## Probabilistic Reasoning Vocabulary

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This file contains some documentation of the initial Cyc vocabulary designed to support probabilistic reasoning. Cyc does not perform probabilistic reasoning itself at present; this vocabulary is designed to support integration of Cyc with other HPKB participants who are working on probabilistic reasoners.

This is supposed to support not only Bayesian Network reasoning, but also other probabilistic reasoning systems. No assumption is made about how the probabilities will be processed. In particular, #$derivedProbability and #$derivedProbability-Range do not commit to the method of derivation. Some Cyc constants should be useful for several approaches, see: #$conditionalProbability, #$conditionallyIndependent, #$conditionallyIndependent-Given, #$priorProbability, #$priorProbability-Range, #$lessLikelyThan-Prior, and #$lessLikelyThan-Derived.

[Note: Cyc's regular #$lessLikelyThan predicate, and its causal and risk predicates, are not now tied in to this vocabulary in any way.]

Some constants are tailored for Bayesian Network reasoning: #$BayesNet, #$bayesNetOfMicrotheory, #$bayesParent and #$bayesParentSet. An explict #$BayesNet needs to be created and associated with a particular #$Microtheory before Baysian Network reasoning can be done in that #$Microtheory. The nodes in the #$BayesNet are random variables for Cyc formulae asserted in the Microtheory, and the links are #$bayesParent links. At present the definitions allow multiple #$BayesNets to be created for one #$Microtheory.

For the time being, at least, probabilities are represented by a #$Real0-1 number, where 0 means certainly false and 1 means certainly true.
#$ProbabilisticCycLConstant probabilistic constants **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> The collection of those Cyc constants (individuals, collections, predicates, functions, and non-atomic terms) created to enable probabilistic reasoning (of various kinds).
> guid: bffc7042-9c29-11b1-9dad-c379636f7270
> direct instance of: #$Collection
> direct specialization of: #$Thing

#$NoteOnProbability note on probability **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> The system of #$ProbabilisticCycLConstants is intended to support several different probabilistic reasoning theories. #$Probability (a specialization of #$Real0-1) is the probability measure. In all contemplated theories of probability, zero means certainly false and one means certainly true. The theories differ on how to combine different values between these extremes. (We may later want to represent probabilities in other, or multiple, ways: logarithms, etc.) If you want to ensure a precise value for a probability (as most Bayesians do), use #$priorProbability and #$derivedProbability (or #$PriorProbabilityFn and #$DerivedProbabilityFn). If you want to allow for ranges (intervals) of probabilities, as some other probabilistic theories need, or to say something is 'more than 80% likely', use #$priorProbability-Range and #$derivedProbability-Range (or #$PriorProbability-RangeFn and #$DerivedProbability-RangeFn).
> guid: bf9c13ad-9c29-11b1-9dad-c379636f7270
> direct instance of: #$Thing #$Individual

#$Probability probabilities **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> The collection of all possible probabilities. A #$Probability is the probability value that an assertion is true, expressed as a real number between zero (for 'certainly false') and one (for 'certainly true'). #$Probability is available for probabilistic reasoning; see #$ProbabilisticCycLConstant.
> guid: bd58df60-9c29-11b1-9dad-c379636f7270
> direct instance of: #$LinearOrderAttributeType #$MeasurableScalarIntervalType
> direct specialization of: #$NonNegativeNumber

