Annals of Mathematics and Artificial Intelligence最新文献

The purpose of this paper is to present a fresh idea on how symbolic learning might be realized via analogical reasoning. For this, we introduce directed analogical proportions between logic programs of the form “P transforms into Q as R transforms into S” as a mechanism for deriving similar programs by analogy-making. The idea is to instantiate a fragment of a recently introduced abstract algebraic framework of analogical proportions in the domain of logic programming. Technically, we define proportions in terms of modularity where we derive abstract forms of concrete programs from a “known” source domain which can then be instantiated in an “unknown” target domain to obtain analogous programs. To this end, we introduce algebraic operations for syntactic logic program composition and concatenation. Interestingly, our work suggests a close relationship between modularity, generalization, and analogy which we believe should be explored further in the future. In a broader sense, this paper is a further step towards a mathematical theory of logic-based analogical reasoning and learning with potential applications to open AI-problems like commonsense reasoning and computational learning and creativity.

Given a Boolean relational specification (F(textbf{X}, textbf{Y})), where (textbf{X}) is a vector of inputs and (textbf{Y}) is a vector of outputs, Boolean functional synthesis requires us to compute a vector of (Skolem) functions (varvec{Psi }(textbf{X})), one for each output in (textbf{Y}), such that (F(textbf{X}, varvec{Psi }(textbf{X})) leftrightarrow exists textbf{Y},F(textbf{X},textbf{Y})) holds. This problem lies at the heart of many applications and has received significant attention in recent years. In this paper, we investigate the role of representation of (F(textbf{X}, textbf{Y})) and of (varvec{Psi }(textbf{X})) in determining the computational hardness of Boolean functional synthesis. We start by showing that an efficient way of existentially quantifying variables from a Boolean formula in a given order yields an efficient solution to Boolean functional synthesis and vice versa. We then propose a semantic normal form, called SynNNF, that guarantees polynomial-time synthesis and characterizes polynomial-time existential quantification for a given order of quantification of variables. We show that several syntactic and other semantic normal forms for Boolean formulas studied in the knowledge compilation literature are subsumed by SynNNF, and that SynNNF is exponentially more succinct than most of them. We also investigate how the representation of the synthesized (Skolem) functions (varvec{Psi }(textbf{X})) affects the complexity of Boolean functional synthesis, and present a map of complexity based on the representations of (F(textbf{X},textbf{Y})) and (varvec{Psi }(textbf{X})). Finally, we propose an algorithm to compile a specification represented as a NNF (including CNF) circuit to SynNNF. We present results of an extensive set of experiments conducted using an implementation of the above algorithm, and two other tools available in the public domain.

Capacity is an important tool in decision-making under risk and uncertainty and multi-criteria decision-making. When learning a capacity-based model, it is important to be able to generate uniformly a capacity. Due to the monotonicity constraints of a capacity, this task reveals to be very difficult. The classical Random Node Generator (RNG) algorithm is a fast-running speed capacity generator, however with poor performance. In this paper, we firstly present an exact algorithm for generating a n elements’ general capacity, usable when (n < 5). Then, we present an improvement of the classical RNG by studying the distribution of the value of each element of a capacity. Furthermore, we divide it into two cases, the first one is the case without any conditions, and the second one is the case when some elements have been generated. Experimental results show that the performance of this improved algorithm is much better than the classical RNG while keeping a very reasonable computation time.

The Bdi model of rational agency has been studied for over three decades. Many robust multiagent systems have been developed, and a number of Bdi logics have been studied. Following this intensive development phase, the importance of integrating Bdi models with inconsistency handling and revision theory have been emphasized. There is also a demand for a tighter connection between Bdi-based implementations and Bdi logics. In this paper, we address these postulates by introducing a novel, paraconsistent logical Bdi model close to implementation, with building blocks that can be represented as Sql/rule-based databases. Importantly, tractability is achieved by reasoning as querying. This stands in a sharp contrast to the high complexity of known Bdi logics. We also extend belief shadowing, a shallow and lightweight alternative to deep and computationally demanding belief revision, to encompass agents’ motivational attitudes.

