Practical Probabilistic Programming

Author: Avi Pfeffer

Publisher: N.A

ISBN: 9781617292330

Category: Computers

Page: 456

View: 8738

Summary Practical Probabilistic Programming introduces the working programmer to probabilistic programming. In it, you'll learn how to use the PP paradigm to model application domains and then express those probabilistic models in code. Although PP can seem abstract, in this book you'll immediately work on practical examples, like using the Figaro language to build a spam filter and applying Bayesian and Markov networks, to diagnose computer system data problems and recover digital images. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the Technology The data you accumulate about your customers, products, and website users can help you not only to interpret your past, it can also help you predict your future! Probabilistic programming uses code to draw probabilistic inferences from data. By applying specialized algorithms, your programs assign degrees of probability to conclusions. This means you can forecast future events like sales trends, computer system failures, experimental outcomes, and many other critical concerns. About the Book Practical Probabilistic Programming introduces the working programmer to probabilistic programming. In this book, you’ll immediately work on practical examples like building a spam filter, diagnosing computer system data problems, and recovering digital images. You’ll discover probabilistic inference, where algorithms help make extended predictions about issues like social media usage. Along the way, you’ll learn to use functional-style programming for text analysis, object-oriented models to predict social phenomena like the spread of tweets, and open universe models to gauge real-life social media usage. The book also has chapters on how probabilistic models can help in decision making and modeling of dynamic systems. What's Inside Introduction to probabilistic modeling Writing probabilistic programs in Figaro Building Bayesian networks Predicting product lifecycles Decision-making algorithms About the Reader This book assumes no prior exposure to probabilistic programming. Knowledge of Scala is helpful. About the Author Avi Pfeffer is the principal developer of the Figaro language for probabilistic programming. Table of Contents PART 1 INTRODUCING PROBABILISTIC PROGRAMMING AND FIGARO Probabilistic programming in a nutshell A quick Figaro tutorial Creating a probabilistic programming application PART 2 WRITING PROBABILISTIC PROGRAMS Probabilistic models and probabilistic programs Modeling dependencies with Bayesian and Markov networks Using Scala and Figaro collections to build up models Object-oriented probabilistic modeling Modeling dynamic systems PART 3 INFERENCE The three rules of probabilistic inference Factored inference algorithms Sampling algorithms Solving other inference tasks Dynamic reasoning and parameter learning
Posted in Computers

Bayesian Methods for Hackers

Probabilistic Programming and Bayesian Inference

Author: Cameron Davidson-Pilon

Publisher: Addison-Wesley Professional

ISBN: 0133902927

Category: Computers

Page: 256

View: 5705

Master Bayesian Inference through Practical Examples and Computation–Without Advanced Mathematical Analysis Bayesian methods of inference are deeply natural and extremely powerful. However, most discussions of Bayesian inference rely on intensely complex mathematical analyses and artificial examples, making it inaccessible to anyone without a strong mathematical background. Now, though, Cameron Davidson-Pilon introduces Bayesian inference from a computational perspective, bridging theory to practice–freeing you to get results using computing power. Bayesian Methods for Hackers illuminates Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib. Using this approach, you can reach effective solutions in small increments, without extensive mathematical intervention. Davidson-Pilon begins by introducing the concepts underlying Bayesian inference, comparing it with other techniques and guiding you through building and training your first Bayesian model. Next, he introduces PyMC through a series of detailed examples and intuitive explanations that have been refined after extensive user feedback. You’ll learn how to use the Markov Chain Monte Carlo algorithm, choose appropriate sample sizes and priors, work with loss functions, and apply Bayesian inference in domains ranging from finance to marketing. Once you’ve mastered these techniques, you’ll constantly turn to this guide for the working PyMC code you need to jumpstart future projects. Coverage includes • Learning the Bayesian “state of mind” and its practical implications • Understanding how computers perform Bayesian inference • Using the PyMC Python library to program Bayesian analyses • Building and debugging models with PyMC • Testing your model’s “goodness of fit” • Opening the “black box” of the Markov Chain Monte Carlo algorithm to see how and why it works • Leveraging the power of the “Law of Large Numbers” • Mastering key concepts, such as clustering, convergence, autocorrelation, and thinning • Using loss functions to measure an estimate’s weaknesses based on your goals and desired outcomes • Selecting appropriate priors and understanding how their influence changes with dataset size • Overcoming the “exploration versus exploitation” dilemma: deciding when “pretty good” is good enough • Using Bayesian inference to improve A/B testing • Solving data science problems when only small amounts of data are available Cameron Davidson-Pilon has worked in many areas of applied mathematics, from the evolutionary dynamics of genes and diseases to stochastic modeling of financial prices. His contributions to the open source community include lifelines, an implementation of survival analysis in Python. Educated at the University of Waterloo and at the Independent University of Moscow, he currently works with the online commerce leader Shopify.
Posted in Computers