#$priorProbability prior probability **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A predicate used for probability statements. (#$priorProbability PROPOSITION PROBNO) means that the a priori probability of the truth of the formula PROPOSITION, in the applicable #$Microtheory, is PROBNO (a real number between zero and one, where zero means certainly false and one means certainly true). In most microtheories, generally, this refers to the probability that PROPOSITION, by itself, would be true if there were no further evidence in the #$Microtheory for or against it, nor knowledge of the truth of anything else other than the #$domainAssumptions of the #$Microtheory. Contrast this with #$derivedProbability and with #$priorProbability-Range. See also the function version of this predicate: #$PriorProbabilityFn. A #$priorProbability may represent an absolute objective probability, a subjective assigned probability, a quantum probability, or an assigned probability based on some internal characteristic of PROPOSITION (including possibly a statement in it of the occurrence of a number of outcomes within a large number of trials). This definition makes no presumption as to determinism versus nondeterminism, nor as to whether probability is only in the mind of some beholder.
> guid: bf50f4ee-9c29-11b1-9dad-c379636f7270
> direct instance of: #$QuantitySlot #$FunctionalSlot

#$priorProbability-Range prior probability - range **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A predicate used for probability statements. (#$priorProbability-Range PROPOSITION PROBRANGE) means that the a priori probability of the truth of the formula PROPOSITION, in the applicable #$Microtheory, is somewhere in range PROBRANGE (either a real number between zero and one, where zero means certainly false and one means certainly true, or an interval between two such numbers). In most microtheories, generally, this refers to the range of probability that PROPOSITION, by itself, would be true if there were no further evidence in the #$Microtheory for or against it, nor knowledge of the truth of anything else other than the #$domainAssumptions of the #$Microtheory. Contrast this with #$derivedProbability and #$priorProbability. A #$priorProbability-Range may represent an absolute objective probability range, a subjective assigned probability range, a quantum probability range, or an assigned probability range based on some internal characteristic of PROPOSITION (including possibly a statement in it of the occurrence of a number of outcomes within a large number of trials). This definition makes no presumption as to determinism versus nondeterminism, nor as to whether probability is only in the mind of some beholder.
> guid: be0dd6f8-9c29-11b1-9dad-c379636f7270
> direct instance of: #$IntervalBasedQuantitySlot

#$derivedProbability derived probability **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A predicate used for probability statements. (#$derivedProbability PROPOSITION PROBNO) means that, in the applicable #$Microtheory, the a posteriori probability of the truth of the formula PROPOSITION, given (and depending on) the current state of knowledge of all other assertions, is PROBNO (a real number between zero and one, where zero means certainly false and one means certainly true). In most microtheories, generally, this refers to the derived probability that PROPOSITION is true given the probabilities of the other #$Assertions and #$domainAssumptions of the #$Microtheory. Contrast this with #$priorProbability and #$derivedProbability-Range. See also the function version of this: #$DerivedProbabilityFn. A #$derivedProbability depends at least partially on, and is in some manner derived from or affected by, the probabilities of some or all of the other #$Assertions in the #$Microtheory (whether prior, derived or conditional) along with the #$domainAssumptions. See also #$conditionalProbability. This definition makes no presumption as to determinism versus nondeterminism, nor as to whether probability is only in the mind of some beholder. The definition allows for any of several different systems of deriving the probability of one assertion from the probabilities of, or conditional probabilities relating, other assertions.
> guid: be2edcf4-9c29-11b1-9dad-c379636f7270
> direct instance of: #$QuantitySlot #$FunctionalSlot

#$derivedProbability-Range derived probability - range **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A predicate used for probability statements. (#$derivedProbability-Range PROPOSITION PROBRANGE) means that, in the applicable #$Microtheory, the a posteriori probability of the truth of the formula PROPOSITION, given (and depending on) the current state of knowledge of all other assertions, is somewhere in the range PROBRANGE (either a real number between zero and one, where zero means certainly false and one means certainly true, or an interval between two such numbers). In most microtheories, generally, this refers to the derived range of derived probability that PROPOSITION is true given the probabilities (or probability ranges) of the other #$Assertions and #$domainAssumptions of the #$Microtheory. Contrast this with #$priorProbability-Range and with #$derivedProbability. A #$derivedProbability-Range depends at least partially on, and is in some manner derived from or affected by, the probabilities of some or all of the other #$Assertions in the #$Microtheory (whether prior, derived or conditional) along with the #$domainAssumptions. This definition makes no presumption as to determinism versus nondeterminism, nor as to whether probability is only in the mind of some beholder. The definition allows for any of several different systems of deriving the probability of one assertion from the probabilities of, or conditional probabilities relating, other assertions.
> guid: be40e1c8-9c29-11b1-9dad-c379636f7270
> direct instance of: #$IntervalBasedQuantitySlot

