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For statistics in probability theory, the Boolean-Poisson model or simply Boolean model for a random subset of the plane (or higher dimensions, analogously)
Boolean model (probability theory)
Boolean_model_(probability_theory)
Mathematical topics based on the works of George Boole
function that determines Boolean values or operators Boolean model (probability theory), a model in stochastic geometry Boolean network, a certain network
Boolean
Branch of mathematics in probability theory
mathematics and probability theory, continuum percolation theory is a branch of mathematics that extends discrete percolation theory to continuous space
Continuum_percolation_theory
Mathematical model of ferromagnetism in statistical mechanics
pseudo-Boolean function; tools from the analysis of Boolean functions can be applied to describe and study it. The configuration probability is given
Ising_model
Overview of and topical guide to logic
form (Boolean algebra) Boolean conjunctive query Boolean-valued model Boolean domain Boolean expression Boolean ring Boolean function Boolean-valued
Outline_of_logic
Interpretation of probability
the Boolean algebra of statements may be finite. Other axiomatizations have been suggested by various authors with the purpose of making the theory more
Bayesian_probability
Analysis of Boolean functions Balanced Boolean function Bent function Boolean algebras canonically defined Boolean function Boolean matrix Boolean-valued function
List of Boolean algebra topics
List_of_Boolean_algebra_topics
English mathematician and philosopher (1815–1864)
function that determines Boolean values or operators Boolean model (probability theory), a model in stochastic geometry Boolean network, a certain network
George_Boole
Classical information retrieval model
The (standard) Boolean model of information retrieval (BIR) is a classical information retrieval (IR) model where documents are retrieved based on whether
Boolean model of information retrieval
Boolean_model_of_information_retrieval
Algebraic manipulation of "true" and "false"
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the
Boolean_algebra
Probability distribution
yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p). A single success/failure
Binomial_distribution
Two closely related models for generating random graphs
graph theory, the Erdős–Rényi models are two closely related models for generating random graphs and the evolution of a random network. These models are
Erdős–Rényi_model
Description of a system using mathematical concepts and language
values, but rather by probability distributions. A deductive model is a logical structure based on a theory. An inductive model arises from empirical
Mathematical_model
Function returning one of only two values
logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory. A Boolean function takes the form f : { 0
Boolean_function
Number measuring the chance an event occurs
computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe
Probability
Mathematical theory on behavior of connected clusters in a random graph
mathematical model for obtaining a random graph, a site is "occupied" with probability p or "empty" (in which case its edges are removed) with probability 1 –
Percolation_theory
Problem of determining if a Boolean formula could be made true
In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY
Boolean satisfiability problem
Boolean_satisfiability_problem
System for reasoning about vagueness
of a probability theory for jointly modelling uncertainty and vagueness. Bart Kosko claims in Fuzziness vs. Probability that probability theory is a subtheory
Fuzzy_logic
number Algebraic logic Boolean algebra (logic) Dialectica space categorical logic Finite model theory Descriptive complexity theory Model checking Trakhtenbrot's
List of mathematical logic topics
List_of_mathematical_logic_topics
Type of random mathematical object
and BIC (Bayesian information criterion). Boolean model (probability theory) Continuum percolation theory Compound Poisson process Cox process Point
Poisson_point_process
set theory. Algebra of sets Axiom of choice Axiom of countable choice Axiom of dependent choice Zorn's lemma Axiom of power set Boolean-valued model Burali-Forti
List_of_set_theory_topics
Branch of mathematics that studies sets
set theory and fuzzy set theory, in which the value of an atomic formula embodying the membership relation is not simply True or False. The Boolean-valued
Set_theory
Derivation of the laws of probability theory
laws of probability theory from a certain set of postulates. This derivation justifies the so-called "logical" interpretation of probability, as the laws
Cox's_theorem
Set of elements in any of some sets
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through
Union_(set_theory)
(lattice theory) Boolean prime ideal theorem (mathematical logic) Bourbaki–Witt theorem (order theory) Cantor's isomorphism theorem (order theory) Dilworth's
List_of_theorems
Discrete set of Boolean variables
A Boolean network consists of a discrete set of Boolean variables each of which has a Boolean function (possibly different for each variable) assigned