Bayesian Programming

Author: Pierre Bessiere,Emmanuel Mazer,Juan Manuel Ahuactzin,Kamel Mekhnacha

Publisher: CRC Press

ISBN: 1439880336

Category: Business & Economics

Page: 380

View: 5790

Probability as an Alternative to Boolean Logic While logic is the mathematical foundation of rational reasoning and the fundamental principle of computing, it is restricted to problems where information is both complete and certain. However, many real-world problems, from financial investments to email filtering, are incomplete or uncertain in nature. Probability theory and Bayesian computing together provide an alternative framework to deal with incomplete and uncertain data. Decision-Making Tools and Methods for Incomplete and Uncertain Data Emphasizing probability as an alternative to Boolean logic, Bayesian Programming covers new methods to build probabilistic programs for real-world applications. Written by the team who designed and implemented an efficient probabilistic inference engine to interpret Bayesian programs, the book offers many Python examples that are also available on a supplementary website together with an interpreter that allows readers to experiment with this new approach to programming. Principles and Modeling Only requiring a basic foundation in mathematics, the first two parts of the book present a new methodology for building subjective probabilistic models. The authors introduce the principles of Bayesian programming and discuss good practices for probabilistic modeling. Numerous simple examples highlight the application of Bayesian modeling in different fields. Formalism and Algorithms The third part synthesizes existing work on Bayesian inference algorithms since an efficient Bayesian inference engine is needed to automate the probabilistic calculus in Bayesian programs. Many bibliographic references are included for readers who would like more details on the formalism of Bayesian programming, the main probabilistic models, general purpose algorithms for Bayesian inference, and learning problems. FAQs Along with a glossary, the fourth part contains answers to frequently asked questions. The authors compare Bayesian programming and possibility theories, discuss the computational complexity of Bayesian inference, cover the irreducibility of incompleteness, and address the subjectivist versus objectivist epistemology of probability. The First Steps toward a Bayesian Computer A new modeling methodology, new inference algorithms, new programming languages, and new hardware are all needed to create a complete Bayesian computing framework. Focusing on the methodology and algorithms, this book describes the first steps toward reaching that goal. It encourages readers to explore emerging areas, such as bio-inspired computing, and develop new programming languages and hardware architectures.
Posted in Business & Economics

Foundations of Probabilistic Logic Programming

Author: Fabrizio Riguzzi

Publisher: River Publishers

ISBN: 8770220182

Category: Computers

Page: 422

View: 9177

Probabilistic Logic Programming extends Logic Programming by enabling the representation of uncertain information. Probabilistic Logic Programming is at the intersection of two wider research fields: the integration of logic and probability and Probabilistic Programming. Logic enables the representation of complex relations among entities while probability theory is useful for model uncertainty over attributes and relations. Combining the two is a very active field of study. Probabilistic Programming extends programming languages with probabilistic primitives that can be used to write complex probabilistic models. Algorithms for the inference and learning tasks are then provided automatically by the system. Probabilistic Logic programming is at the same time a logic language, with its knowledge representation capabilities, and a Turing complete language, with its computation capabilities, thus providing the best of both worlds. Since its birth, the field of Probabilistic Logic Programming has seen a steady increase of activity, with many proposals for languages and algorithms for inference and learning. Foundations of Probabilistic Logic Programming aims at providing an overview of the field with a special emphasis on languages under the Distribution Semantics, one of the most influential approaches. The book presents the main ideas for semantics, inference, and learning and highlights connections between the methods. Many examples of the book include a link to a page of the web application http://cplint.eu where the code can be run online.
Posted in Computers