#$conditionalProbability conditional probability **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A predicate used for probability statements. (#$conditionalProbability PROPOSITION1 PROPOSITION2 PROBNO) means that the probability of PROPOSITION1 being true, given that PROPOSITION2 is known to be true, in the applicable #$Microtheory, is PROBNO (a real number between zero and one, where zero means certainly false and one means certainly true). Most typically, PROPOSITION2 is actually a conjunction of multiple propositions. In most microtheories, generally, this #$conditionalProbability refers to the conditional probability that PROPOSITION1 is true given only that PROPOSITION2, and the #$domainAssumptions accessible in the applicable #$Microtheory, are true, without regard to any further evidence or the truth of any other assertions. See also #$conditionalProbabilitySet, #$priorProbability, #$derivedProbability, #$conditionallyIndependent, and the function version of this predicate: #$ConditionalProbabilityFn. This definition makes no presumption as to determinism versus nondeterminism, nor as to whether probability is only in the mind of some beholder. The definition allows for any of several different systems of deriving the probability of one assertion from the probabilities of, or conditional probabilities relating, other assertions.
> guid: be7f058d-9c29-11b1-9dad-c379636f7270
> direct instance of: #$FunctionalPredicate #$TernaryPredicate

#$conditionalProbabilitySet conditional probability set **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A predicate used for probability statements. (#$conditionalProbabilitySet PROPOSITION SETOFPROPOSITIONS PROBNO) means that the probability of PROPOSITION being true, given that all the propositions in SETOFPROPOSITIONS are known to be true, in the applicable #$Microtheory, is PROBNO (a real number between zero and one, where zero means certainly false and one means certainly true). In most microtheories, generally, this #$conditionalProbabilitySet refers to the conditional probability that PROPOSITION is true given only that the propositions in SETOFPROPOSITIONS, and the #$domainAssumptions accessible in the applicable #$Microtheory, are true, without regard to any further evidence or the truth of any other assertions. See also #$conditionalProbability, #$priorProbability, #$derivedProbability, #$conditionallyIndependent, and the function version of this predicate: #$ConditionalProbabilitySetFn. This definition makes no presumption as to determinism versus nondeterminism, nor as to whether probability is only in the mind of some beholder. The definition allows for any of several different systems of deriving the probability of one assertion from the probabilities of, or conditional probabilities relating, other assertions.
> guid: bfcef6cd-9c29-11b1-9dad-c379636f7270
> direct instance of: #$TernaryPredicate

#$conditionallyIndependent conditionally independent **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A predicate used for probability statements. (#$conditionallyIndependent PROPOSITION1 PROPOSITION2) means that, in the applicable #$Microtheory, PROPOSITION1 and PROPOSITION2 are conditionally independent of each other, that is, truth or falsehood of one does not increase or decrease the #$derivedProbability that the other is true. They are, in a sense, irrelevant to each other. In most microtheories, generally, the #$conditionallyIndependent statement means that when all we know in the #$Microtheory are its accessible #$domainAssumptions, then the truths of the two formulae are probabilistically independent. See also #$conditionalProbability and #$conditionallyIndependent-Given. This definition makes no presumption as to determinism versus nondeterminism, nor as to whether probability is only in the mind of some beholder. The definition allows for any of several different systems of deriving the probability of one assertion from the probabilities of, or conditional probabilities relating, other assertions.
> guid: bfb43bd4-9c29-11b1-9dad-c379636f7270
> direct instance of: #$IrreflexiveBinaryPredicate #$SymmetricBinaryPredicate