Boolean_network
Sorting method in information retrieval
probabilistic model, probability theory has been used as a principal means for modeling the retrieval process in mathematical terms. The probability model of information
Ranking (information retrieval)
Ranking_(information_retrieval)
Probability distribution modeling a coin toss which need not be fair
In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution
Bernoulli_distribution
Logical modeling technique
the probability of occurrence. ETA uses a type of modeling technique called "event tree", which branches events from one single event using Boolean logic
Event_tree_analysis
"Solving and Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer". In Creignou, N.; Le Berre, D. (eds.). Theory and Applications of Satisfiability
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Graph generated by a random process
process which generates them. The theory of random graphs lies at the intersection between graph theory and probability theory. From a mathematical perspective
Random_graph
Estimate of the importance of a word in a document
much theory, aside from a connection to Zipf's law. Attempts have been made to put idf on a probabilistic footing, by estimating the probability that
Tf–idf
Theory of machine learning
Cryptographic limitations on learning Boolean formulae and finite automata. In Proceedings of the 21st Annual ACM Symposium on Theory of Computing, pages 433–444
Computational_learning_theory
Inherent difficulty of computational problems
resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and
Computational complexity theory
Computational_complexity_theory
Pair of logical equivalences
and Boolean algebra, however, they also play an important role in reasoning and computation. De Morgan's laws are utilized in probability theory, allowing
De_Morgan's_laws
Model of computational complexity
In computational complexity theory, the decision tree model is the model of computation in which an algorithm can be considered to be a decision tree,
Decision_tree_model
Computational Formula that can be measured in terms of True or False
complexity theory, the language TQBF is a formal language consisting of the true quantified Boolean formulas. A (fully) quantified Boolean formula is
True quantified Boolean formula
True_quantified_Boolean_formula
Measure of algorithmic complexity
(1968). "Logical basis for information theory and probability theory". IEEE Transactions on Information Theory. 14 (5): 662–664. doi:10.1109/TIT.1968
Kolmogorov_complexity
Theories in mathematical logic
first-order theory is given by a set of axioms in some language. This entry lists some of the more common examples used in model theory and some of their
List_of_first-order_theories
Study of random spatial patterns
construction of elaborate random spatial patterns. The simplest version, the Boolean model, places a random compact object at each point of a Poisson point process
Stochastic_geometry
Data structure for approximate set membership
counting Bloom filter variant); the more items added, the larger the probability of false positives. Bloom proposed the technique for applications where
Bloom_filter
Branch of logic
Finite model theory is a subarea of model theory. Model theory is the branch of logic which deals with the relation between a formal language (syntax)
Finite_model_theory
Study of abstract machines and automata
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical
Automata_theory
Academic field of logic and rhetoric
p. 182–183). The theory postulates this as an ideal model, and not something one expects to find as an empirical fact. The model can however serve as
Argumentation_theory
List of statements that appear to contradict themselves
theorem: Why do measured quantum particles not satisfy mathematical probability theory? Double-slit experiment: Matter and energy can act as a wave or as
List_of_paradoxes
Model in network science
Bianconi–Barabási model depends on the fitness distribution ρ ( η ) {\displaystyle \rho (\eta )} . There are two scenarios that can happen based on the probability distribution
Bianconi–Barabási_model
Concept in model theory
In model theory, interpretation of a structure M in another structure N (typically of a different signature) is a technical notion that approximates the
Interpretation_(model_theory)
Scale-free network generation algorithm
choosing an existing link, the probability of selecting a particular page would be proportional to its degree. The BA model claims that this explains the
Barabási–Albert_model
Bayesian model comparison – see Bayes factor Bayesian multivariate linear regression Bayesian network Bayesian probability Bayesian search theory Bayesian
List_of_statistics_articles
Representation of a type of random process
In statistics, an autoregressive (AR) model is a modelled representation of a type of random process. It can be used to describe time-varying processes
Autoregressive_model
Study of discrete mathematical structures
of combinatorial structures using tools from complex analysis and probability theory. In contrast with enumerative combinatorics which uses explicit combinatorial
Discrete_mathematics
