Establishing convergent semantics for weighted argumentation graphs is a long-standing fundamental issue. Particularly, it is challenging to develop convergent semantics for weighted bipolar argumentation graphs (wBAG), which include both support and attack relations on weighted arguments. Existing semantics in the literature are not general enough in the sense that they only apply to acyclic graphs or special cyclic cases. In this paper, we provide an elegant solution to this issue by adopting the so-called bilateral gradual semantics, so that the strength of arguments can be defined as the limits of iterative functions that always converge for any wBAG including cyclic ones. A preliminary experimental analysis shows that our semantics appear quite efficient in calculating argument strength. Overall, this paper offers a solid and promising foundation for weighted bipolar argumentation in theoretical and practical aspects.

Abstract argumentation is a reasoning model for evaluating arguments. Recently, gradual semantics has received considerable attention in weighted argumentation, which assigns an acceptability degree to each argument as its strength. In this paper, we aim to enhance gradual semantics by non-reciprocally incorporating the notion of rejectability degree. Such a setting offers a bilateral perspective on argument strength, enabling more comprehensive argument evaluations in practical situations. To this end, we first provide a set of principles for our semantics, taking both the acceptability and rejectability degrees into account, and propose three novel semantics conforming to the above principles. These semantics are defined as the limits of iterative sequences that always converge in any given weighted argumentation system, making them preferable for real-world applications.

Showing that a problem is hard for a model of computation is one of the most challenging tasks in theoretical computer science, logic and mathematics. For example, it remains beyond reach to find an explicit problem that cannot be computed by polynomial size propositional formulas (PF). As a model of computation, logic programs (LP) under answer set semantics are as expressive as PF and also \(\mathtt{NP}\) -complete for satisfiability checking. In this article, we show that the PAR problem is hard for LP, i.e., deciding whether a binary string contains an odd number of \(1\) ’s requires exponential size LP. The proof idea is first to transform logic programs into equivalent boolean circuits and then apply a probabilistic method known as random restriction to obtain an exponential lower bound. Based on the main result, we generalize a sufficient condition for identifying hard problems for LP and give a separation map for an LP family from a computational point of view, whose members are all equally expressive and share the same reasoning complexity.

This paper proposes a fuzzy approach for reasoning about action and change in timed domains. In our method, actions and world states are modeled as fuzzy sets over time axis. Thus, their temporal relations and time constraints can be modeled as fuzzy rules. So, our method handles well the issue that action happens at an approximate time and then the states also change at an approximate time, which has not been solved well in the existing work. Finally, our method is used to solve the classic problem of rail-road crossing control in a fuzzy environment. The theoretical and simulation analysis shows that the controller using our method works well.

We propose a new method for view-invariant action recognition based on the rank constraint on the family of planar homographies associated with triplets of body points. We represent action as a sequence of poses and we use the fact that the family of homographies associated with two identical poses would have rank 4 to gauge similarity of the pose between two subjects, observed by different perspective cameras and from different viewpoints. Extensive experimental results show that our method can accurately identify action from video sequences when they are observed from totally different viewpoints with different camera parameters.

In this paper we investigate the existence of model-equivalence reduction between NP-logic systems which are logic systems with model existence problem in NP. It is shown that among all NP-systems with model checking problem in NP, the existentially quantified propositional logic (\exists PF) is maximal with respect to poly-time model-equivalent reduction. However, \exists PF seems not a maximal NP-system in general because there exits a NP-system with model checking problem D^P-complete.

We propose a new view-invariant measure for action recognition. For this purpose, we introduce the idea that the motion of an articulated body can be decomposed into rigid motions of planes defined by triplets of body points. Using the fact that the homography induced by the motion of a triplet of body points in two identical pose transitions reduces to the special case of a homology, we use the equality of two of its eigenvalues as a measure of the similarity of the pose transitions between two subjects, observed by different perspective cameras and from different viewpoints. Experimental results show that our method can accurately identify human pose transitions and actions even when they include dynamic timeline maps, and are obtained from totally different viewpoints with different unknown camera parameters.

A moving plane observed by a fixed camera induces a fundamental matrix F across multiple frames, where the ratios among the elements in the upper left 2×2 submatrix are herein referred to as the Fundamental Ratios. We show that fundamental ratios are invariant to camera parameters, and hence can be used to identify similar plane motions from varying viewpoints. For action recognition, we decompose a body posture into a set of point triplets (planes). The similarity between two actions is then determined by the motion of point triplets and hence by their associated fundamental ratios, providing thus view-invariant recognition of actions. Results evaluated over 255 semi-synthetic video data with 100 independent trials at a wide range of noise levels, and also on 56 real videos of 8 different classes of actions, confirm that our method can recognize actions under substantial amount of noise, even when they have dynamic timeline maps, and the viewpoints and camera parameters are unknown and totally different.

We propose a new template-based approach for view invariant recognition of body poses, based on geometric constraints derived from the motion of body point triplets. In addition to spatial information our templates encode temporal information of body pose transitions. Unlike existing methods that study a body pose as a whole, we decompose it into a number of body point triplets, and compare their motions to our templates. Using the fact that the homography induced by the motion of a triplet of body points in two identical body pose transitions reduces to the special case of a homology, we exploit the equality of two of its eigenvalues to impose constraints on the similarity of the pose transitions between two subjects, observed by different perspective cameras and from different viewpoints. Extensive experimental results show that our method can accurately identify human poses from video sequences when they are observed from totally different viewpoints with different camera parameters.

In this paper, we present a new approach for view-invariant action recognition using constraints derived from the eigenvalues of planar homographies associated with triplets of body points. Unlike existing methods that study an action as a whole, or break it down into individual poses, we represent an action as a sequence of pose transitions. Using the fact that the homography induced by the motion of a triplet of body points in two identical pose transitions reduces to the special case of a homology, we exploit the equality of two of its eigenvalues to impose constraints on the similarity of the pose transitions between two subjects, observed by different perspective cameras and from different viewpoints. Experimental results show that our method can accurately identify human pose transitions and actions even when they include dynamic timeline maps, and are obtained from totally different viewpoints with different camera parameters.

The knowledge of camera intrinsic and extrinsic parameters is useful, as it allows us to make world measurements. Unfortunately, calibration information is rarely available in video surveillance systems and is difficult to obtain once the system is installed. Auto-calibrating cameras using moving objects (humans) has recently attracted a lot of interest. Two methods were proposed by Lv-Nevatia (2002) and Krahnstoever-Mendonca (2005). The inherent difficulty of the problem lies in the noise that is generally present in the data. We propose a robust and a general linear solution to the problem by adopting a formulation different from the existing methods. The uniqueness of our formulation lies in recognizing two fundamental matrices present in the geometry obtained by observing pedestrians, and then using their properties to impose linear constraints on the unknown camera parameters. Experiments with synthetic as well as real data are presented -indicating the practicality of the proposed system.