#$conditionallyIndependent-Given conditionally independent - given **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A predicate used for probability statements. (#$conditionallyIndependent-Given PROPOSITION1 PROPOSITION2 PROPOSITION3) means that, in the applicable #$Microtheory, PROPOSITION1 and PROPOSITION2 are conditionally independent of each other given the truth of PROPOSITION3. That is, given the truth of the third, the truth or falsehood of either of the first two does not increase or decrease the #$derivedProbability that the other is true. They are, in a sense, irrelevant to each other when PROPOSITION3 is known to be true. Most typically, PROPOSITION3 is a conjunction of multiple propositions (but see also #$conditionallyIndependent-GivenSet). In most microtheories, generally, the #$conditionallyIndependent-Given statement means that when all we know in the #$Microtheory are its accessible #$domainAssumptions, and PROPOSITION3, then the truths of the two formulae are probabilistically independent. See also #$conditionalProbability and #$conditionallyIndependent. To declare two propositions independent given a set of propositions, use #$conditionallyIndependent-GivenSet. This definition makes no presumption as to determinism versus nondeterminism, nor as to whether probability is only in the mind of some beholder. The definition allows for any of several different systems of deriving the probability of one assertion from the probabilities of, or conditional probabilities relating, other assertions.
> guid: bd7d8244-9c29-11b1-9dad-c379636f7270
> direct instance of: #$TernaryPredicate

#$conditionallyIndependent-GivenSet conditionally independent - given set **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A predicate used for probability statements. (#$conditionallyIndependent-GivenSet PROPOSITION1 PROPOSITION2 SETOFPROPOSITIONS) means that, in the applicable #$Microtheory, PROPOSITION1 and PROPOSITION2 are conditionally independent of each other given the truth of all the propositions in the set SETOFPROPOSITIONS. That is, given the truth of the propositions in the set, the truth or falsehood of either of the two propostion arguments does not increase or decrease the #$derivedProbability that the other is true. They are, in a sense, irrelevant to each other when the propositions in SETOFPROPOSITIONS is known to be true. In most microtheories, generally, the #$conditionallyIndependent-GivenSet statement means that when all we know in the #$Microtheory are its accessible #$domainAssumptions, and the assertions in SETOFPROPOSITIONS, then the truths of the two formulae are probabilistically independent. See also #$conditionalProbability and #$conditionallyIndependent. To declare two propositions independent given a single proposition (which could be a conjunction), use #$conditionallyIndependent-Given. This definition makes no presumption as to determinism versus nondeterminism, nor as to whether probability is only in the mind of some beholder. The definition allows for any of several different systems of deriving the probability of one assertion from the probabilities of, or conditional probabilities relating, other assertions.
> guid: be2eeba6-9c29-11b1-9dad-c379636f7270
> direct instance of: #$TernaryPredicate

#$PriorProbabilityFn prior probability fn **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A function used for probability statements. (#$PriorProbabilityFn PROPOSITION), applied to the #$CycLAssertion PROPOSITION, yields its a priori probability of being true, in the applicable #$Microtheory. The result is a real number between zero and one, where zero means certainly false and one means certainly true. In most microtheories, generally, this refers to the probability that PROPOSITION, by itself, would be true if there were no further evidence in the #$Microtheory for or against it, nor knowledge of the truth of anything else other than the #$domainAssumptions of the #$Microtheory. Contrast this with the predicate form #$priorProbability and with the functions #$DerivedProbabilityFn and #$PriorProbability-RangeFn. A #$PriorProbabilityFn may represent an absolute objective probability, a subjective assigned probability, a quantum probability, or an assigned probability based on some internal characteristic of PROPOSITION (including possibly a statement in it of the occurrence of a number of outcomes within a large number of trials). This definition makes no presumption as to determinism versus nondeterminism, nor as to whether probability is only in the mind of some beholder.
> guid: c022e43a-9c29-11b1-9dad-c379636f7270
> direct instance of: #$UnaryFunction #$Individual

