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A probabilistic proposition is a proposition with a measured probability of being true for an arbitrary person at an arbitrary time. They may be contrasted
Probabilistic_proposition
Bearer of truth values
deterministic propositions express certain information, while probabilistic propositions indicate degrees of uncertainty. Normative propositions express what
Proposition
Applications of logic under uncertainty
confidence of a proposition, as opposed to performing some sort of probabilistic entailment. Historically, attempts to quantify probabilistic reasoning date
Probabilistic_logic
Artificial intelligence project
knowledgebase of millions of human validated true/false statements, or probabilistic propositions. It ran from 2000 to 2005. Participants in the project created
Mindpixel
Reasoning for mathematical statements
must demonstrate that the statement is true in all possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture
Mathematical_proof
Method of deriving conclusions
with distinct systems using different rules of inference. For example, propositional logic examines how statements formed through logical operators like
Rule_of_inference
Material supporting an assertion
Evidence for a proposition is what supports the proposition. It is usually understood as an indication that the proposition is true. The exact definition
Evidence
Branch of artificial intelligence
2019-07-03. Retrieved 2019-07-03. Littman, Michael L. (1997). Probabilistic Propositional Planning: Representations and Complexity. Fourteenth National
Automated planning and scheduling
Automated_planning_and_scheduling
Programming paradigm
Probabilistic logic programming is a programming paradigm that combines logic programming with probabilities. Most approaches to probabilistic logic programming
Probabilistic logic programming
Probabilistic_logic_programming
Probabilistic Computation Tree Logic (PCTL) is an extension of computation tree logic (CTL) that allows for probabilistic quantification of described
Probabilistic_CTL
Position combining atheism and agnosticism
of evidential standards, the burden of proof, negative atheism, or probabilistic degrees of belief rather than as a simple claim of certainty or denial
Agnostic_atheism
Number measuring the chance an event occurs
to determine pricing and make trading decisions. Governments apply probabilistic methods in environmental regulation, entitlement analysis, and financial
Probability
Probabilistic latent semantic analysis Probabilistic metric space Probabilistic proposition Probabilistic relational model Probability Probability bounds analysis
List_of_statistics_articles
Psychologist
was a psychologist who is known for his theory of probabilistic functionalism and his proposition that representative design is essential in psychological
Egon_Brunswik
Study of correct reasoning
propositions or claims that can be true or false. An important feature of propositions is their internal structure. For example, complex propositions
Logic
can lead to a false one. A propositional fallacy is an error that concerns compound propositions. For a compound proposition to be true, the truth values
List_of_fallacies
Awareness of facts
knowledge, also known as theoretical knowledge, descriptive knowledge, propositional knowledge, and knowledge-that, is an awareness of facts that can be
Declarative_knowledge
Algebraic manipulation of "true" and "false"
fuzzy logic and probabilistic logic. In these interpretations, a value is interpreted as the "degree" of truth – to what extent a proposition is true, or
Boolean_algebra
Paradox arising from the question of what constitutes evidence for a statement
that when a proposition, X, provides evidence in favor of another proposition Y, then X also provides evidence in favor of any proposition that is logically
Raven_paradox
Probabilistic theory of knowledge
order to draw probabilistic inferences based on new evidence, it is necessary to already have a prior probability assigned to the proposition in question
Bayesian_epistemology
Knowledge acquired by means of the senses
probabilistic and deductive reasoning, suggest that evidence has to be propositional in nature, i.e. that it is correctly expressed by propositional attitude
Empirical_evidence
Concept of philosophy and logic used to express modal claims
possible worlds. For instance, in the relational semantics for classical propositional modal logic, the formula ◊ P {\displaystyle \Diamond P} (read as "possibly
Possible_world
Natural-language "if" sentences about what may be the case
proposals include truth-functional analyses, pragmatics-augmented accounts, probabilistic ("suppositional") approaches, possible-worlds semantics, and restrictor
Indicative_conditional
Intelligence of machines
action (it is not "deterministic"). It must choose an action by making a probabilistic guess and then reassess the situation to see if the action worked. Alongside
Artificial_intelligence
Computational complexity
computer science). Occasionally NL is referred to as RL due to its probabilistic definition below; however, this name is more frequently used to refer
NL_(complexity)
Learning logic programs from data
in ACE) ProGolem Probabilistic inductive logic programming adapts the setting of inductive logic programming to learning probabilistic logic programs.
