We present a framework to obtain valid inequalities for reverse convex set: the set of points in polyhedron that lie outside given open set. Reverse sets arise many models, including bilevel optimization and polynomial optimization. An intersection cut is well-known inequality generated from basic solution lies within introduce deriving solutions first propose an extension cuts defines two-term...

Any recursively enumerable extension of intuitionistic arithmetic which obeys the disjunction property obeys the numerical existence property. Any recursively enumerable extension of intuitionistic arithmetic proves its own disjunction property if and only if it proves its own inconsistency.

Abstract We systematically study several versions of the disjunction and existence properties in modal arithmetic. First, we newly introduce three classes $\mathrm {B}$ , $\Delta (\mathrm {B})$ $\Sigma formulas arithmetic basic them. Then, prove implications between properties. In particular, among other things, that for any consistent recursively enumerable extension T $\mathbf {PA}(\mathbf {K...

We present disjunction category (DC) labels, a new label format for enforcing information flow in the presence of mutually distrusting parties. DC labels can be ordered to form a lattice, based on propositional logic implication and conjunctive normal form. We introduce and prove soundness of decentralized privileges that are used in declassifying data, in addition to providing a notion of priv...

For the purposes of this note, I will assume that the Gricean account of scalar implicature is correct. I admit that I don’t have any qualms about making this assumption, since as far as I can tell, the Gricean account is the only game in town. But I thought I should mention it. With this preliminary out of the way, let us proceed to the problem area, and start by considering the following exam...

In this paper we address some central problems of combination of logics through the study of a very simple but highly informative case, the combination of the logics of disjunction and conjunction. At first it seems that it would be very easy to combine such logics, but the following problem arises: if we combine these logics in a straightforward way, distributivity holds. On the other hand, di...

Universal/existential quantifiers can be seen as generalization of logical conjunction/disjunction. The universal (existential) quantification of an open proposition is the conjunction (disjunction) of all its possible instantiations. In other words, conjunction (disjunction) is a special kind of universal (existential) quantification where the domain of the variable is restricted to the set of...

Reciprocal translocations produce imbalances by three types of disjunction which are, in decreasing frequency, adjacent 1, 3:1, and adjacent 2. Adjacent 1 disjunction produces duplication deficiencies of inverse topography to those of adjacent 2. The imbalanced chromosome segments in one of these types are balanced in the other. The disjunction 3:1 produces pure trisomies and monosomies. The fo...