#$PriorProbability-RangeFn prior probability - range fn **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A function used for probability statements. (#$PriorProbability-RangeFn PROPOSITION), applied to the #$CycLAssertion PROPOSITION, yields a range of two real numbers between zero and one that includes the a priori probability that PROPOSITION is true, in the applicable #$Microtheory. In most microtheories, generally, this refers to the range of probability that PROPOSITION, by itself, would be true if there were no further evidence in the #$Microtheory for or against it, nor knowledge of the truth of anything else other than the #$domainAssumptions of the #$Microtheory. Contrast this with the predicate form #$priorProbability-Range and with the functions #$DerivedProbability-RangeFn #$PriorProbabilityFn. A #$PriorProbability-RangeFn may represent an absolute objective probability range, a subjective assigned probability range, a quantum probability range, or an assigned probability range based on some internal characteristic of PROPOSITION (including possibly a statement in it of the occurrence of a number of outcomes within a large number of trials). This definition makes no presumption as to determinism versus nondeterminism, nor as to whether probability is only in the mind of some beholder.
> guid: bfe36d97-9c29-11b1-9dad-c379636f7270
> direct instance of: #$UnaryFunction #$Individual

#$DerivedProbabilityFn derived probability fn **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A function used for probability statements. (#$DerivedProbabilityFn PROPOSITION), applied to the #$CycLAssertion PROPOSITION, yields, in the applicable #$Microtheory, the a posteriori probability of the truth of the formula PROPOSITION, given (and depending on) the current state of knowledge of other assertions. The result is a real number between zero and one, where zero means certainly false and one means certainly true. In most microtheories, generally, this refers to the derived probability that PROPOSITION is true given the probabilities or truth values of the other #$Assertions and #$domainAssumptions of the #$Microtheory. Contrast this with the predicate form #$derivedProbability and with the functions #$PriorProbabilityFn and #$DerivedProbability-RangeFn. The result of #$DerivedProbabilityFn depends at least partially on, and is in some manner derived from or affected by, the probabilities of some or all of the other #$Assertions in the #$Microtheory (whether prior, derived or conditional) along with the #$domainAssumptions. See also #$conditionalProbability. This definition makes no presumption as to determinism versus nondeterminism, nor as to whether probability is only in the mind of some beholder. The definition allows for any of several different systems of deriving the probability of one assertion from the probabilities of, or conditional probabilities relating, other assertions.
> guid: bf613f81-9c29-11b1-9dad-c379636f7270
> direct instance of: #$UnaryFunction #$Individual

#$DerivedProbability-RangeFn derived probability - range fn **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A function used for probability statements. (#$DerivedProbability-RangeFn PROPOSITION), applied to the #$CycLAssertion PROPOSITION, yields, in the applicable #$Microtheory, the range of a posteriori probability of the truth of the formula PROPOSITION, given (and depending on) the current state of knowledge of other assertions. This result is a number or range of numbers somewhere within the range 0-1 (either a real number between zero and one, where zero means certainly false and one means certainly true, or an interval between two such numbers). In most microtheories, generally, this refers to the derived range of derived probability that PROPOSITION is true given the probabilities (or probability ranges) of the other #$Assertions and #$domainAssumptions of the #$Microtheory. Contrast this with the predicate form #$derivedProbability-Range and with the functions #$DerivedProbabilityFn and #$PriorProbability-RangeFn. The result of a use of #$DerivedProbability-RangeFn on a proposition depends at least partially on, and is in some manner derived from or affected by, the probabilities of some or all of the other #$Assertions in the #$Microtheory (whether prior, derived or conditional) along with the #$domainAssumptions. This definition makes no presumption as to determinism versus nondeterminism, nor as to whether probability is only in the mind of some beholder. The definition allows for any of several different systems of deriving the probability of one assertion from the probabilities of, or conditional probabilities relating, other assertions.
> guid: bfd242aa-9c29-11b1-9dad-c379636f7270
> direct instance of: #$UnaryFunction #$Individual

