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a rational consequence relation is a non-monotonic consequence relation satisfying certain properties listed below. A rational consequence relation is
Rational_consequence_relation
Relationship where one statement follows from another
(3) The logical consequence relation has a modal component. The most widely prevailing view on how best to account for logical consequence is to appeal to
Logical_consequence
Quality of being agreeable to reason
characterize rationality in relation to goals, such as acquiring truth in the case of theoretical rationality. Internalists believe that rationality depends
Rationality
Philosophical terms
"instrumental rationality" and "value rationality" refer to two types of action identified by sociologist Max Weber. Instrumental rationality is a type of
Instrumental and value rationality
Instrumental_and_value_rationality
Psychotherapy
Rational emotive behavior therapy (REBT), previously called rational therapy and rational emotive therapy, is an active-directive, philosophically and
Rational emotive behavior therapy
Rational_emotive_behavior_therapy
Topics referred to by the same term
station Ranchi Rays, Indian field hockey team Rational consequence relation, a type of consequence relation in mathematical logic Ramsbottom Carbon Residue
RCR
Class of models in the behavioral sciences
Rational choice modeling refers to the use of decision theory (the theory of rational choice) as a set of guidelines to help understand economic and social
Rational_choice_model
Formal logic whose entailment relation is not monotonic
Logic programming Negation as failure Stable model semantics Rational consequence relation Strasser, Christian; Antonelli, G. Aldo. "Non-Monotonic Logic"
Non-monotonic_logic
Topics referred to by the same term
science, named after Dov Gabbay Logic Gabbay-makinson conditions (Rational consequence relation), a term in Logic This disambiguation page lists articles associated
Gabbay
Unforeseen outcomes of an action
In the social sciences, unintended consequences (sometimes unanticipated consequences or unforeseen consequences, more colloquially called knock-on effects)
Unintended_consequences
Material supporting an assertion
In epistemology, evidence is what justifies beliefs or what makes it rational to hold a certain doxastic attitude. For example, a perceptual experience
Evidence
Number that is not a ratio of integers
periodic), and in many other ways. As a consequence of Cantor's proof that the real numbers are uncountable and the rationals countable, it follows that almost
Irrational_number
Set whose elements all belong to another set
is an element of B. The validity of this technique can be seen as a consequence of universal generalization: the technique shows ( c ∈ A ) ⇒ ( c ∈ B
Subset
Class of ethical theories
never simply as a means, but always at the same time as an end; Every rational being must so act as if he were through his maxim always a legislating
Deontology
Social science theory
Rational choice institutionalism (RCI) is a theoretical approach to the study of institutions arguing that actors use institutions to maximize their utility
Rational choice institutionalism
Rational_choice_institutionalism
Type of binary relation
This relation fails to be well-founded even though the entire set has a minimum element, namely the empty string. The set of non-negative rational numbers
Well-founded_relation
Inner state causing goal-directed behavior
spontaneously acts out of anger without reflecting on the consequences of their actions. Rational and irrational motivation play a key role in the field
Motivation
concept was introduced by Sen (1969) to study the consequences of Arrow's theorem. A binary relation T over a set X is quasitransitive if for all a, b
Quasitransitive_relation
Set of statements constructed to describe a set of facts which clarifies causes
causes, context, and consequences of those facts. It may establish rules or laws, and clarifies the existing rules or laws in relation to any objects or
Explanation
Logical connective
logical consequence (or logical implication) for the semantic consequence relation with the symbol ⊨ {\displaystyle \models } . In which case the relation becomes
Material_conditional
Theory that life is meaningless
conflict with a seemingly meaningless world. This conflict can be between rational humanity and an irrational universe, between intention and outcome, or
Absurdism
the extensions of predicates (in the first-order logic case). Rational consequence relation Shoham, Y. (1987), "Nonmonotonic logics: Meaning and utility"
Preferential_entailment
One-to-one correspondence
that f ( a ) = b {\displaystyle f(a)=b} . Equivalently, a bijection is a relation between two sets such that each element of either set is paired with exactly
Bijection
Algebraic structure with addition, multiplication, and division
and division are defined and behave as the corresponding operations on rational numbers do. A field is thus a fundamental algebraic structure that is widely
Field_(mathematics)
Formal language that can be expressed using a regular expression
science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined by a regular expression
Regular_language
Function that preserves distinctness
algebraic structures is an embedding. Unlike surjectivity, which is a relation between the graph of a function and its codomain, injectivity is a property
Injective_function
Cognitive bias about one's own skill
have a general tendency to think that one is better than average. The rational explanation holds that overly positive prior beliefs about one's skills
