KD is nullary

Clones with Nullary Operations

This article discusses clones with nullary operations and the corresponding relational clones, both defined on arbitrary sets. By means of two pairs of kernel and closure operators, the relationship between such clones and clones in the traditional sense, i.e. without nullary operations, is investigated, and in particular the latter type of clones is located in the lattice of all clones. Finall...

A note on clones with nullary operations

KD 45 is not a doxastic logic

The modal logic KD45 is frequently presented as the standard account of the logic of belief for a single agent, where perhaps that agent is viewed as having the doxastic properties of a deductive database. However, KD45 is absurdly strong for such a reading. Specifically, • K, D and 5 together are logically incoherent, even as an account of the theory of a trivial database. • K and 5 together m...

Blending margins: the modal logic K has nullary unification type

We investigate properties of the formula p → 2p in the basic modal logic K. We show that K satisfies an infinitary weak variant of the rule of margins, which leads to a description of a complete set of unifiers of p → 2p. Using this information, we establish that K has nullary unification type. Moreover, we show that the formula p → 2p is admissibly saturated, but not exact.

Cutting Edge: Multiple autoimmune pathways in kd/kd mice.

The kidney disease (kd) mutation was transferred to a C57BL/6 (B6) background by selection for closely linked microsatellite markers. The resulting congenic strain, B6.kd, was mated with partners homozygous for targeted mutations of CD4, CD8, CD28, IL-2, recombinase-activating gene-1 (Rag-1), ICAM-1, or beta(2)-microglobulin. In most of the resulting double mutants, kidney disease occurred as r...