#$ConditionalProbabilityFn conditional probability fn **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A function used for probability statements. (#$ConditionalProbabilityFn PROPOSITION1 PROPOSITION2) applied to two #$Assertions, results in the probability of PROPOSITION1 being true given that PROPOSITION2 is known to be true, in the applicable #$Microtheory. It yields a real number between zero and one, where zero means certainly false and one means certainly true. Most typically, PROPOSITION2 is actually a conjunction of multiple propositions. In most microtheories, generally, this #$ConditionalProbabilityFn refers to the conditional probability that PROPOSITION1 is true given only that PROPOSITION2, and the #$domainAssumptions accessible in the applicable #$Microtheory, are true, without regard to any further evidence or the truth of any other assertions. See also #$ConditionalProbabilitySetFn, #$PriorProbabilityFn, #$DerivedProbabilityFn, #$conditionallyIndependent, and the predicate version of this function: #$conditionalProbability. This definition makes no presumption as to determinism versus nondeterminism, nor as to whether probability is only in the mind of some beholder. The definition allows for any of several different systems of deriving the probability of one assertion from the probabilities of, or conditional probabilities relating, other assertions.
> guid: bf8557a4-9c29-11b1-9dad-c379636f7270
> direct instance of: #$BinaryFunction #$Individual

#$ConditionalProbabilitySetFn conditional probability set fn **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A function used for probability statements. (#$ConditionalProbabilitySetFn PROPOSITION SETOFPROPOSITIONS) applied to an #$CycLAssertion and a set of #$Assertions, results in the probability of PROPOSITION being true given that all the propositions in SETOFPROPOSITIONS are known to be true, in the applicable #$Microtheory. It yields a real number between zero and one, where zero means certainly false and one means certainly true. In most microtheories, generally, this #$ConditionalProbabilitySetFn refers to the conditional probability that PROPOSITION is true given only that the propositions that are elements of SETOFPROPOSITIONS, and the #$domainAssumptions accessible in the applicable #$Microtheory, are true, without regard to any further evidence or the truth of any other assertions. See also #$ConditionalProbabilityFn, #$PriorProbabilityFn, #$DerivedProbabilityFn, #$conditionallyIndependent, and the predicate version of this function: #$conditionalProbabilitySet. This definition makes no presumption as to determinism versus nondeterminism, nor as to whether probability is only in the mind of some beholder. The definition allows for any of several different systems of deriving the probability of one assertion from the probabilities of, or conditional probabilities relating, other assertions.
> guid: bdc7c640-9c29-11b1-9dad-c379636f7270
> direct instance of: #$BinaryFunction #$Individual

#$lessLikelyThan-Prior less likely than - prior **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A predicate used for probability statements. (#$lessLikelyThan-Prior PROPOSITION1 PROPOSITION2) means that, in the applicable #$Microtheory, the a priori probability that PROPOSITION1 is true is less than the a priori probability that PROPOSITION2 is true. This predicate does not say what the probabilities actually are numerically; it is just an ordering (or rather partial ordering) relation between the two propositions. In most microtheories, generally, this #$lessLikelyThan-Prior means that the 'prior' probability that PROPOSITION1 is true is less than the 'prior' probability that PROPOSITION2 is true, given only the truth of the #$domainAssumptions accessible in the applicable #$Microtheory, without regard to any further evidence or the truth of any other assertions. Contrast this with #$lessLikelyThan (which makes no claim of dependence on or independence from other assertions) and with #$lessLikelyThan-Derived (which assumes dependence on other assertions). This definition makes no presumption as to determinism versus nondeterminism, nor as to whether probability is only in the mind of some beholder.
> guid: bfce3d30-9c29-11b1-9dad-c379636f7270
> direct instance of: #$ComparisonPredicate #$AsymmetricBinaryPredicate #$TransitiveBinaryPredicate

