17164164
Towards Measuring Similarity in Description Logics
We review several kinds of previously studied concept similarity measures, and then rephrase them in terms of a simple DL. We discuss the difficulties encountered in trying to generalize these formulations to more complex DLs, and settle on one based on probability/information theory as being the most principled. 1 Motivation and Goals The idea of measuring concept similarity has received considerable attention in several domains, including psychology, cognitive science, and computational linguistics and information retrieval. This work has been applied and extended recently in the field of Information Integration, which often relies on ontologies and hence concepts described in DLs. Most past work has concentrated on the similarity of “atomic” concepts (word senses), rather than composite, defined concepts, which are the stock-in-trade of DLs. This has sometimes been characterized as the difference between considering nouns appearing in a dictionary, e.g. WordNet, and general arbitrary noun phrases. The modest goal of this paper is to consider the problem of generalizing previous efforts to define similarity for primitive concepts to composite ones. To this end, we review three classes of approaches found in the current literature, rephrase them in terms of a very simple description logic, and then try to generalize this to a complex DL. These extensions invite a host of new questions that we leave open for further research. To begin with, we make several observations about possible real-valued function(s) sim(C,D) that would measure concept similarity in general. First, any effort to assess simlarity via absolute numeric values seems ill-advised — in small experiments even human judgments have been shown to correlate only in the .91 to .94 range. A less exacting target is to use sim to provide relative orderings over concepts. Some researchers have studied a complementary measure, distance dist(C,D), which can similarly be used for ordering alternatives. To the extent that two functions provide similar orderings (e.g., consistently differing by a constant factor) they are essentially indistinguishable for our purposes. Nonetheless, there are two important general properties that are widely agreed to be desirable for sim(C,D): 1. sim(C,D) is positively correlated with the amount of commonality between C and D. 2. sim(C,D) is negatively correlated with the amount of difference between C and D. The key question then becomes how to measure “commonality”; in turn, this is related to how information about the concept is captured. 2 Three approaches to concept similarity Clearly, in order to compare concepts we need to consider what information we have available about them. We follow Rodriguez [14] in categorizing a variety of approaches, and for each we give a few of the best known functions, which we shall follow. Feature-based Models In this approach, a concept C is characterized by a a set of features ftrs(C). In his pioneering work on similarity, the psychologist Amos Tversky [16] introduced two families of measures: the “contrast model”, where the similarity of C and D is a linear function: contrasttv(C,D) = θf(ftrs(C) ∩ ftrs(D)) − αf(ftrs(C) \ ftrs(D))− βf(ftrs(D) \ ftrs(C)), where \ is set difference, θ, α, and β are non-negative constants, and where f(.) is often taken as the count of features in the set (written |.|). Tversky also proposed a normalized “ratio model”, where similarity is a fraction involving these sets:
1960492
Challenges in securing voice over IP
Although VoIP offers lower cost and greater flexibility, it can also introduce significant risks and vulnerabilities. This article explains the challenges of VoIP security and outlines steps for helping to secure an organization's VoIP network.
456544
The Tractability of Global Constraints
Constraint propagation is one of the techniques central to the success of constraint programming. Fast algorithms are used to prune the search space either before or during backtracking search. Propagating global constraints is intractable in general. In this paper, we characterize a number of important questions related to constraint propagation. For example, we consider the two questions: "Is this problem generalized arc-consistent?" and "What are the maximal generalized arc-consistent domains?". We identify dependencies between the tractability and intractability of these questions for finite domain variables. Finally, we prove intractability for a range of global constraints.
1064003
Towards an Understanding of Hill-Climbing Procedures for SAT
Recently several local hill-climbing procedures for propositional satisfiability have been proposed which are able to solve large and difficult problems beyond the reach of conventional algorithms like Davis-Putnam. By the introduction of some new variants of these procedures, we provide strong experimental evidence to support our conjecture that neither greediness nor randomness is important in these procedures. One of the variants introduced seems to offer significant improvements over earlier procedures. In addition, we investigate experimentally how performance depends on their parameters. Our results suggest that runtime scales less than simply exponentially in the problem size.
14427821
A calculus for and termination of rippling
Rippling is a type of rewriting developed for inductive theorem proving that uses annotations to direct search. Rippling has many desirable properties: for example, it is highly goal directed, usually involves little search, and always terminates. In this paper we give a new and more general formalization of rippling. We introduce a simple calculus for rewriting annotated terms, close in spirit to first-order rewriting, and prove that is has the formal properties desired of rippling. Next we develop criteria for proving the termination of such annotated rewriting, and introduce orders on annotated terms that lead to termination. In addition, we show how to make rippling more flexible by adapting the termination orders to the problem domain. Our work has practical as well as theoretical advantages: it has led to a very simple implementation of rippling that has been integrated in the Edinburgh CLAM system.
5729340
A Divergence Critic for Inductive Proof
Inductive theorem provers often diverge. This paper describes a simple critic, a computer program which monitors the construction of inductive proofs attempting to identify diverging proof attempts. Divergence is recognized by means of a "difference matching" procedure. The critic then proposes lemmas and generalizations which "ripple" these differences away so that the proof can go through without divergence. The critic enables the theorem prover Spike to prove many theorems completely automatically from the definitions alone.
27430046
Automatic Identification of Mathematical Concepts
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