Probabilistic Programming

Author: S. Vajda

Publisher: Academic Press

ISBN: 1483268373

Category: Mathematics

Page: 140

View: 9987

Probabilistic Programming discusses a high-level language known as probabilistic programming. This book consists of three chapters. Chapter I deals with “wait-and-see problems that require waiting until an observation is made on the random elements, while Chapter II contains the analysis of decision problems, particularly of so-called two-stage problems. The last chapter focuses on “chance constraints, such as constraints that are not expected to be always satisfied, but only in a proportion of cases or “with given probabilities. This text specifically deliberates the decision regions for optimality, probability distributions, Kall's Theorem, and two-stage programming under uncertainty. The complete problem, active approach, quantile rules, randomized decisions, and nonzero order rules are also covered. This publication is suitable for developers aiming to define and automatically solve probability models.
Posted in Mathematics

Machine Learning

A Probabilistic Perspective

Author: Kevin P. Murphy

Publisher: MIT Press

ISBN: 0262018020

Category: Computers

Page: 1067

View: 4941

A comprehensive introduction to machine learning that uses probabilistic models and inference as a unifying approach.
Posted in Computers

A Practical Theory of Programming

Author: Eric C.R. Hehner

Publisher: Springer Science & Business Media

ISBN: 1441985964

Category: Computers

Page: 247

View: 5701

There are several theories of programming. The first usable theory, often called "Hoare's Logic", is still probably the most widely known. In it, a specification is a pair of predicates: a precondition and postcondition (these and all technical terms will be defined in due course). Another popular and closely related theory by Dijkstra uses the weakest precondition predicate transformer, which is a function from programs and postconditions to preconditions. lones's Vienna Development Method has been used to advantage in some industries; in it, a specification is a pair of predicates (as in Hoare's Logic), but the second predicate is a relation. Temporal Logic is yet another formalism that introduces some special operators and quantifiers to describe some aspects of computation. The theory in this book is simpler than any of those just mentioned. In it, a specification is just a boolean expression. Refinement is just ordinary implication. This theory is also more general than those just mentioned, applying to both terminating and nonterminating computation, to both sequential and parallel computation, to both stand-alone and interactive computation. And it includes time bounds, both for algorithm classification and for tightly constrained real-time applications.
Posted in Computers

Uncertainty Reasoning for the Semantic Web II

International Workshops URSW 2008-2010 Held at ISWC and UniDL 2010 Held at Floc, Revised Selected Papers

Author: Fernando Bobillo,Paulo C. G. Costa,Claudia d'Amato,Nicola Fanizzi,Kathryn B. Laskey,Kenneth J. Laskey,Thomas Lukasiewicz,Matthias Nickles,Michael Pool

Publisher: Springer

ISBN: 3642359752

Category: Computers

Page: 331

View: 8819

This book contains revised and significantly extended versions of selected papers from three workshops on Uncertainty Reasoning for the Semantic Web (URSW), held at the International Semantic Web Conferences (ISWC) in 2008, 2009, and 2010 or presented at the first international Workshop on Uncertainty in Description Logics (UniDL), held at the Federated Logic Conference (FLoC) in 2010. The 17 papers presented were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on probabilistic and Dempster-Shafer models, fuzzy and possibilistic models, inductive reasoning and machine learning, and hybrid approaches.
Posted in Computers