#$lessLikelyThan-Derived less likely than - derived **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A predicate used for probability statements. (#$lessLikelyThan-Derived PROPOSITION1 PROPOSITION2) means that, in the applicable #$Microtheory, the a posteriori #$derivedProbability that PROPOSITION1 is true is less than the a posteriori #$derivedProbability that PROPOSITION2 is true, taking into account other evidence and the truth or falsehood of other assertions. This predicate does not say what the probabilities actually are numerically; it is just an ordering (or rather partial ordering) relation between the two propositions. In most microtheories, generally, this #$lessLikelyThan-Derived means that the probability that PROPOSITION1 is true is less than the probability that PROPOSITION2 is true, given the probabilities of other #$Assertions in the #$Microtheory and the #$domainAssumptions accessible in the #$Microtheory. Contrast this with #$lessLikelyThan (which makes no claim of dependence on or independence from other assertions) and with #$lessLikelyThan-Prior (which does not take into account any dependence on other assertions). This definition makes no presumption as to determinism versus nondeterminism, nor as to whether probability is only in the mind of some beholder. The definition allows for any of several different systems of deriving the probability of one assertion from the probabilities of, or conditional probabilities relating, other assertions.
> guid: bf1c9453-9c29-11b1-9dad-c379636f7270
> direct instance of: #$ComparisonPredicate #$AsymmetricBinaryPredicate #$TransitiveBinaryPredicate

#$BayesNet bayes net **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> The collection of all Bayesian Networks intended for probability reasoning. A #$BayesNet is a network of nodes in which the nodes are random variables that each typically represent the likelihood of a proposition being true (expressed as a real number between zero and one, where zero means certainly false and one means certainly true). See #$bayesNetOfMicrotheory. Each #$BayesNet interconnects a set of propositions (or symbols associated with propositions) together forming a #$DirectedAcyclicGraph in which the links (the #$bayesParent link) represent a probabilistic conditional dependence between the directly linked nodes. Such a network may be established by asserting (or concluding) #$bayesParent predications linking pairs of propositions. There is a 'closed-world assumption' for every #$BayesNet, in that pairs of propositions not explicitly linked with #$bayesParent are assumed to be not linked. In addition, a node is #$conditionallyIndependent-Given the truth values of its #$bayesParents (and no other nodes) - from all nodes other than its 'descendants' in the #$BayesNet. A #$BayesNet is a representation of the entire (strictly positive) joint probability distribution over the random variables. The #$derivedProbability of a node can be calculated from the probabilities of its #$bayesParents. (There are always one or more 'source' nodes with no #$bayesParents.) Theoretically, viewed as evidential links based on the joint probability distribution, the #$bayesParent links are bidirectional. The direction of the links is obtained formally due to an asymmetry between 'parents' and 'children': the truth of a node induces a conditional dependence among its #$bayesParents (the 'explaining away' effect), which does not seem to apply to its Bayesian 'child' nodes. Most Bayesian network theorists consider that the directions on the links correspond to the direction of causal influence, and hence to the direction of time. The name 'Bayesian' is due to the Reverend Thomas Bayes, whose inversion rule was published posthumously in 1763, and later developed by Laplace. Bayesian Networks were devised chiefly by Judea Pearl in the 1980s.
> guid: be14b328-9c29-11b1-9dad-c379636f7270
> direct instance of: #$Collection
> direct specialization of: #$DirectedAcyclicGraph