Dunning–Kruger_effect
Branch of pure mathematics
fashion (analytic number theory). One may also study real numbers in relation to rational numbers, as for instance how irrational numbers can be approximated
Number_theory
Mapping of mathematical formulas to a particular meaning
but there is no requirement that it satisfy any of the field axioms. The rational numbers Q , {\displaystyle \mathbb {Q} ,} the real numbers R {\displaystyle
Structure (mathematical logic)
Structure_(mathematical_logic)
Central concept in Kantian moral philosophy
expected consequences. He claimed that because lying to the murderer would treat him as a mere means to another end, the lie denies the rationality of another
Categorical_imperative
Whether a decision problem has an effective method to derive the answer
semantic and syntactic consequence. In other settings, such as linear logic, the syntactic consequence (provability) relation may be used to define the
Decidability_(logic)
Uniqueness of countable dense linear orders
equivalent. Another consequence of Cantor's proof is that every finite or countable linear order can be embedded into the rationals, or into any unbounded
Cantor's_isomorphism_theorem
Act which takes other individuals into account
relation, instrumentally rational, goal-instrumental ones, zweckrational): actions which are planned and taken after evaluating the goal in relation to
Social_action
rational number ε > 0, there exists an integer N such that for all natural numbers n > N, one has |xn − yn| < ε. This defines an equivalence relation
Construction of the real numbers
Construction_of_the_real_numbers
Collection of mathematical objects
infinite sets include the integers ( Z {\displaystyle \mathbb {Z} } ), the rational numbers ( Q {\displaystyle \mathbb {Q} } ), the real numbers ( R {\displaystyle
Set_(mathematics)
Special semigroup of positive rational numbers
be true as a consequence of the following property of the 3x + 1 semigroup: The 3x + 1 semigroup S equals the set of all positive rationals a/b in lowest
3x_+_1_semigroup
Study of general and fundamental questions
like existence, knowledge, mind, reason, language, and value. It is a rational and critical inquiry that reflects on its methods and assumptions. Historically
Philosophy
Association of one output to each input
establishes a relation between the elements of the domain and some (possibly all) elements of the codomain. Mathematically, a binary relation between two
Function_(mathematics)
Mathematical function such that every output has at least one input
binary relation between X and Y by identifying it with its function graph. A surjective function with domain X and codomain Y is then a binary relation between
Surjective_function
Form of reasoning
argument. The relation between the premises and the conclusion of a deductive argument is usually referred to as "logical consequence". According to
Deductive_reasoning
Set of the elements not in a given subset
the set of real numbers and Q {\displaystyle \mathbb {Q} } is the set of rational numbers, then R ∖ Q {\displaystyle \mathbb {R} \setminus \mathbb {Q} }
Complement_(set_theory)
Rule, guide or inevitable consequence
principle in mathematics. The principle states that every event has a rational explanation. The principle has a variety of expressions, all of which are
Principle
Misleading use of a term with multiple meanings
an example: Since only man [human] is rational. And no woman is a man [male]. Therefore, no woman is rational. The first instance of "man" implies the
Equivocation
State of mind
rationality but it is more common to find separate treatments of specific forms of rationality that leave the relation to other forms of rationality open
Mental_state
Equivalence of partially ordered sets
ordering of the rational numbers. Explicit order isomorphisms between the quadratic algebraic numbers, the rational numbers, and the dyadic rational numbers are
Order_isomorphism
Family of logics for natural-language and counterfactual conditionals
Kraus, Lehmann, and Magidor's systems C/P/R characterize rational, defeasible consequence; the flat (non-nested) fragment of several conditional logics
Conditional_logic
School of thought on cognition and problem-solving
other movements, such as media literacy, neuro-linguistic programming and rational emotive behavior therapy. In the 1946 "Silent and Verbal Levels" diagram
General_semantics
Index of articles associated with the same name
Order in mathematics may refer to: Total order and partial order, a binary relation generalizing the usual ordering of numbers and of words in a dictionary
Order_(mathematics)
Describes statistically the splitting of primes in a given Galois extension of Q
extension K {\displaystyle K} of the field Q {\displaystyle \mathbb {Q} } of rational numbers. Generally speaking, a prime integer will factor into several ideal
Chebotarev_density_theorem
Algebraic curve in mathematics
of two points P and Q with rational coordinates has again rational coordinates, since the line joining P and Q has rational coefficients. This way, one
Elliptic_curve
prototypical apartness relation is that of the real numbers: two real numbers are said to be apart if there exists (one can construct) a rational number between
Apartness_relation
Computation modulo a fixed integer
a − b = km. Congruence modulo m is a congruence relation, meaning that it is an equivalence relation compatible with addition, subtraction, and multiplication
Modular_arithmetic
Mathematical concept
{\displaystyle f\circ f^{-1}=\operatorname {id} _{Y}.} This statement is a consequence of the implication that for f to be invertible it must be bijective.