Inductive_logic_programming
Rules in probabilistic logic
In probabilistic logic, the Fréchet inequalities, also known as the Boole–Fréchet inequalities, are rules implicit in the work of George Boole and explicitly
Fréchet_inequalities
Logical connective AND
{\displaystyle (A\to C)\to ((A\land B)\to C)} when C {\displaystyle C} is a false proposition. If A {\displaystyle A} implies ¬ B {\displaystyle \neg B} , then both
Logical_conjunction
Lake District, UK, 2006. M. Wachter & R. Haenni, "Probabilistic Equivalence Checking with Propositional DAGs", Technical Report iam-2006-001, Institute
Propositional directed acyclic graph
Propositional_directed_acyclic_graph
Phenomenon whereby language is used to discuss possible situations
meanings of other natural language expressions, including counterfactuals, propositional attitudes, evidentials, habituals, and generics. Modality has been studied
Modality_(semantics)
Study of the semantics, or interpretations, of formal and natural languages
originally investigated by Leon Henkin, who studied Henkin quantifiers. Probabilistic semantics originated from Hartry Field and has been shown equivalent
Semantics_(logic)
Inference seeking the simplest and most likely explanation
are white ( A ) {\displaystyle (A)} , one may infer the categorical proposition "All swans are white" ( B ) {\displaystyle (B)} . The conclusion B {\displaystyle
Abductive_reasoning
Evidence that either supports or counters a scientific theory
Science – Systematic endeavour to gain knowledge Probabilistic causation Probabilistic argumentation Probabilistic logic – Applications of logic under uncertainty
Scientific_evidence
Branch of linguistics and semiotics relating context to meaning
neuroscientific experiments, and computational modeling. Formal and probabilistic approaches (such as the Rational Speech Act framework) model pragmatic
Pragmatics
Paradox about the perception of probability
0.99. On those grounds, it is presumed to be rational to accept the proposition that ticket 1 of the lottery will not win. Since the lottery is fair
Lottery_paradox
Mathematical rule for inverting probabilities
philosopher. Bayes used conditional probability to provide an algorithm (his Proposition 9) that uses evidence to calculate limits on an unknown parameter. His
Bayes'_theorem
Subjective attitude that something is true
believe that snow is white is comparable to accepting the truth of the proposition "snow is white". However, holding a belief does not require active introspection
Belief
Steps in reasoning
demonstrated by the Wason selection task. Another example, involving probabilistic reasoning, is the conjunction fallacy, where people judge a conjunction
Inference
Theory in psychology
mental models and reasoning has extended the theory to account for probabilistic inference and counterfactual thinking. Psychology of reasoning Johnson-Laird
Mental model theory of reasoning
Mental_model_theory_of_reasoning
Physical law for entropy and heat
system is uncorrelated at some time in the past; this allows for simple probabilistic treatment. This assumption is usually thought as a boundary condition
Second_law_of_thermodynamics
Test for the acceptability of conditionals via hypothetical belief revision
research traditions, namely, in the theory of § Belief revision, in § Probabilistic approaches to conditionals, in § Possible-worlds semantics, and in dynamic
Ramsey_test
Type of probabilistic logic
Subjective logic is a type of probabilistic logic that explicitly takes epistemic uncertainty and source trust into account. In general, subjective logic
Subjective_logic
Mathematical formula for the number of Young tableaux
imply the hook length formula. Greene, Nijenhuis, and Wilf found a probabilistic proof using the hook walk in which the hook lengths appear naturally
Hook_length_formula
Philosophy that accords primacy only to human thought
natural way to be both a realist and a relativist about, for example, the proposition that chocolate is tasty—it is part of reality (a subjective fact) that
Subjectivism
Method of statistical inference
Bayesian inference is used in probabilistic numerics to solve numerical problems The problem considered by Bayes in Proposition 9 of his essay, "An Essay
Bayesian_inference
Mathematical framework to model epistemic uncertainty
degree of belief in a proposition depends primarily upon the number of answers (to the related questions) containing the proposition, and the subjective
Dempster–Shafer_theory
Concept in probability theory
ISBN 978-0-387-79051-0. Devroye, Luc; Györfi, Laszlo; Lugosi, Gabor (1996-04-04). A Probabilistic Theory of Pattern Recognition (Corrected ed.). New York: Springer.
