in a compressible group generalize to unital groups with compression bases. AMS Classification: Primar...

We provide algebraic semantics together with a sound and complete sequent calculus for information update due to epistemic actions. This semantics is flexible enough to accommodate incomplete as well as wrong information e.g. due to secrecy and deceit, as well as nested knowledge. We give a purely algebraic treatment of the muddy children puzzle, which moreover extends to situations where the c...