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Probabilistic Logic Programming
Probabilistic logic programming is a programming paradigm that combines logic programming with probabilities. Most approaches to probabilistic logic programming are based on the ''distribution semantics,'' which splits a program into a set of probabilistic facts and a logic program. It defines a probability distribution on interpretations of the Herbrand structure, Herbrand universe of the program. Languages Most approaches to probabilistic logic programming are based on the ''distribution semantics,'' which underlies many languages such as Probabilistic Horn Abduction, PRISM, Independent Choice Logic , probabilistic Datalog, Logic Programs with Annotated Disjunctions, ProbLog, P-log, and CP-logic. While the number of languages is large, many share a common approach so that there are transformations with Time complexity, linear complexity that can translate one language into another. Semantics Under the distribution semantics, a probabilistic logic program is interpreted as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Programming Paradigm
Programming paradigms are a way to classify programming languages based on their features. Languages can be classified into multiple paradigms. Some paradigms are concerned mainly with implications for the execution model of the language, such as allowing side effects, or whether the sequence of operations is defined by the execution model. Other paradigms are concerned mainly with the way that code is organized, such as grouping a code into units along with the state that is modified by the code. Yet others are concerned mainly with the style of syntax and grammar. Common programming paradigms include: * imperative in which the programmer instructs the machine how to change its state, ** procedural which groups instructions into procedures, ** object-oriented which groups instructions with the part of the state they operate on, * declarative in which the programmer merely declares properties of the desired result, but not how to compute it ** functional in which the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Herbrand Universe
In first-order logic, a Herbrand structure ''S'' is a structure over a vocabulary σ that is defined solely by the syntactical properties of σ. The idea is to take the symbols of terms as their values, e.g. the denotation of a constant symbol ''c'' is just "''c''" (the symbol). It is named after Jacques Herbrand. Herbrand structures play an important role in the foundations of logic programming. Herbrand universe Definition The ''Herbrand universe'' serves as the universe in the ''Herbrand structure''. Example Let , be a first-order language with the vocabulary * constant symbols: ''c'' * function symbols: ''f''(·), ''g''(·) then the Herbrand universe of (or ) is . Notice that the relation symbols are not relevant for a Herbrand universe. Herbrand structure A ''Herbrand structure'' interprets terms on top of a ''Herbrand universe''. Definition Let ''S'' be a structure, with vocabulary σ and universe ''U''. Let ''W'' be the set of all terms over σ and '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistic Programming
Probabilistic programming (PP) is a programming paradigm in which probabilistic models are specified and inference for these models is performed automatically. It represents an attempt to unify probabilistic modeling and traditional general purpose programming in order to make the former easier and more widely applicable.Pfeffer, Avrom (2014), ''Practical Probabilistic Programming'', Manning Publications. p.28. It can be used to create systems that help make decisions in the face of uncertainty. Programming languages used for probabilistic programming are referred to as "probabilistic programming languages" (PPLs). Applications Probabilistic reasoning has been used for a wide variety of tasks such as predicting stock prices, recommending movies, diagnosing computers, detecting cyber intrusions and image detection. However, until recently (partially due to limited computing power), probabilistic programming was limited in scope, and most inference algorithms had to be written ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistic Database
Most real databases contain data whose correctness is uncertain. In order to work with such data, there is a need to quantify the integrity of the data. This is achieved by using probabilistic databases. A probabilistic database is an uncertain database in which the possible worlds have associated probabilities. Probabilistic database management systems are currently an active area of research. "While there are currently no commercial probabilistic database systems, several research prototypes exist..." Probabilistic databases distinguish between the logical data model and the physical representation of the data much like relational databases do in the ANSI-SPARC Architecture. In probabilistic databases this is even more crucial since such databases have to represent very large numbers of possible worlds, often exponential in the size of one world (a classical database), succinctly. Terminology In a probabilistic database, each tuple is associated with a probability between 0 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient Descent
In mathematics, gradient descent (also often called steepest descent) is a first-order iterative optimization algorithm for finding a local minimum of a differentiable function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent. Conversely, stepping in the direction of the gradient will lead to a local maximum of that function; the procedure is then known as gradient ascent. Gradient descent is generally attributed to Augustin-Louis Cauchy, who first suggested it in 1847. Jacques Hadamard independently proposed a similar method in 1907. Its convergence properties for non-linear optimization problems were first studied by Haskell Curry in 1944, with the method becoming increasingly well-studied and used in the following decades. Description Gradient descent is based on the observation that if the multi-variable function F(\mathbf) is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expectation–maximization Algorithm
In statistics, an expectation–maximization (EM) algorithm is an iterative method to find (local) maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the ''E'' step. These parameter-estimates are then used to determine the distribution of the latent variables in the next E step. History The EM algorithm was explained and given its name in a classic 1977 paper by Arthur Dempster, Nan Laird, and Donald Rubin. They pointed out that the method had been "proposed many times in special circumstances" by earlier authors. One of the earliest is the gene-counting method for estimating alle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial Time
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor. Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally express ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compiler
In computing, a compiler is a computer program that translates computer code written in one programming language (the ''source'' language) into another language (the ''target'' language). The name "compiler" is primarily used for programs that translate source code from a high-level programming language to a low-level programming language (e.g. assembly language, object code, or machine code) to create an executable program. Compilers: Principles, Techniques, and Tools by Alfred V. Aho, Ravi Sethi, Jeffrey D. Ullman - Second Edition, 2007 There are many different types of compilers which produce output in different useful forms. A '' cross-compiler'' produces code for a different CPU or operating system than the one on which the cross-compiler itself runs. A '' bootstrap compiler'' is often a temporary compiler, used for compiling a more permanent or better optimised compiler for a language. Related software include, a program that translates from a low-level language ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propositional Calculus
Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them. Compound propositions are formed by connecting propositions by logical connectives. Propositions that contain no logical connectives are called atomic propositions. Unlike first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or quantifiers. However, all the machinery of propositional logic is included in first-order logic and higher-order logics. In this sense, propositional logic is the foundation of first-order logic and higher-order logic. Explanation Logical connectives are found in natural languages. In English for example, some examples are "and" ( conjunction), "or" ( disjunction), "not" (negation) and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knowledge Compilation
Knowledge compilation is a family of approaches for addressing the intractability of a number of artificial intelligence problems. A propositional model is compiled in an off-line phase in order to support some queries in polynomial time. Many ways of compiling a propositional models exist.Adnan Darwiche, Pierre Marquis,A Knowledge Compilation Map, Journal of Artificial Intelligence Research 17 (2002) 229-264 Different compiled representations have different properties. The three main properties are: * The compactness of the representation * The queries that are supported in polynomial time * The transformations of the representations that can be performed in polynomial time Classes of representations Some examples of diagram classes include OBDDs, FBDDs, and non-deterministic OBDDs, as well as MDD. Some examples of formula In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
