Inference Step Research Articles

The dynamics of awareness

Classical epistemic logic describes implicit knowledge of agents about facts and knowledge of other agents based on semantic information. The latter is produced by acts of observation or communication that are described well by dynamic epistemic logics. What these logics do not describe, however, is how significant information is also produced by acts of inference—and key axioms of the system merely postulate “deductive closure”. In this paper, we take the view that all information is produced by acts, and hence we also need a dynamic logic of inference steps showing what effort on the part of the agent makes a conclusion explicit knowledge. Strong omniscience properties of agents should be seen not as static idealizations, but as the result of dynamic processes that agents engage in. This raises two questions: (a) how to define suitable information states of agents and matching notions of explicit knowledge, (b) how to define natural processes over these states that generate new explicit knowledge. To this end, we use a static base from the existing awareness literature, extending it into a dynamic system that includes traditional acts of observation, but also adding and dropping formulas from the current ‘awareness’ set. We give a completeness theorem, and we show how this dynamics updates explicit knowledge. Then we extend our approach to multi-agent scenarios where awareness changes may happen privately. Finally, we mention further directions and related approaches. Our contribution can be seen as a ‘dynamification’ of existing awareness logics.

Parallel evidence propagation on multicore processors

We propose a parallel evidence propagation method on general-purpose multicore processors. Evidence propagation is a major step in exact inference, a key problem in exploring probabilistic graphical models. We explore the parallelism in evidence propagation at various levels. First, given an arbitrary junction tree, we construct a directed acyclic graph (DAG) with weighted nodes, each denoting a computation task for evidence propagation. Since the execution time of the tasks varies significantly, we develop a workload-aware scheduler to allocate the tasks to the cores of the processors. The scheduler monitors the workload of each core and dynamically allocates tasks to support load balance across the cores. In addition, we integrate a module in the scheduler to partition the tasks converted from cliques with large potential tables so as to achieve improved load balance. We implemented the proposed method using Pthreads on both AMD and Intel quadcore processors. For a representative set of junction trees, our method achieved almost linear speedup. The execution time of our method was around twice as fast as an OpenMP-based implementation on both the platforms.

PEER-TO-PEER REASONING FOR INTERLINKED ONTOLOGIES

The Semantic Web is commonly perceived as a web of partially-interlinked machine readable data. This data is inherently distributed and resembles the structure of the web in terms of resources being provided by different parties at different physical locations. A number of infrastructures for storing and querying distributed semantic web data, primarily encoded in RDF have been developed. While there are first attempts for integrating RDF Schema reasoning into distributed query processing, almost all the work on description logic reasoning as a basis for implementing inference in the Web Ontology Language OWL still assumes a centralized approach where the complete terminology has to be present on a single system and all inference steps are carried out on this system. We have designed and implemented a distributed reasoning method that preserves soundness and completeness of reasoning under the original OWL import semantics and has beneficial properties regarding parallel computation and overhead caused by communication effort and additional derivations. The method is based on sound and complete resolution methods for the description logic [Formula: see text] that we modify to work in a distributed setting.

Proofs – are they objective?

The concept of proof may be given a first approximate explanation by saying that a proof is a chain of valid inferences from known truths such that at each inference step the conclusion is seen to follow from the premisses. A natural reaction to this explanation is to say that whether something “is seen to follow” may depend on a subject, and to ask whether this does not make proofs subjective in character. We cannot simply skip the phrase “is seen to” in this explanation, if the validity of ...

Learning Visual Object Categories for Robot Affordance Prediction

A fundamental requirement of any autonomous robot system is the ability to predict the affordances of its environment. The set of affordances define the actions that are available to the agent given the robot’s context. A standard approach to affordance learning is direct perception, which learns direct mappings from sensor measurements to affordance labels. For example, a robot designed for cross-country navigation could map stereo depth information and image features directly into predictions about the traversability of terrain regions. While this approach can succeed for a small number of affordances, it does not scale well as the number of affordances increases. In this paper, we show that visual object categories can be used as an intermediate representation that makes the affordance learning problem scalable. We develop a probabilistic graphical model which we call the Category—Affordance (CA) model, which describes the relationships between object categories, affordances, and appearance. This model casts visual object categorization as an intermediate inference step in affordance prediction. We describe several novel affordance learning and training strategies that are supported by our new model. Experimental results with indoor mobile robots evaluate these different strategies and demonstrate the advantages of the CA model in affordance learning, especially when learning from limited size data sets.