Bayesian Analysis with Python

Author: Osvaldo Martin

Publisher: Packt Publishing Ltd

ISBN: 1785889850

Category: Computers

Page: 282

View: 4861

Unleash the power and flexibility of the Bayesian framework About This Book Simplify the Bayes process for solving complex statistical problems using Python; Tutorial guide that will take the you through the journey of Bayesian analysis with the help of sample problems and practice exercises; Learn how and when to use Bayesian analysis in your applications with this guide. Who This Book Is For Students, researchers and data scientists who wish to learn Bayesian data analysis with Python and implement probabilistic models in their day to day projects. Programming experience with Python is essential. No previous statistical knowledge is assumed. What You Will Learn Understand the essentials Bayesian concepts from a practical point of view Learn how to build probabilistic models using the Python library PyMC3 Acquire the skills to sanity-check your models and modify them if necessary Add structure to your models and get the advantages of hierarchical models Find out how different models can be used to answer different data analysis questions When in doubt, learn to choose between alternative models. Predict continuous target outcomes using regression analysis or assign classes using logistic and softmax regression. Learn how to think probabilistically and unleash the power and flexibility of the Bayesian framework In Detail The purpose of this book is to teach the main concepts of Bayesian data analysis. We will learn how to effectively use PyMC3, a Python library for probabilistic programming, to perform Bayesian parameter estimation, to check models and validate them. This book begins presenting the key concepts of the Bayesian framework and the main advantages of this approach from a practical point of view. Moving on, we will explore the power and flexibility of generalized linear models and how to adapt them to a wide array of problems, including regression and classification. We will also look into mixture models and clustering data, and we will finish with advanced topics like non-parametrics models and Gaussian processes. With the help of Python and PyMC3 you will learn to implement, check and expand Bayesian models to solve data analysis problems. Style and approach Bayes algorithms are widely used in statistics, machine learning, artificial intelligence, and data mining. This will be a practical guide allowing the readers to use Bayesian methods for statistical modelling and analysis using Python.
Posted in Computers

Biological Sequence Analysis

Probabilistic Models of Proteins and Nucleic Acids

Author: Richard Durbin,Sean R. Eddy,Anders Krogh,Graeme Mitchison

Publisher: Cambridge University Press

ISBN: 113945739X

Category: Science

Page: N.A

View: 7422

Probabilistic models are becoming increasingly important in analysing the huge amount of data being produced by large-scale DNA-sequencing efforts such as the Human Genome Project. For example, hidden Markov models are used for analysing biological sequences, linguistic-grammar-based probabilistic models for identifying RNA secondary structure, and probabilistic evolutionary models for inferring phylogenies of sequences from different organisms. This book gives a unified, up-to-date and self-contained account, with a Bayesian slant, of such methods, and more generally to probabilistic methods of sequence analysis. Written by an interdisciplinary team of authors, it aims to be accessible to molecular biologists, computer scientists, and mathematicians with no formal knowledge of the other fields, and at the same time present the state-of-the-art in this new and highly important field.
Posted in Science

Building Probabilistic Graphical Models with Python

Author: Kiran R Karkera

Publisher: Packt Publishing Ltd

ISBN: 1783289015

Category: Computers

Page: 172

View: 5007

This is a short, practical guide that allows data scientists to understand the concepts of Graphical models and enables them to try them out using small Python code snippets, without being too mathematically complicated. If you are a data scientist who knows about machine learning and want to enhance your knowledge of graphical models, such as Bayes network, in order to use them to solve real-world problems using Python libraries, this book is for you.This book is intended for those who have some Python and machine learning experience, or are exploring the machine learning field.
Posted in Computers

Statistical Relational Artificial Intelligence

Logic, Probability, and Computation

Author: Luc De Raedt,Kristian Kersting,Sriraam Natarajan,David Poole

Publisher: Morgan & Claypool Publishers

ISBN: 1627058427

Category: Computers

Page: 189

View: 7336

An intelligent agent interacting with the real world will encounter individual people, courses, test results, drugs prescriptions, chairs, boxes, etc., and needs to reason about properties of these individuals and relations among them as well as cope with uncertainty. Uncertainty has been studied in probability theory and graphical models, and relations have been studied in logic, in particular in the predicate calculus and its extensions. This book examines the foundations of combining logic and probability into what are called relational probabilistic models. It introduces representations, inference, and learning techniques for probability, logic, and their combinations. The book focuses on two representations in detail: Markov logic networks, a relational extension of undirected graphical models and weighted first-order predicate calculus formula, and Problog, a probabilistic extension of logic programs that can also be viewed as a Turing-complete relational extension of Bayesian networks.
Posted in Computers

Inductive Logic Programming

20th International Conference, ILP 2010, Florence, Italy, June 27-30, 2010, Revised Papers

Author: Paolo Frasconi,Francesca A. Lisi

Publisher: Springer Science & Business Media

ISBN: 3642212948

Category: Computers

Page: 278

View: 4512

This book constitutes the thoroughly refereed post-proceedings of the 20th International Conference on Inductive Logic Programming, ILP 2010, held in Florence, Italy in June 2010. The 11 revised full papers and 15 revised short papers presented together with abstracts of three invited talks were carefully reviewed and selected during two rounds of refereeing and revision. All current issues in inductive logic programming, i.e. in logic programming for machine learning are addressed, in particular statistical learning and other probabilistic approaches to machine learning are reflected.
Posted in Computers

Programming Robots with ROS

A Practical Introduction to the Robot Operating System

Author: Morgan Quigley,Brian Gerkey,William D. Smart

Publisher: "O'Reilly Media, Inc."