We investigate Tiered Coalition Formation Games (TCFGs), a cooperative game inspired by the stratification of Pokémon on the fan website, Smogon. It is known that, under match-up oriented preferences, Nash and core stability are equivalent. We previously introduced a notion of socially conscious stability for TCFGs, and introduced a game variant with fixed k-length tier lists. In this work we show that in tier lists under match-up oriented preferences, socially conscious stability is equivalent to Nash stability and to core stability, but in k-tier lists, the three stability notions are distinct. We also give a necessary condition for tier list stability in terms of robustness (the minimum in-tier utility of an agent). We introduce a notion of approximate Nash stability and approximately socially conscious stability, and provide experiments on the empirical run time of our k-tier local search algorithm, and the performance of our algorithms for generating approximately socially consciously stable tier lists.

Feature models are commonly used to specify the valid configurations of product lines. As industrial feature models are typically complex, researchers and practitioners employ various automated analyses to study the configuration spaces. Many of these automated analyses require that numerous complex computations are executed on the same feature model, for example by querying a SAT or #SATsolver. With knowledge compilation, feature models can be compiled in a one-time effort to a target language that enables polynomial-time queries for otherwise more complex problems. In this work, we elaborate on the potential of employing knowledge compilation on feature models. First, we gather various feature-model analyses and study their computational complexity with regard to the underlying computational problem and the number of solver queries required for the respective analysis. Second, we collect knowledge-compilation target languages and map feature-model analyses to the languages that make the analysis tractable. Third, we empirically evaluate publicly available knowledge compilers to further inspect the potential benefits of knowledge-compilation target languages.

In supervised learning, the Universum, a third class that is not a part of either class in the classification task, has proven to be useful. In this study we propose (N( mathfrak {U} )TBSVM), a Newton-based approach for solving in the primal space the optimization problems related to Twin Bounded Support Vector Machines with Universum data (( mathfrak {U} )TBSVM). In the N( mathfrak {U} )TBSVM, the constrained programming problems of ( mathfrak {U} )TBSVM are converted into unconstrained optimization problems, and a generalization of Newton’s method for solving the unconstrained problems is introduced. Numerical experiments on synthetic, UCI, and NDC data sets show the ability and effectiveness of the proposed N( mathfrak {U} )TBSVM. We apply the suggested method for gender detection from face images, and compare it with other methods.

Families of new, multi-level integer 2D arrays are introduced here as an extension of the well-known binary Legendre sequences that are derived from quadratic residues. We present a construction, based on Fourier and Finite Radon Transforms, for families of periodic perfect arrays, each of size (ptimes p) for many prime values p. Previously delta functions were used as the discrete projections which, when back-projected, build 2D perfect arrays. Here we employ perfect sequences as the discrete projected views. The base family size is (p+1). All members of these multi-level array families have perfect autocorrelation and constant, minimal cross-correlation. Proofs are given for four useful and general properties of these new arrays. 1) They are comprised of odd integers, with values between at most (-p) and (+p), with a zero value at just one location. 2) They have the property of ‘conjugate’ spatial symmetry, where the value at location (i, j) is always the negative of the value at location ((p-i, p-j)). 3) Any change in the value assigned to the array’s origin leaves all of its off-peak autocorrelation values unchanged. 4) A family of (p+1), (ptimes p) arrays can be compressed to size ((p+1)^2) and each family member can be exactly and rapidly unpacked in a single (ptimes p) decompression pass.

We introduce a hedonic game form, Hedonic Expertise Games (HEGs), that naturally models a variety of settings where agents with complementary qualities would like to form groups. Students forming groups for class projects, and hackathons in which software developers, graphic designers, project managers, and other domain experts collaborate on software projects, are typical scenarios modeled by HEGs. This game form possesses the common ranking property, and additionally, the coalitional utility function is monotone. We present comprehensive results for the existence/nonexistence of stable and efficient partitions of HEGs with respect to the most common stability and optimality concepts used in the literature. Specifically, we show that an HEG instance may not have a strict core stable partition, and yet every HEG instance has a strong Nash stable and Pareto optimal partition. Furthermore, it may be the case that none of the socially-optimal partitions of an HEG instance is Nash stable or core stable. However, it is guaranteed that every socially-optimal partition is contractually Nash stable. We show that all these existence/nonexistence results also hold for the monotone hedonic games with common ranking property (monotone HGCRP). We also present several results for HEGs from the computational complexity perspective, some of which are as follows: A contractually Nash stable partition (and a Nash stable partition in a restricted setting) can be found in polynomial time. A strong Nash stable partition can be approximated within a factor of (1-1/e), and this bound is tight even for approximating core stable partitions. We present a natural game dynamics for monotone HGCRP that converges to a Nash stable partition in a relatively low number of moves.