529377
Encoding Functional Relations in Scunak
We describe how a set-theoretic foundation for mathematics can be encoded in the new system Scunak. We then discuss an encoding of the construction of functions as functional relations in untyped set theory. Using the dependent type theory of Scunak, we can define object level application and lambda abstraction operators (in the spirit of higher-order abstract syntax) mediating between functions in the (meta-level) type theory and (object-level) functional relations. The encoding has also been exported to Automath and Twelf.
18741005
Reasoning in Extensional Type Theory with Equality
We describe methods for automated theorem proving in extensional type theory with primitive equality. We discuss a complete, cut-free sequent calculus as well as a compact representation of cut-free (ground) proofs as extensional expansion dags. Automated proof search can be realized using a few operations to manipulate extensional expansion dags with variables. These search operations form a basis for complete search procedures. Procedures based on these ideas are implemented in the higher-order theorem prover Tps.
14859195
Solving for Set Variables in Higher-Order Theorem Proving
In higher-order logic, we must consider literals with flexible (set variable) heads. Set variables may be instantiated with logical formulas of arbitrary complexity. An alternative to guessing the logical structures of instantiations for set variables is to solve for sets satisfying constraints. Using the Knaster-Tarski Fixed Point Theorem [15], constraints whose solutions require recursive definitions can be solved as fixed points of monotone set functions. In this paper, we consider an approach to higher-order theorem proving which intertwines conventional theorem proving in the form of mating search with generating and solving set constraints.
13531439
Combining Type Theory and Untyped Set Theory
We describe a dependent type theory with proof irrelevance. Within this framework, we give a representation of a form of Mac Lane set theory and discuss automated support for constructing proofs within this set theory. One of the novel aspects of the representation is that one is allowed to use any class (in the set theory) as a type (in the type theory). Such class types allow a natural way of representing partial functions (e.g., the first and second operators on the class of Kuratowski ordered pairs). We also discuss how automated search can be used to construct proofs. In particular, the first-order prover Vampire can be called to solve a challenge problem (the injective Cantor Theorem) which is notoriously difficult for higher-order automated provers.
27008190
Tutorial: Using TPS for Higher-Order Theorem Proving and ETPS for Teaching Logic
TPS is an automated theorem proving system which can be used to prove theorems of first- or higher-order logic automatically, interactively, or in a combination of these modes of operation. Proofs in TPS are presented in natural deduction style. ETPS is a program which was obtained from TPS by deleting all the facilities for proving theorems automatically. ETPS can be used by students to learn how to prove theorems interactively. The objective of the tutorial is to teach participants how to make effective use of TPS and ETPS.
12173886
VR-VIBE: A Virtual Environment for Co-operative Information Retrieval
We present a virtual reality application called VR-VIBE which is intended to support the co-operative browsing and filtering of large document stores. VR-VIBE extends a visualisation approach proposed in a previous two dimensional system called VIBE into three dimensions, allowing more information to be visualised at one time and supporting more powerful styles of interaction, The essence of VR-VIBE is that multiple users can explore the results of applying several simultaneous queries to a corpus of documents. By arranging the queries into a spatial framework, the system shows the relative attraction of each document to each query by its spatial position and also shows the absolute relevance of each document to all of the queries. Users may then navigate the space, select individual documents, control the display according to a dynamic relevance threshold and dynamically drag the queries to new positions to see the effect on the document space. Co-operative browsing is supported by directly embodying users and providing them with the ability to interact over live audio connections and to attach brief textual annotations to individual documents. Finally, we conclude with some initial observations gleaned from our experience of constructing VR-VIBE and using it in the laboratory setting.
829668
Prediction of Boundaries Between Intrinsically Ordered and Disordered Protein Regions
Using proteins with both disordered and ordered regions collected through literature searches and database scanning, we assembled a set of 24-residue long segments centered on their order/disorder boundaries as well as a larger set of non-boundary segments consisting of either order or disorder. We analyzed position-specific amino acid compositions around the order/disorder boundaries and found more than thirty significant (p < 0.05) compositional differences between boundary and non-boundary data. From this analysis, we constructed several logistic regression predictors of order/disorder boundaries using slightly different data modeling approaches. Exact boundary prediction accuracies were estimated to be in the range from 74% to 80% for the different predictors.
34334066
Haptics in augmented reality
An augmented reality system merges synthetic sensory information into a user's perception of a three-dimensional environment. An important performance goal for an augmented reality system is that the user perceives a single seamless environment. In most augmented reality systems the user views a real world augmented only with visual information and is not provided with a means to interact with the virtual objects. We describe an augmented reality system that, in addition to visual augmentation, merges synthetic haptic input into the user's perception of the real environment. Our system uses a PHANToM/sup TM/ haptic interface device to generate the haptic sensory input in real-time. The system allows user interactions such as moving or lifting a virtual object, and demonstrates interactions between virtual and real objects. Methods to provide proper visual occlusion between real and virtual objects are also described.
15122204
Action Representation and Purpose: Re-evaluating the Foundations of Computational Vision
The traditional goal of computer vision, to reconstruct, or recover properties of, the scene has recently been challenged by advocates of a new purposive approach in which the vision problem is defined in terms of the goals of an active agent. In the starkest light the debate can be characterized as one about the role of explicit representations. The extreme traditionalists strive for a detailed representation of the 3D world while the other extreme adopts a strict behaviorist stance which eschews representations in favor of “direct sensing.” This panel will explore the roles of action, representation, and purpose in computer vision and, in doing so, will hopefully discover areas of agreement.
6978911
Information Theoretic Sensor Data Selection for Active Object Recognition and State Estimation
We introduce a formalism for optimal sensor parameter selection for iterative state estimation in static systems. Our optimality criterion is the reduction of uncertainty in the state estimation process, rather than an estimator-specific metric (e.g., minimum mean squared estimate error). The claim is that state estimation becomes more reliable if the uncertainty and ambiguity in the estimation process can be reduced. We use Shannon's information theory to select information-gathering actions that maximize mutual information, thus optimizing the information that the data conveys about the true state of the system. The technique explicitly takes into account the a priori probabilities governing the computation of the mutual information. Thus, a sequential decision process can be formed by treating the a priori probability at a certain time step in the decision process as the a posteriori probability of the previous time step. We demonstrate the benefits of our approach in an object recognition application using an active camera for sequential gaze control and viewpoint selection. We describe experiments with discrete and continuous density representations that suggest the effectiveness of the approach.