In this work we show how to use the focused intuitionistic logic system LJF as a framework for encoding several different intuitionistic and classical proof systems. The proof systems are encoded in a strong level of adequacy, namely the level of (open) derivations. Furthermore we show how to prove relative completeness between the different systems. By relative completeness we mean that the sy...

We present a new class of graded irreducible representations Leavitt path algebra. This is in the sense that its representation space not isomorphic to any existing simple Chen modules. The corresponding modules complete list which are graded, creating an exhaustive class: annihilator module equal either or this type. Our characterization primitive ideals algebra terms properties underlying gra...

The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...

We prove the #P-hardness of the counting problems associated with various satisfiability, graph, and combinatorial problems, when restricted to planar instances. These problems include 3Sat, 1-3Sat, 1-Ex3Sat, Minimum Vertex Cover, Minimum Dominating Set, Minimum Feedback Vertex Set, X3C, Partition Into Triangles, and Clique Cover. We also prove the NP-completeness of the Ambiguous Satisfiabilit...

In this paper we discuss two hybrid languages , L(∀) and L(↓), and provide them with complete axiomatizations. Both languages combine features of modal and classical logic. Like modal languages, they contain modal operators and have a Kripke semantics. Unlike modal languages, in these systems it is possible to ‘label’ states by using ∀ and ↓ to bind special state variables . This paper explores...

DEFINITION A relational query language Q is BP-complete if for each relational database D, the set of all relations defined by the queries of Q on D is equal to the set of all first-order definable relations over D. More formally, fix some infinite universe U of atomic data elements. A relational database schema S is a finite set of relation names, each with an associated arity. A relational da...

This is an exposition of Lambek’s strengthening and generalization of the deduction theorem in categories related to intuitionistic propositional logic. Essential notions of category theory are introduced so as to yield a simple reformulation of Lambek’s Functional Completeness Theorem, from which its main consequences can be readily drawn. The connections of the theoremwith combinatory logic, ...

The page-number of a directed acyclic graph (a DAG, for short) is the minimum k which DAG has topological order and k-coloring its edges such that no two same color cross, i.e., have alternating endpoints along order. In 1999, Heath Pemmaraju conjectured recognition DAGs with 2 NP-complete proved recognizing 6 [SIAM J. Computing, 1999]. Binucci et al. recently strengthened this result by provin...

The detection and parametrization of molecular clumps is the first step in studying them. We propose a method based on Local Density Clustering algorithm while physical parameters those are measured using Multiple Gaussian Model algorithm. One advantage applying to clump segmentation, high accuracy under different signal-to-noise levels. able deal with overlapping whose can be derived reliably....