ISBN: 1449325513

Category: Computers

Page: 448

View: 9642

Want to develop novel robot applications, but don’t know how to write a mapping or object-recognition system? You’re not alone, but you’re certainly not without help. By combining real-world examples with valuable knowledge from the Robot Operating System (ROS) community, this practical book provides a set of motivating recipes for solving specific robotics use cases. Ideal for enthusiasts, from students in robotics clubs to professional robotics scientists and engineers, each recipe describes a complete solution using ROS open source libraries and tools. You’ll learn how to complete tasks described in the recipes, as well as how to configure and recombine components for other tasks. If you’re familiar with Python, you’re ready to go. Learn fundamentals, including key ROS concepts, tools, and patterns Program robots that perform an increasingly complex set of behaviors, using the powerful packages in ROS See how to easily add perception and navigation abilities to your robots Integrate your own sensors, actuators, software libraries, and even a whole robot into the ROS ecosystem Learn tips and tricks for using ROS tools and community resources, debugging robot behavior, and using C++ in ROS
Posted in Computers

Heavy-Tail Phenomena

Probabilistic and Statistical Modeling

Author: Sidney I. Resnick

Publisher: Springer Science & Business Media

ISBN: 0387242724

Category: Business & Economics

Page: 404

View: 2073

This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. Heavy tails are characteristic of many phenomena where the probability of a single huge value impacts heavily. Record-breaking insurance losses, financial-log returns, files sizes stored on a server, transmission rates of files are all examples of heavy-tailed phenomena. Key features: * Unique text devoted to heavy-tails * Emphasizes both probability modeling and statistical methods for fitting models. Most treatments focus on one or the other but not both * Presents broad applicability of heavy-tails to the fields of data networks, finance (e.g., value-at- risk), insurance, and hydrology * Clear, efficient and coherent exposition, balancing theory and actual data to show the applicability and limitations of certain methods * Examines in detail the mathematical properties of the methodologies as well as their implementation in Splus or R statistical languages * Exposition driven by numerous examples and exercises Prerequisites for the reader include a prior course in stochastic processes and probability, some statistical background, some familiarity with time series analysis, and ability to use (or at least to learn) a statistics package such as R or Splus. This work will serve second-year graduate students and researchers in the areas of applied mathematics, statistics, operations research, electrical engineering, and economics.
Posted in Business & Economics

Probabilistic Reasoning in Intelligent Systems

Networks of Plausible Inference

Author: Judea Pearl

Publisher: Elsevier

ISBN: 0080514898

Category: Computers

Page: 552

View: 4384

Probabilistic Reasoning in Intelligent Systems is a complete and accessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty. The author provides a coherent explication of probability as a language for reasoning with partial belief and offers a unifying perspective on other AI approaches to uncertainty, such as the Dempster-Shafer formalism, truth maintenance systems, and nonmonotonic logic. The author distinguishes syntactic and semantic approaches to uncertainty--and offers techniques, based on belief networks, that provide a mechanism for making semantics-based systems operational. Specifically, network-propagation techniques serve as a mechanism for combining the theoretical coherence of probability theory with modern demands of reasoning-systems technology: modular declarative inputs, conceptually meaningful inferences, and parallel distributed computation. Application areas include diagnosis, forecasting, image interpretation, multi-sensor fusion, decision support systems, plan recognition, planning, speech recognition--in short, almost every task requiring that conclusions be drawn from uncertain clues and incomplete information. Probabilistic Reasoning in Intelligent Systems will be of special interest to scholars and researchers in AI, decision theory, statistics, logic, philosophy, cognitive psychology, and the management sciences. Professionals in the areas of knowledge-based systems, operations research, engineering, and statistics will find theoretical and computational tools of immediate practical use. The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.
Posted in Computers