Inverse_function
Mathematical concept
that rα1 − v0 is not a rational number. Continue; at each step use the least real from the r sequence that does not have a rational difference with any element
Transfinite_induction
Optimal maintenance process in industrial plants
are high probability but for which failure has low consequences. This strategy allows for a rational investment of inspection resources. RBI assists a
Risk-based_inspection
Area of mathematical logic
the original signature. The opposite relation is called an expansion - e.g. the (additive) group of the rational numbers, regarded as a structure in the
Model_theory
Ancient algorithm for generating prime numbers
the random access machine model is O(n log log n) operations, a direct consequence of the fact that the prime harmonic series asymptotically approaches
Sieve_of_Eratosthenes
Number used to approximate the square root of 2
known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations
Pell_number
Branch of elementary mathematics
arithmetic is about calculations with positive and negative integers. Rational number arithmetic involves operations on fractions of integers. Real number
Arithmetic
Class of mathematical expression
equivalence relation and its equivalence classes are then defined to be the rational numbers. It is in the formal proof that this relation is an equivalence
Division_by_zero
Axioms for the natural numbers
ζ be the order type of the integers, and η be the order type of the rationals, the order type of any countable nonstandard model of PA is ω + ζ·η, which
Peano_axioms
Analytic function in mathematics
ζ(3), and as a consequence, the number was named after him. The values at negative integer points, also found by Euler, are rational numbers and play
Riemann_zeta_function
Factors influencing economic decisions
cognitive limitations are somewhat the consequence of our limited ability to foresee the future, hampering the rationality of decision. Daniel Kahneman further
Behavioral_economics
Probabilistic primality test
≡ 1 (mod n) holds trivially for a ≡ 1 (mod n), because the congruence relation is compatible with exponentiation. And ad = a20d ≡ −1 (mod n) holds trivially
Miller–Rabin_primality_test
Proof in set theory
He lets "φν denote any sequence of rationals in [0, 1]." Cantor lets φν denote a sequence enumerating the rationals in [0, 1], which is the kind of sequence
Cantor's_diagonal_argument
Concept in psychology
literature or Victorian Studies, painting and poetry. Ruth M.J. Byrne in The Rational Imagination: How People Create Alternatives to Reality (2005) proposed
Counterfactual_thinking
Basic framework of mathematics
etc. in particular. This may also include the philosophical study of the relation of this framework with reality. The term "foundations of mathematics" was
Foundations_of_mathematics
Mathematical construction of a set with an equivalence relation
mathematics, a setoid (X, ~) is a set (or type) X equipped with an equivalence relation ~. A setoid may also be called E-set, Bishop set, or extensional set. Setoids
Setoid
relation. Arithmetic operations on positive rational numbers and the order relation on positive rationals are defined just as in elementary school and
Implementation of mathematics in set theory
Implementation_of_mathematics_in_set_theory
Challenge in U.S. constitutional law
as the "rational basis test", which may sometimes indicate that a statute is invalid on its face because it does not posit any rational relation to a legitimate
Facial_challenge
Rational-number approximation of a real number
by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated by rational numbers
Diophantine_approximation
Impossible task in computing
problem of deciding whether a given first-order sentence is a logical consequence of a given finite set of sentences, but validity in first-order theories
Entscheidungsproblem
Size of a possibly infinite set
natural numbers N {\displaystyle \mathbb {N} } and the set of all rational numbers Q {\displaystyle \mathbb {Q} } , and thus | N | = | Q | {\displaystyle
Cardinal_number
Number represented as a0+1/(a1+1/...)