#$bayesNetOfMicrotheory bayes net of microtheory **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A predicate used for probability reasoning using 'Bayesian Networks'. (#$bayesNetOfMicrotheory BNET MT) means that the #$BayesNet BNET has been created for the #$Microtheory MT. This means that all of the nodes in BNET are propositions (Cyc formulae) that are asserted in MT, and are linked to one another by #$bayesParent assertions in the same MT. This predicate associates the network, a #$DirectedAcyclicGraph, with the microtheory. For every #$BayesNet there is exactly one #$Microtheory with which it is associated, but (at present) one #$Microtheory may have multiple #$BayesNets associated with it. Some, but possibly not all, of the #$CycLAssertions in the #$Microtheory will be nodes in the #$BayesNet.
> guid: bed4998a-9c29-11b1-9dad-c379636f7270
> direct instance of: #$AntiTransitiveBinaryPredicate #$AsymmetricBinaryPredicate #$FunctionalSlot

#$bayesParent bayes parent **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A predicate used for probability statements. (#$bayesParent PROPOSITION1 PROPOSITION2 BAYESNET) means that the truth or falsehood of PROPOSITION2 influences the likelihood of PROPOSITION1 being true, and that PROPOSITION2 is an immediate 'parent node' of the PROPOSITION1 node in the Bayesian Network BAYESNET representing probabilistic influence in the applicable #$Microtheory. That is, the second formula is a direct parent of the first in the #$BayesNet. Note that PROPOSITION1 and PROPOSITION2 cannot be #$conditionallyIndependent in the #$Microtheory if one is a #$bayesParent of the other. Given the truth values of all of a node's #$bayesParent nodes, then all of its further ancestor nodes and other non-descendant nodes are #$conditionallyIndependent of it in the applicable #$Microtheory. To relate a node to the set of all of its parent nodes, use #$bayesParentSet. The direction is obtained from the conditional dependence --- given the truth of a node --- among its #$bayesParents (the 'explaining away' effect), which does not seem to apply among its Bayesian 'child' nodes. Many Bayesian network theorists consider that the directions on the links correspond to the direction of causal influence, and hence to the direction of time.
> guid: bdbbd144-9c29-11b1-9dad-c379636f7270
> direct instance of: #$TernaryPredicate
> direct specialization of: #$connectedInSystem

#$bayesParentSet bayes parent set **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> A predicate used for probability statements. (#$bayesParentSet PROPOSITION SETOFPROPOSITIONS BAYESNET) means that the truth or falsehood of each of the assertions in the set SETOFPROPOSITIONS influences the likelihood of PROPOSITION being true, and that each member of SETOFPROPOSITIONS is an immediate 'parent node' of the PROPOSITION node in the Bayesian Network BAYESNET representing probabilistic influence in the applicable #$Microtheory. That is, each formula in SETOFPROPOSTIONS is a direct parent of PROPOSITION in the #$BayesNet. Note that PROPOSITION and any proposition in SETOFPROPOSITIONS cannot be #$conditionallyIndependent in the #$Microtheory since one is a #$bayesParent of the other. Given the truth values of all the members of SETOFPROPOSITIONS (#$bayesParent nodes), then all of PROPOSITION's further ancestor nodes and other non-descendant nodes are #$conditionallyIndependent of it in the applicable #$Microtheory. To relate a node to a single one of its parent nodes, rather than the whole set, use #$bayesParent.
> guid: c128c2c7-9c29-11b1-9dad-c379636f7270
> direct instance of: #$TernaryPredicate

#$portionOf percentage **COMMENT NOT REVIEWED** **GAFs NOT REVIEWED**

> (#$portionOf SET1 SET2 NUM) means that the portion of members of SET1 that are also members of SET2 is NUM. In other words, the fraction of the cardinality of SET1 and the cardinality of the intersection of SET1 and SET2. For example, (#$portionOf (#$ResidentsFn #$Netherlands) #$UnemployedPerson X) means that unemployment in the Netherlands is X.
> guid: beccb3d3-9c29-11b1-9dad-c379636f7270
> direct instance of: #$TernaryPredicate

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