Bayesian Rationality

The Probabilistic Approach to Human Reasoning

Author: Mike Oaksford,Nick Chater

Publisher: Oxford University Press

ISBN: 9780198524496

Category: Philosophy

Page: 330

View: 2933

For almost 2,500 years, the Western concept of what is to be human has been dominated by the idea that the mind is the seat of reason - humans are, almost by definition, the rational animal. In this text a more radical suggestion for explaining these puzzling aspects of human reasoning is put forward.
Posted in Philosophy

Practical Bayesian Inference

A Primer for Physical Scientists

Author: Coryn A. L. Bailer-Jones

Publisher: Cambridge University Press

ISBN: 1108127673

Category: Mathematics

Page: N.A

View: 1835

Science is fundamentally about learning from data, and doing so in the presence of uncertainty. This volume is an introduction to the major concepts of probability and statistics, and the computational tools for analysing and interpreting data. It describes the Bayesian approach, and explains how this can be used to fit and compare models in a range of problems. Topics covered include regression, parameter estimation, model assessment, and Monte Carlo methods, as well as widely used classical methods such as regularization and hypothesis testing. The emphasis throughout is on the principles, the unifying probabilistic approach, and showing how the methods can be implemented in practice. R code (with explanations) is included and is available online, so readers can reproduce the plots and results for themselves. Aimed primarily at undergraduate and graduate students, these techniques can be applied to a wide range of data analysis problems beyond the scope of this work.
Posted in Mathematics

Practical Data Science with R

Author: Nina Zumel,John Mount

Publisher: Manning Publications

ISBN: 9781617291562

Category: Computers

Page: 416

View: 8804

Summary Practical Data Science with R lives up to its name. It explains basic principles without the theoretical mumbo-jumbo and jumps right to the real use cases you'll face as you collect, curate, and analyze the data crucial to the success of your business. You'll apply the R programming language and statistical analysis techniques to carefully explained examples based in marketing, business intelligence, and decision support. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the Book Business analysts and developers are increasingly collecting, curating, analyzing, and reporting on crucial business data. The R language and its associated tools provide a straightforward way to tackle day-to-day data science tasks without a lot of academic theory or advanced mathematics. Practical Data Science with R shows you how to apply the R programming language and useful statistical techniques to everyday business situations. Using examples from marketing, business intelligence, and decision support, it shows you how to design experiments (such as A/B tests), build predictive models, and present results to audiences of all levels. This book is accessible to readers without a background in data science. Some familiarity with basic statistics, R, or another scripting language is assumed. What's Inside Data science for the business professional Statistical analysis using the R language Project lifecycle, from planning to delivery Numerous instantly familiar use cases Keys to effective data presentations About the Authors Nina Zumel and John Mount are cofounders of a San Francisco-based data science consulting firm. Both hold PhDs from Carnegie Mellon and blog on statistics, probability, and computer science at win-vector.com. Table of Contents PART 1 INTRODUCTION TO DATA SCIENCE The data science process Loading data into R Exploring data Managing data PART 2 MODELING METHODS Choosing and evaluating models Memorization methods Linear and logistic regression Unsupervised methods Exploring advanced methods PART 3 DELIVERING RESULTS Documentation and deployment Producing effective presentations
Posted in Computers

Practical Aspects of Declarative Languages

20th International Symposium, PADL 2018, Los Angeles, CA, USA, January 8–9, 2018, Proceedings

Author: Francesco Calimeri,Kevin Hamlen,Nicola Leone

Publisher: Springer

ISBN: 3319733052

Category: Computers

Page: 203

View: 6199

This book constitutes the proceedings of the 20th International Symposium on Practical Aspects of Declarative Languages, PADL 2018, held in Los Angeles, CA, USA, in January 2018 and collocated with the 45th ACM SIGPLAN Symposium on Principles of Programming Languages.The 13 regular papers presented in this volume together with the abstracts of 2 invited talks were carefully reviewed and selected from 23 submissions. They deal with functional programming; constraint programming and business rules; prolog and optimization; and answer set programming.
Posted in Computers