Queueing theory Recurrence period density entropy Variance gamma process / fnc Wiener equation Boolean model Buffon's needle Geometric probability Hadwiger's
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Relationship in which one statement follows from another
penguin}. Abstract algebraic logic Ampheck Boolean algebra (logic) Boolean domain Boolean function Boolean logic Causality Deductive reasoning Logic gate
Logical_consequence
Computer hardware technology that uses quantum mechanics
information eventually quickly decoheres. While programmers may depend on probability theory when designing a randomized algorithm, quantum-mechanical notions
Quantum_computing
Determining the probability of future events based on past events
represents probabilities of statements. Occam's razor says the "simplest theory, consistent with the data is most likely to be correct". The "simplest theory" is
Inductive_probability
Mixing property of Markov chains and graphs
In theoretical computer science, graph theory, and mathematics, the conductance is a parameter of a Markov chain that is closely tied to its mixing time
Conductance_(graph_theory)
Computable number Definable number Halting probability Algorithmic information theory Algorithmic probability Data compression Advice (complexity) Amortized
List of computability and complexity topics
List_of_computability_and_complexity_topics
Axiomatic set theories based on the principles of mathematical constructivism
admits a surjection from a Boolean topos onto it, relating to classical statements being provable intuitionistically. In type theory, the expression " x →
Constructive_set_theory
Network whose degree distribution follows a power law
generative model that mixes preferential attachment with a baseline probability of gaining a link. Another generative model is the copy model studied by
Scale-free_network
with some fixed probability. Using the tools of percolation theory, a new type model referred to as a blinking Boolean-Poisson model, was proposed to
Stochastic geometry models of wireless networks
Stochastic_geometry_models_of_wireless_networks
Probabilistic classification algorithm
at quantifying uncertainty (with naive Bayes models often producing wildly overconfident probabilities). However, they are highly scalable, requiring
Naive_Bayes_classifier
American mathematician (1916–2001)
information theory", and the man who laid the foundations of the Information Age. Shannon was among the first to describe the use of Boolean algebra—essential
Claude_Shannon
topology and set theory. Cohen 1. Paul Cohen 2. Cohen forcing is a method for constructing models of ZFC 3. A Cohen algebra is a Boolean algebra whose
Glossary_of_set_theory
List of algebraic structures List of Boolean algebra topics List of category theory topics List of cohomology theories List of commutative algebra topics
Lists_of_mathematics_topics
Field of knowledge
heavy use of models. Areas of mathematics used in the social sciences include probability theory, statistics, differential equations, game theory, optimization
Mathematics
Branch of discrete mathematics
problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas
Combinatorics
Value indicating the relation of a proposition to truth
algebras, compared to Boolean algebra semantics of classical propositional calculus. Philosophy portal Psychology portal Bayesian probability Circular reasoning
Truth_value
Complexity class used to classify decision problems
in NP. The Boolean satisfiability problem (SAT), where we want to know whether or not a certain formula in propositional logic with Boolean variables is
NP_(complexity)
Theory within consciousness research
Integrated information theory (IIT) proposes a mathematical model for the consciousness of a system. It comprises a framework ultimately intended to explain
Integrated_information_theory
Logic with discrete truth values
finite-valued logic. However, finite-valued logic can be applied in Boolean-valued modeling, description logics, and defuzzification of fuzzy logic. A finite-valued
Finite-valued_logic
measurement — it can be a Boolean value, a real number, a vector (in which case it is also called a data vector), etc. decision rule decision theory degrees of freedom
Glossary of probability and statistics
Glossary_of_probability_and_statistics
Mathematical term; concerning axioms used to derive theorems
the theory of probabilities to theoretical physics. Israel comments also on cultural resistance, at least in France and Italy, to this "German model" and
Axiomatic_system
Class of artificial neural network
graphical model of RBMs corresponds to that of factor analysis. Restricted Boltzmann machines are trained to maximize the product of probabilities assigned
Restricted_Boltzmann_machine
Israeli mathematician
works included papers on limits of planar graphs,[BS] noise sensitivity of Boolean functions[BKS1] and first passage percolation[BKS2]. With Olle Häggström
Itai_Benjamini
Taxonomy of statistical data elements
in that dichotomous categorical variables may be represented with the Boolean data type, polytomous categorical variables with arbitrarily assigned integers
Statistical_data_type
Academic field
