Query answering in resource-based answer set semantics

In recent work we defined resource-based answer set semantics, which is an extension to answer set semantics stemming from the study of its relationship with linear logic. In fact, the name of the new semantics comes from the fact that in the linear-logic formulation every literal (including negative ones) were considered as a resource. In this paper, we propose a query-answering procedure reminiscent of Prolog for answer set programs under this extended semantics as an extension of XSB-resolution for logic programs with negation.1We prove formal properties of the proposed procedure. Under consideration for acceptance in TPLP.

A FIRST ORDER PREDICATE LOGIC FORMULATION OF THE 3D RECONSTRUCTION PROBLEM AND ITS SOLUTION SPACE

This paper defines the 3D reconstruction problem as the process of reconstructing a 3D scene from numerous 2D visual images of that scene. It is well known that this problem is ill-posed, and numerous constraints and assumptions are used in 3D reconstruction algorithms in order to reduce the solution space. Unfortunately, most constraints only work in a certain range of situations and often constraints are built into the most fundamental methods (e.g. Area Based Matching assumes that all the pixels in the window belong to the same object). This paper presents a novel formulation of the 3D reconstruction problem, using a voxel framework and first order logic equations, which does not contain any additional constraints or assumptions. Solving this formulation for a set of input images gives all the possible solutions for that set, rather than picking a solution that is deemed most likely. Using this formulation, this paper studies the problem of uniqueness in 3D reconstruction and how the solution space changes for different configurations of input images. It is found that it is not possible to guarantee a unique solution, no matter how many images are taken of the scene, their orientation or even how much color variation is in the scene itself. Results of using the formulation to reconstruct a few small voxel spaces are also presented. They show that the number of solutions is extremely large for even very small voxel spaces (5 × 5 voxel space gives 10 to 107 solutions). This shows the need for constraints to reduce the solution space to a reasonable size. Finally, it is noted that because of the discrete nature of the formulation, the solution space size can be easily calculated, making the formulation a useful tool to numerically evaluate the usefulness of any constraints that are added.

A logical model of HCP

For an arbitrary undirected graphG, we are designing a logical model for the Hamiltonian Cycle Problem (HCP), using tools of Boolean algebra only. The obtained model is a logic formulation of the conditions for the existence of the Hamiltonian cycle, and usesmBoolean variables, wheremis the number of the edges of a graph. This Boolean expression is true if and only if an initial graph is Hamiltonian. In general, the obtained Boolean expression may have an exponential length (the number of Boolean literals) and may be used for construction of the solution algorithm.