sufficient condition for a rational number to be a convergent of the continued fraction of a given real number. A consequence of this criterion, often called
Simple_continued_fraction
Coincidence in mathematics
small integer or to a multiple or power of ten, or more generally, to a rational number with a small denominator. Other kinds of mathematical coincidences
Mathematical_coincidence
Mathematical set of all subsets of a set
number of elements in S is infinite), such as the set of integers or rationals, but not possible for example if S is the set of real numbers, in which
Power_set
Area of mathematics
any R > r. If f is a rational function of degree d, then T(r,f) ~ d log r; in fact, T(r,f) = O(log r) if and only if f is a rational function. The order
Nevanlinna_theory
Mathematical function with no sudden changes
a rational number}}\\0&{\text{ if }}x{\text{ is irrational}}.\end{cases}}} is continuous at all irrational numbers and discontinuous at all rational numbers
Continuous_function
Philosophical concept
contaminate rationality. Value judgments have the form: if one acted in a particular way (or valued this object), then certain consequences would ensue
Instrumental and intrinsic value
Instrumental_and_intrinsic_value
Lack of self-control
reason, desire, and action by challenging the intuitive assumption that rational judgment governs an agent's behavior. For example, there can be an instance
Akrasia
Major unsolved problem in transcendental number theory
conjecture about the transcendence degree of certain field extensions of the rational numbers Q {\displaystyle \mathbb {Q} } , which would establish the transcendence
Schanuel's_conjecture
Idea that everyone faces consequence as they deserve
deserve" – that actions will necessarily have morally fair and fitting consequences for the actor. For example, the assumptions that noble actions will eventually
Just-world_fallacy
Military strategy during the Cold War with regard to the use of nuclear weapons
rational choice and game-theoretic models of decision making (see game theory). Rational deterrence theory entails: Rationality: actors are rational Unitary
Deterrence_theory
Logical principle
{2}}} . Clearly (excluded middle) this number is either rational or irrational. If it is rational, the proof is complete, and a = 2 {\displaystyle a={\sqrt
Law_of_excluded_middle
Reasoning for mathematical statements
starting with an assumption, and with each subsequent formula a logical consequence of the preceding ones. This definition makes the concept of proof amenable
Mathematical_proof
Type of mathematical expression
ratios are a more general family of objects, called rational fractions, rational expressions, or rational functions, depending on context. This is analogous
Polynomial
Economics theorem
{\displaystyle \omega \in \Omega } to tangible consequences x ∈ X {\displaystyle x\in X} . A preference relation ≿ {\displaystyle \succsim } over acts in F
Savage's subjective expected utility model
Savage's_subjective_expected_utility_model
Description of physical properties at the atomic and subatomic scale
{1}{2}}\left|{\bigl \langle }[A,B]{\bigr \rangle }\right|.} Another consequence of the canonical commutation relation is that the position and momentum operators are Fourier
Quantum_mechanics
Mental state denoting commitment to act
number of major or minor consequences with them. The agent is usually unaware of many of them. In relation to these consequences, the agent is acting unintentionally
Intention
market would be conditioned upon the completeness of markets, the perfect rationality of agents, and the comprehensiveness of information. This would produce
Capital_market_imperfections
Study of fundamental reality
through space and time. Rational psychology focuses on metaphysical foundations and problems concerning the mind, such as its relation to matter and the freedom
Metaphysics
Relation between sides of a right triangle
of the consequences of the Pythagorean theorem is that line segments whose lengths are incommensurable (so the ratio of which is not a rational number)
Pythagorean_theorem
Transcendental single-variable function
_{0}^{\theta }\log |\sec(t)|\,dt=\Lambda (\theta +\pi /2)+\theta \log 2.} For rational values of θ / π {\displaystyle \theta /\pi } (that is, for θ / π = p /
Clausen_function
Theorised tendency towards war between emerging and existing powers
"inadvertent escalation" whereas the Peloponnesian war was an outcome of rational calculations. Others have questioned Allison's reading of Thucydides. In
Thucydides_Trap
Totality of psychological phenomena