An alternate approach to network probability structures is the network probability matrix, which models the probability of edges occurring in a network
Network_science
algebra Poisson–Mellin–Newton cycle Poisson–Lie group Probability theory Boolean-Poisson model Poisson bootstrap Poisson distribution Compound Poisson
List of things named after Siméon Denis Poisson
List_of_things_named_after_Siméon_Denis_Poisson
Study of collection and analysis of data
Inferences made using mathematical statistics employ the framework of probability theory, which deals with the analysis of random phenomena. A standard statistical
Statistics
Logical connective
built on foundations such as modal logic, relevance logic, probability theory, and causal models. Similar discrepancies have been observed by psychologists
Material_conditional
Theory of logic to account for observations from quantum theory
propositions to a Boolean algebra. Consequently, quantum logic struggles to represent the passage of time. One possible workaround is the theory of quantum filtrations
Quantum_logic
American logician (born 1934)
technique in set theory and models of Peano arithmetic. Further, he has results in the foundations of probability, defining probabilities on first-order
Haim_Gaifman
central role in topos theory of the sub-object classifier. In the usual category of sets, this is the two-element set of Boolean truth-values, true and
History_of_topos_theory
Probabilistic graphical representation of causal relationships
{\displaystyle m} parent nodes represent m {\displaystyle m} Boolean variables, then the probability function could be represented by a table of 2 m {\displaystyle
Bayesian_network
System including an indeterminate value
the more commonly known bivalent logics (such as classical sentential or Boolean logic) which provide only for true and false. Emil Leon Post is credited
Three-valued_logic
Variable representing a random phenomenon
(2014), Introduction to Queueing Theory and Stochastic Teletraffic Models (PDF), arXiv:1307.2968 Zukerman, Moshe (2014), Basic Probability Topics (PDF)
Random_variable
Statistical evaluation method
total operating characteristic (TOC) is a statistical method to compare a Boolean variable versus a rank variable. TOC can measure the ability of an index
Total operating characteristic
Total_operating_characteristic
Diagram that shows all possible logical relations between a collection of sets
diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer
Venn_diagram
Method of deriving conclusions
2022, Lead section, § 2. Proof Theory Demey, Kooi & Sack 2023, Lead section, § 1. Combining Logic and Probability Theory, § 2.1 Probabilistic Semantics
Rule_of_inference
Form of reasoning
displaying short descriptions of redirect targets Decision theory – Branch of applied probability theory Defeasible reasoning – Reasoning that is rationally
Deductive_reasoning
Algebraic ring that need not have additive negative elements
lattices. The smallest semiring that is not a ring is the two-element Boolean algebra, for instance with logical disjunction ∨ {\displaystyle \lor }
Semiring
Probabilistic optimization technique and metaheuristic
search space is discrete (for example the traveling salesman problem, the boolean satisfiability problem, protein structure prediction, and job-shop scheduling)
Simulated_annealing
Topological model
domain of the mask elements is {0,1,2,F,*}, or {T,F,*} for the boolean form. The simpler models 4-Intersection and 9-Intersection were proposed before DE-9IM
DE-9IM
Method of logical reasoning
"credible" according to some theory of evidence. Examples include a many-valued logic, Dempster–Shafer theory, or probability theory with rules for inference
Inductive_reasoning
Set of elements common to all of some sets
In set theory, the intersection of two sets A {\displaystyle A} and B , {\displaystyle B,} denoted by A ∩ B , {\displaystyle A\cap B,} is the set containing
Intersection_(set_theory)
Inference seeking the simplest and most likely explanation
explicitly so in his influential 1883 "A theory of probable inference", in which he returns to involving probability in the hypothetical conclusion. Like
Abductive_reasoning
In mathematics, a statement that has been proven
law can also refer to an axiom, a rule of inference, or, in probability theory, a probability distribution. Elisha Scott Loomis. "The Pythagorean proposition:
Theorem
In probability theory, a conditional event algebra (CEA) is an alternative to a standard, Boolean algebra of possible events (a set of possible events
Conditional_event_algebra
Clustering and community detection algorithm
C_prime changes the quality function in the positive direction, set the probability that the community of v to exp(1/θ * ∆HP(v → C)) else set it to 0 for
Leiden_algorithm
Machine learning algorithm
box or open-box model. If a given situation is observable in a model the explanation for the condition is easily explained by Boolean logic. By contrast
Decision_tree_learning
Interpretation of quantum mechanics
interpreting quantum probabilities as Bayesian in some manner. QBism deals with common questions in the interpretation of quantum theory about the nature
QBism
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