Total variation distance of probability measures
Total_variation_distance_of_probability_measures
Foundations of probability theory
of probability as the likelihood or credibility of arbitrary logical propositions. The Dutch book arguments show that rational agents must make bets which
Probability_axioms
Subfield of artificial intelligence
these systems are normally based on fuzzy and non-classical logics or probabilistic methods made differentiable for use within neural networks. Neuro-symbolic
Neuro-symbolic_AI
Type of cryptographic security
secrecy is a term used in formal proof-based cryptography for making propositions about the security of cryptographic protocols. It is a stronger notion
Strong_secrecy
systematically applies the principle of conditioned predication (syadvada) to any proposition, yielding seven distinct truth values instead of the classical two (true/false)
Jaina_seven-valued_logic
Theory and paradigm of statistics
supports the proposition A {\displaystyle A} . P ( A ∣ B ) {\displaystyle P(A\mid B)} is the posterior probability, the probability of the proposition A {\displaystyle
Bayesian_statistics
Syllogism with conditional premise(s)
not hold in all logics, including, for example, non-monotonic logic, probabilistic logic and default logic. The reason for this is that these logics describe
Hypothetical_syllogism
Class of statistical models
A staged tree is a probabilistic model for a process consisting of a sequence of discrete-valued events described by a tree diagram (also known as an
Staged_tree_(mathematics)
Objection to the doomsday argument
as stated, the negation of the SIA is a theorem of Dieks' system. A proposition similar to the SIA can be derived from Dieks' system, but it is necessary
Self-indication assumption doomsday argument rebuttal
Self-indication_assumption_doomsday_argument_rebuttal
Data structure for Boolean functions
of Propositional Knowledge Bases". International Joint Conference on Artificial Intelligence. Riguzzi, Fabrizio (2023). Foundations of probabilistic logic
Sentential_decision_diagram
Paradox in decision theory
the probabilistic information available to the decision-maker is incomplete, these attempts sometimes focus on quantifying the non-probabilistic ambiguity
Ellsberg_paradox
formulas. PCTL: Probabilistic CTL; an extension of CTL which allows for probabilistic quantification of described properties. PLTL: Probabilistic Linear Temporal
List_of_model_checking_tools
Problem of determining if a Boolean formula could be made true
computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT)
Boolean satisfiability problem
Boolean_satisfiability_problem
Book by Stuart J. Russell and Peter Norvig
topics like searching algorithms and first-order logic, propositional logic and probabilistic reasoning to advanced topics such as multi-agent systems
Artificial Intelligence: A Modern Approach
Artificial_Intelligence:_A_Modern_Approach
Closed interval [0,1] on the real number line
fuzzy logic and probabilistic logic. In these interpretations, a value is interpreted as the "degree" of truth – to what extent a proposition is true, or
Unit_interval
Relationship where one statement follows from another
Deductive reasoning Logic gate Logical graph Peirce's law Probabilistic logic Propositional calculus Sole sufficient operator Strawson entailment Strict
Logical_consequence
Branch of machine learning
specifically, the probabilistic interpretation considers the activation nonlinearity as a cumulative distribution function. The probabilistic interpretation
Deep_learning
Methods to test or prove primality
advent of modern cryptography. Although many current tests result in a probabilistic output (N is either shown composite, or probably prime, such as with
Elliptic_curve_primality
Graphoid math statements
"given that we know" may obtain different interpretations, including probabilistic, relational and correlational, depending on the application. These interpretations
Graphoid
Method of proof in mathematics
non-constructive proofs show that if a certain proposition is false, a contradiction ensues; consequently the proposition must be true (proof by contradiction)
Constructive_proof
Subset of artificial intelligence
to be reinventions of the generalised linear models of statistics. Probabilistic reasoning was also employed, especially in automated medical diagnosis
Machine_learning
Conditional probability used in Bayesian statistics
probability contains everything there is to know about an uncertain proposition (such as a scientific hypothesis, or parameter values), given prior knowledge
Posterior_probability
Type of randomized algorithm
hard problems, such as some variants of the Davis–Putnam algorithm for propositional satisfiability (SAT), also utilize non-deterministic decisions, and
Las_Vegas_algorithm
American mathematician and statistician
reduced by a factor of 2 every shuffle. When entropy is viewed as the probabilistic distance, riffle shuffling seems to take less time to mix, and the threshold
Persi_Diaconis
Model for reasoning with uncertain beliefs and evidence
model used to evaluate the probability that a given proposition is true from other propositions that are assigned probabilities. It was developed by
Transferable_belief_model
Even integers as sums of two primes
even number can be expressed as the sum of at most three primes." This proposition is similar to, but weaker than, Goldbach's conjecture. Paul Erdős said
Goldbach's_conjecture
Bound on probability of a random variable being far from its mean
(January 2005). Probability and Computing: Randomized Algorithms and Probabilistic Analysis (Repr. ed.). Cambridge [u.a.]: Cambridge Univ. Press. ISBN 978-0-521-83540-4
Chebyshev's_inequality
Computer science field