Traditional Logic, Modern Logic and Natural Language

In a recent paper Johan van Benthem reviews earlier work done by himself and colleagues on ‘natural logic’. His paper makes a number of challenging comments on the relationships between traditional logic, modern logic and natural logic. I respond to his challenge, by drawing what I think are the most significant lines dividing traditional logic from modern. The leading difference is in the way logic is expected to be used for checking arguments. For traditionals the checking is local, i.e. separately for each inference step. Between inference steps, several kinds of paraphrasing are allowed. Today we formalise globally: we choose a symbolisation that works for the entire argument, and thus we eliminate intuitive steps and changes of viewpoint during the argument. Frege and Peano recast the logical rules so as to make this possible. I comment also on the traditional assumption that logical processing takes place at the top syntactic level, and I question Johan’s view that natural logic is ‘natural’.

Guest editorial: special issue on structured prediction

Structured Prediction or Structured Classification (Bakir et al. 2007) is the task of predicting a collection of related variables given some input. The relationship between the variables to be predicted is often complex. An example of such complex dependencies is machine translation, where the input is a sequence of words in the source natural language and the output is a sequence of words in the target natural language. Here, each word in the target language relates not only to the words in the source language, but also to the other (arbitrarily far) words in the target sequence. As a field, structured prediction has some unique challenges, several of which are addressed by the papers in this issue. One of the most obvious of these is that the output spaces in question are often exponential in size, and so the complexity, both of these spaces and the learned models, can result in computationally infeasible learning and inference algorithms. In many cases, therefore, efficient optimization remains an open problem in structured prediction. Two papers in this special issue (Hsu et al. 2009; Sutton and McCallum 2009) address this problem. An important source of complexity in structured prediction algorithms is in the iterative nature of the training step: Often, training is done EM-style, where model parameters are estimated at each step, and then inference is performed based on these parameters. In models with complex structure, this inference step

Text-Like Segmentation of General Audio for Content-Based Retrieval

Automatic detection of (semantically) meaningful audio segments, or audio scenes, is an important step in high-level semantic inference from general audio signals, and can benefit various content-based applications involving both audio and multimodal (multimedia) data sets. Motivated by the known limitations of traditional low-level feature-based approaches, we propose in this paper a novel approach to discover audio scenes, based on an analysis of audio elements and key audio elements, which can be seen as equivalents to the words and keywords in a text document, respectively. In the proposed approach, an audio track is seen as a sequence of audio elements, and the presence of an audio scene boundary at a given time stamp is checked based on pair-wise measuring the semantic affinity between different parts of the analyzed audio stream surrounding that time stamp. Our proposed model for semantic affinity exploits the proven concepts from text document analysis, and is introduced here as a function of the distance between the audio parts considered, and the co-occurrence statistics and the importance weights of the audio elements contained therein. Experimental evaluation performed on a representative data set consisting of 5 h of diverse audio data streams indicated that the proposed approach is more effective than the traditional low-level feature-based approaches in solving the posed audio scene segmentation problem.

Structured prediction by joint kernel support estimation

Discriminative techniques, such as conditional random fields (CRFs) or structure aware maximum-margin techniques (maximum margin Markov networks (M3N), structured output support vector machines (S-SVM)), are state-of-the-art in the prediction of structured data. However, to achieve good results these techniques require complete and reliable ground truth, which is not always available in realistic problems. Furthermore, training either CRFs or margin-based techniques is computationally costly, because the runtime of current training methods depends not only on the size of the training set but also on properties of the output space to which the training samples are assigned. We propose an alternative model for structured output prediction, Joint Kernel Support Estimation (JKSE), which is rather generative in nature as it relies on estimating the joint probability density of samples and labels in the training set. This makes it tolerant against incomplete or incorrect labels and also opens the possibility of learning in situations where more than one output label can be considered correct. At the same time, we avoid typical problems of generative models as we do not attempt to learn the full joint probability distribution, but we model only its support in a joint reproducing kernel Hilbert space. As a consequence, JKSE training is possible by an adaption of the classical one-class SVM procedure. The resulting optimization problem is convex and efficiently solvable even with tens of thousands of training examples. A particular advantage of JKSE is that the training speed depends only on the size of the training set, and not on the total size of the label space. No inference step during training is required (as M3N and S-SVM would) nor do we have calculate a partition function (as CRFs do). Experiments on realistic data show that, for suitable kernel functions, our method works efficiently and robustly in situations that discriminative techniques have problems with or that are computationally infeasible for them.

