Adding Threshold Concepts to the Description Logic EL

We introduce an extension of the lightweight Description Logic EL that allows us to de_ne concepts in an approximate way. For this purpose, we use a graded membership function, which for each individual and concept yields a number in the interval [0, 1] expressing the degree to which the individual belongs to the concept. Threshold concepts C~t for ~ then collect all the individuals that belong to C with degree ~ t. We generalize a well-known characterization of membership in EL concepts to construct a specific graded membership function deg, and investigate the complexity of reasoning in the Description Logic τEL(deg), which extends EL by threshold concepts defined using deg. We also compare the instance problem for threshold concepts of the form C>t in τEL(deg) with the relaxed instance queries of Ecke et al

Extending the Description Logic τEL(deg) with Acyclic TBoxes

In a previous paper, we have introduced an extension of the lightweight Description Logic EL that allows us to define concepts in an approximate way. For this purpose, we have defined a graded membership function deg, which for each individual and concept yields a number in the interval [0; 1] expressing the degree to which the individual belongs to the concept. Threshold concepts C~t for ~ 2 ∈ {, ≥} then collect all the individuals that belong to C with degree ~ t. We have then investigated the complexity of reasoning in the Description Logic τEL(deg), which is obtained from EL by adding such threshold concepts. In the present paper, we extend these results, which were obtained for reasoning without TBoxes, to the case of reasoning w.r.t. acyclic TBoxes. Surprisingly, this is not as easy as might have been expected. On the one hand, one must be quite careful to define acyclic TBoxes such that they still just introduce abbreviations for complex concepts, and thus can be unfolded. On the other hand, it turns out that, in contrast to the case of EL, adding acyclic TBoxes to τEL(deg) increases the complexity of reasoning by at least on level of the polynomial hierarchy

Decidability and Complexity of Threshold Description Logics Induced by Concept Similarity Measures

In a recent research paper, we have proposed an extension of the lightweight Description Logic (DL) EL in which concepts can be defined in an approximate way. To this purpose, the notion of a graded membership function m, which instead of a Boolean membership value 0 or 1 yields a membership degree from the interval [0; 1], was introduced. Threshold concepts can then, for example, require that an individual belongs to a concept C with degree at least 0:8. Reasoning in the threshold DL T EL(m) obtained this way of course depends on the employed graded membership function m. The paper defines a specific such function, called deg, and determines the exact complexity of reasoning in T EL(deg). In addition, it shows how concept similarity measures (CSMs) ~ satisfying certain properties can be used to define graded membership functions m~, but it does not investigate the complexity of reasoning in the induced threshold DLs T EL(m~). In the present paper, we start filling this gap. In particular, we show that computability of ~ implies decidability of T EL(m~), and we introduce a class of CSMs for which reasoning in the induced threshold DLs has the same complexity as in T EL(deg)

Quantum Logic between Remote Quantum Registers

We analyze two approaches to quantum state transfer in solid-state spin systems. First, we consider unpolarized spin-chains and extend previous analysis to various experimentally relevant imperfections, including quenched disorder, dynamical decoherence, and uncompensated long range coupling. In finite-length chains, the interplay between disorder-induced localization and decoherence yields a natural optimal channel fidelity, which we calculate. Long-range dipolar couplings induce a finite intrinsic lifetime for the mediating eigenmode; extensive numerical simulations of dipolar chains of lengths up to L=12 show remarkably high fidelity despite these decay processes. We further consider the extension of the protocol to bosonic systems of coupled oscillators. Second, we introduce a quantum mirror based architecture for universal quantum computing which exploits all of the spins in the system as potential qubits. While this dramatically increases the number of qubits available, the composite operations required to manipulate "dark" spin qubits significantly raise the error threshold for robust operation. Finally, as an example, we demonstrate that eigenmode-mediated state transfer can enable robust long-range logic between spatially separated Nitrogen-Vacancy registers in diamond; numerical simulations confirm that high fidelity gates are achievable even in the presence of moderate disorder.Comment: 15 pages, 10 figure

Comparison of Various Pipelined and Non-Pipelined SCl 8051 ALUs

This paper describes the development of an 8-bit SCL 8051 ALU with two versions: SCL 8051 ALU with nsleep and sleep signals and SCL 8051 ALU without nsleep. Both versions have combinational logic (C/L), registers, and completion components, which all utilize slept gates. Both three-stage pipelined and non-pipelined designs were examined for both versions. The four designs were compared in terms of area, speed, leakage power, average power and energy per operation. The SCL 8051 ALU without nsleep is smaller and faster, but it has greater leakage power. It also has lower average power, and less energy consumption than the SCL 8051 ALU with both nsleep and sleep signals. The pipelined SCL 8051 ALU is bigger, slower, and has larger leakage power, average power and energy consumption than the non-pipelined SCL 8051 ALU

A Declarative Semantics for CLP with Qualification and Proximity

Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause annotations based on uncertain truth values, qualification values as a generalization of uncertain truth values, and unification based on proximity relations. On the other hand, the CLP scheme has established itself as a powerful extension of LP that supports efficient computation over specialized domains while keeping a clean declarative semantics. In this paper we propose a new scheme SQCLP designed as an extension of CLP that supports qualification values and proximity relations. We show that several previous proposals can be viewed as particular cases of the new scheme, obtained by partial instantiation. We present a declarative semantics for SQCLP that is based on observables, providing fixpoint and proof-theoretical characterizations of least program models as well as an implementation-independent notion of goal solutions.Comment: 17 pages, 26th Int'l. Conference on Logic Programming (ICLP'10