model-checking problem consists of verifying whether a formula in the propositional logic is satisfied by a given structure. Property checking is used for
Model_checking
Conjecture on zeros of the zeta function
reached the region of typical behavior of the zeta function. Denjoy's probabilistic argument for the Riemann hypothesis is based on the observation that
Riemann_hypothesis
Reformulation of Floyd-Hoare logic
strongest-postconditions. Probabilistic predicate transformers are an extension of predicate transformers for probabilistic programs. Such programs have
Predicate transformer semantics
Predicate_transformer_semantics
Complexity class used to classify decision problems
using only deterministic machines. If we permit the verifier to be probabilistic (this, however, is not necessarily a BPP machine), we get the class
NP_(complexity)
Axiom in set theory
Kurt Gödel and Paul Cohen. Freiling claims that probabilistic intuition strongly supports this proposition while others disagree. There are several versions
Freiling's_axiom_of_symmetry
How one process influences another
approaches to causality. These include the (mentioned above) regularity, probabilistic, counterfactual, mechanistic, and manipulationist views. The five approaches
Causality
influence decision-making. The fourth part formulates the theory’s main propositions. Emotional choice theory subscribes to a definition of "emotion" as a
Emotional_choice_theory
List of concepts in artificial intelligence
drive his model of situational logic. probabilistic programming (PP) A programming paradigm in which probabilistic models are specified and inference for
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
Mathematical theory for handling uncertainty
The proposition "the possibility level that the bottle is full is 0.5" describes a degree of belief. One way to interpret 0.5 in that proposition is to
Possibility_theory
Interpretation of probability
can be seen as an extension of propositional logic that enables reasoning with hypotheses; that is, with propositions whose truth or falsity is unknown
Bayesian_probability
Number divisible only by 1 and itself
whether an arbitrary given number n {\displaystyle n} is prime are probabilistic (or Monte Carlo) algorithms, meaning that they have a small random chance
Prime_number
Reasoning of knowledge about knowledge
the representation and reasoning of knowledge about knowledge. While propositional logic can only express facts, autoepistemic logic can express knowledge
Autoepistemic_logic
Italian Dominican friar and philosopher (1225–1274)
former is akin to something like "certainty", whereas the latter is more probabilistic in nature. In other words, Thomas thought Christian doctrines were "fitting"
Thomas_Aquinas
Philosophical view that events are determined by prior events
adequate determinism and interpretations of quantum mechanics explore probabilistic or emergent constraints on macroscopic phenomena. Philosophical varieties
Determinism
often claimed these tools could "think like a human". Judea Pearl's Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, an
History of artificial intelligence
History_of_artificial_intelligence
Family of logics for natural-language and counterfactual conditionals
between possible worlds, on context and background information, or on probabilistic support rather than on a simple two-valued truth table. These systems
Conditional_logic
1995 US criminal trial
University Press. ISBN 978-1-108-31113-7. OLUMIDE, KUNLE (2010). "A PROBABILISTIC AND GRAPHICAL ANALYSIS OF EVIDENCE IN O.J. SIMPSON'S MURDER CASE USING
Murder_trial_of_O._J._Simpson
Movement in Western philosophy
satisfactory in approximating causal explanation. Hempel later proposed a probabilistic model of scientific explanation: The inductive-statistical (IS) model
Logical_positivism
P Q R S T U V W X Y Z See also References A-proposition A type of standard-form categorical proposition, asserting that all members of the subject category
Glossary_of_logic
Form of incorrect argument in natural language
natural language. An argument is a series of propositions, called the premises, together with one more proposition, called the conclusion. The premises in
Informal_fallacy
Paradox involving infinity
12:30pm, the third at 12:15pm, and so on. As a consequence of these propositions, the person will certainly be killed by a Reaper before 1pm; however
Grim_Reaper_paradox
programming A formalism and a methodology for having a technique to specify probabilistic models and solve problems when less than the necessary information is
Glossary_of_computer_science
Hypothesis about sapient life and the universe
anthropic principle (also known as the observation selection effect) is the proposition that the range of possible observations made about a universe is limited
Anthropic_principle
Mathematical theorem in stochastic processes
Probability: Theory and Examples, Cambridge Series in Statistical and Probabilistic Mathematics (4. ed.), Cambridge University Press, ISBN 978-0-521-76539-8
Doob_decomposition_theorem
Processing of natural language by a computer
systems, which are also more costly to produce. the larger such a (probabilistic) language model is, the more accurate it becomes, in contrast to rule-based
Natural_language_processing
Mental representation of the external world
possibility represents only what is true in that possibility according to the proposition. However, mental models can represent what is false, temporarily assumed
Mental_model
Concept in natural language processing
human reading t would be justified in inferring the proposition expressed by h from the proposition expressed by t.) The relation is directional because
Textual_entailment
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