Combining logical and algebraic techniques for natural style proving in elementary analysis

PCS (Proving-Computing-Solving) introduced by B. Buchberger in 2001 and S-Decomposition, introduced by T. Jebelean in 2001, are strategies for handling proof problems by combining logic inference steps (e.g., modus ponens, Skolemization, instantiation) with rewriting steps (application of definitions) and solving procedures based on algebraic techniques (e.g., Groebner Bases, Cylindrical Algebraic Decomposition). If one formalizes the main notions of elementary analysis like continuity, convergence, etc., usually a sequence of alternating quantifier blocks appears in the quantifier prefix of the corresponding formula. This makes the proof problems involving these notions difficult. The S-Decomposition strategy is especially suitable for property-preserving problems like continuity of sum, because it is designed for handling problems where the goal and the main assumptions have a similar structure. During proof deduction, existentially quantified goals and universal assumptions are handled by introducing metavariables, if no suitable ground instance is known in advance. For finalizing proof attempts, the metavariables must be instantiated in such a way that they satisfy the cumulated algebraic constraints collected during the proof attempt. The instantiation problem is considered to be difficult in a purely logical calculus. Appropriate instances can be often found using quantifier elimination (QE) over real closed fields. In order to obtain witness terms we utilize the QE method based on cylindrical algebraic decomposition (CAD) invented by G. Collins in 1973. However, the QE method alone is not sufficient. One needs to pre-process the (closed, quantified) conjectured formula and post-process the resulting CAD-structure after the call of the QE algorithm.

Adaptation and complexity in repeated games

The paper presents a learning model for two-player infinitely repeated games. In an inference step players construct minimally complex inferences of strategies based on observed play, and in an adaptation step players choose minimally complex best responses to an inference. When players randomly select an inference from a probability distribution with full support the set of steady states is a subset of the set of Nash equilibria in which only stage game Nash equilibria are played. When players make ‘cautious’ inferences the set of steady states is the subset of self-confirming equilibria with Nash outcome paths. When players use different inference rules, the set of steady states can lie between the previous two cases.

The Cognitive Processes of Formal Inferences

Theoretical research is predominately an inductive process; while applied research is mainly a deductive process. Both inference processes are based on the cognitive process and means of abstraction. This article describes the cognitive processes of formal inferences such as deduction, induction, abduction, and analogy. Conventional propositional arguments adopt static causal inference. This article introduces more rigorous and dynamic inference methodologies, which are modeled and described as a set of cognitive processes encompassing a series of basic inference steps. A set of mathematical models of formal inference methodologies is developed. Formal descriptions of the four forms of cognitive processes of inferences are presented using Real-Time Process Algebra (RTPA). The cognitive processes and mental mechanisms of inferences are systematically explored and rigorously modeled. Applications of abstraction and formal inferences in both the revilement of the fundamental mechanisms of the brain and the investigation of next generation cognitive computers are explored.

SEMANTIC DERIVATION VERIFICATION: TECHNIQUES AND IMPLEMENTATION

Automated Theorem Proving (ATP) systems are complex pieces of software, and thus may have bugs that make them unsound. In order to guard against unsoundness, the derivations output by an ATP system may be semantically verified by trusted ATP systems that check the required semantic properties of each inference step. Such verification needs to be augmented by structural verification that checks that inferences have been used correctly in the context of the overall derivation. This paper describes techniques for semantic verification of derivations, and reports on their implementation and testing in the GDV verifier.

Robust stochastic dominance: A semi-parametric approach

Lorenz curves and second-order dominance criteria, the fundamental tools for stochastic dominance, are known to be sensitive to data contamination in the tails of the distribution. We propose two ways of dealing with the problem: (1) Estimate Lorenz curves using parametric models and (2) combine empirical estimation with a parametric (robust) estimation of the upper tail of the distribution using the Pareto model. Approach (2) is preferred because of its flexibility. Using simulations we show the dramatic effect of a few contaminated data on the Lorenz ranking and the performance of the robust semi-parametric approach (2). Since estimation is only a first step for statistical inference and since semi-parametric models are not straightforward to handle, we also derive asymptotic covariance matrices for our semi-parametric estimators.

An example of formalizing recent mathematical results in Mizar

This paper describes an example of the successful formalization of quite advanced and new mathematics using the Mizar system. It shows that although much effort is required to formalize nontrivial facts in a formal computer deduction system, still it is possible to obtain the level of full logical correctness of all inference steps. We also discuss some problems encountered during the formalization, and try to point out some of the features of the Mizar system responsible for that. The formalization described in this paper allows also for contrasting the linguistic capability of the Mizar language and some of the phrases commonly used in “informal” mathematical papers that the Mizar system lacks, and consequently presents the methods of how to cope with it during the formalization. Yet, apart from the problems, this paper shows some definite benefits from using a formal computer system in the work of a mathematician.

Modeling trajectory of dynamic clusters in image time-series for spatio-temporal reasoning

During the last decades, satellites have acquired incessantly high-resolution images of many Earth observation sites. New products have arisen from this intensive acquisition process: high-resolution satellite image time-series (SITS). They represent a large data volume with a rich information content and may open a broad range of new applications. This paper presents an information mining concept which enables a user to learn and retrieve spatio-temporal structures in SITS. The concept is based on a hierarchical Bayesian modeling of SITS information content which enables us to link the interest of a user to specific spatio-temporal structures. The hierarchy is composed of two inference steps: an unsupervised modeling of dynamic clusters resulting in a graph of trajectories, and an interactive learning procedure based on graphs which leads to the semantic labeling of spatio-temporal structures. Experiments performed on a SPOT image time-series demonstrate the concept capabilities.

Conditioning against the Grain

This paper discusses counterexamples to the thesis that the probabilities of conditionals are conditional probabilities. It is argued that the discrepancy is systematic and predictable, and that conditional probabilities are crucially involved in the apparently deviant interpretations. Furthermore, the examples suggest that such conditionals have a less prominent reading on which their probability is in fact the conditional probability, and that the two readings are related by a simple step of abductive inference. Central to the proposal is a distinction between causal and purely stochastic dependence between variables.

Configuration irrigation schedule based on expert systems and operations research

This paper presents configuration design knowledge to solve irrigation scheduling problem in agriculture domain and a general approach for configuration management knowledge. It also introduces a Configuration Agriculture Irrigation Schedule (CAIS) tool that produces the configuration irrigation schedule design according to the CommonKADS methodology. A configuration that satisfy the user requirements, and that additionally satisfy some optimality criteria is required. By integrating Dynamic programming and inference knowledge, with demand including different objective, that it is used in generating the inference steps (PPSM) to select the suitable components of the inference steps minimizing the number of components and/or maximizing the accuracy of the result of each inference step. Operations Research techniques greatly improved the understanding of the interactions of a large number of components and enhanced the decision selection under uncertain outcomes.

Approximate symbolic pattern matching for protein sequence data

In protein sequences, often two sequences that share similar substrings have similar functional properties. Learning of the characteristics and properties of an unknown protein is much easier if its likely functional properties can be predicted by finding the substrings already known from other protein sequences. The sequence pattern search algorithm proposed in this paper searches for similar matches between a pattern and a sequence by using fuzzy logic and calculates the degree of similarity from a sequence inference step. Proteins from 11 domain families are used for simulation and the result shows that the proposed algorithm is capable of identifying sequences that have a similar pattern compared to their family protein motifs.

Efficient Substitution in Hoare Logic Expressions

Substitution plays an important role in Hoare Logic, as it is used in interpreting assignments. When writing a computer-based realization of Hoare Logic, it is therefore important to choose a good implementation for it. In this paper we compare different definitions and implementations of substitution in a logical framework, in an effort to maximize efficiency.We start by defining substitution as a logical formula. In a conventional approach, this is done by specifying the syntactic changes substitution performs on expressions. We choose instead a semantic definition that describes the behavioral relation between the original expression and its substituted counterpart.Next, we use this semantic definition as an abstract specification, and compare two of its concrete implementations. The first we consider is the usual one, that operates recursively over the structure of the term. This requires a number of inference steps proportional to the size of the expression, which is unacceptable for many practical applications. We therefore propose a different method, that makes better use of the primitives provided by the logical framework, and manages to reduce the complexity to a quantity proportional to the number of free variables.We conclude the paper outlining a refinement technique that, by taking advantage of some simple program analysis information, holds promise of improving the results presented even further.