of others without rational basis. Psychotic disorders are among the most severe mental illnesses and involve a distorted relation to reality in the form
Mind
Capacity for control, discretion or political self-governance
provides a sense of rational autonomy, simply meaning one rationally possesses the motivation to govern their own life. Rational autonomy entails making
Autonomy
Meromorphic function
{\displaystyle \mathbb {R} ^{+}} is still needed. This is a trivial consequence of the Bohr–Mollerup theorem for the gamma function where strictly logarithmic
Polygamma_function
American sociologist (1917 – 2011)
meanings of the term "rationality" in relation to the way people behave. Garfinkel mentions Schütz's paper on the issues of rationality and his various meanings
Harold_Garfinkel
Theory of media objectivity
view point and be disinterested observers." For topics in this sphere rational and informed people hold differing views within limited range. These topics
Hallin's_spheres
Integer side lengths of a right triangle
establishes that each rational point of the x-axis goes over to a rational point of the unit circle. The converse, that every rational point of the unit circle
Pythagorean_triple
RATIONAL CONSEQUENCE-RELATION
RATIONAL CONSEQUENCE-RELATION
Boy/Male
Hindu, Indian, Tamil
Revolving; Pearl
Girl/Female
Christian, German, Greek, Hebrew
Noble; Kind; Rational; Great Happiness
Boy/Male
Hindu
Rational
Girl/Female
Arabic, Muslim
Result; Consequence
Boy/Male
American, Anglo, British, English, Teutonic
National Protector; Wealthy Defender
Girl/Female
Hindu, Indian
Rational
Boy/Male
Hindu, Indian
National Player
Boy/Male
Muslim
Talker, Speaker, Rational
Boy/Male
Gujarati, Hindu, Indian
Lord of Pleasure
Girl/Female
Hindu, Indian
Rational
Girl/Female
Indian
Optional
Boy/Male
Tamil
Rational
Boy/Male
Indian
Talker, Speaker, Rational
Girl/Female
German, Greek
Noble; Kind; Rational
Boy/Male
Hindu
Rational
Boy/Male
Muslim/Islamic
Categorical (decision) talker, speaker, rational
Boy/Male
English
National protector.
Boy/Male
Arabic, Muslim
National Leader
Boy/Male
Tamil
Rational
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Animated; Rational
RATIONAL CONSEQUENCE-RELATION
RATIONAL CONSEQUENCE-RELATION
Girl/Female
Indian, Telugu
Honestly
Girl/Female
Indian, Sanskrit
Surrender of Devotion
Surname or Lastname
English
English : variant spelling of Wilson.
Girl/Female
Tamil
Boy/Male
Hindu, Indian
Hot Rayed; The Sun
Male
Hungarian
Hungarian, Slovak and Slovenian form of Hebrew David, DÃVID means "beloved."
Girl/Female
Arabic, Australian, German, Turkish
Favoured by God
Male
Egyptian
, Jesus, or, God saves.
Boy/Male
British, English, Latin
Raven; Variant of Corbet; Black-haired; Dark as a Raven
Girl/Female
French American German
Nobility. French form of the Old German Adalheidis, a compound of 'athal' (noble) and 'haida'...
RATIONAL CONSEQUENCE-RELATION
RATIONAL CONSEQUENCE-RELATION
RATIONAL CONSEQUENCE-RELATION
RATIONAL CONSEQUENCE-RELATION
RATIONAL CONSEQUENCE-RELATION
a.
Following as a consequence, result, or logical inference; consequent.
n.
Chain of causes and effects; consecution.
n.
Remote consequence.
a.
Given to foolish or visionary expectations; whimsical; fanciful; as, a notional man.
n.
A rational being.
a.
Not rational; void of reason or understanding; as, brutes are irrational animals.
a.
Of or pertaining to fractions or a fraction; constituting a fraction; as, fractional numbers.
a.
Relatively small; inconsiderable; insignificant; as, a fractional part of the population.
v. t.
To supply with rations, as a regiment.
a.
Agreeable to reason; not absurd, preposterous, extravagant, foolish, fanciful, or the like; wise; judicious; as, rational conduct; a rational man.
a.
Expressing the type, structure, relations, and reactions of a compound; graphic; -- said of formulae. See under Formula.
a.
Having reason, or the faculty of reasoning; endowed with reason or understanding; reasoning.
n.
That which follows from propositions by rational deduction; that which is deduced from reasoning or argumentation; a conclusion, or inference.
adv.
In a rational manner.
a.
Involving an option; depending on the exercise of an option; left to one's discretion or choice; not compulsory; as, optional studies; it is optional with you to go or stay.
n.
Importance with respect to what comes after; power to influence or produce an effect; value; moment; rank; distinction.
a.
Following by necessary inference or rational deduction; as, a proposition consequent to other propositions.
a.
Of or pertaining to a nation; common to a whole people or race; public; general; as, a national government, language, dress, custom, calamity, etc.
a.
Relating to the reason; not physical; mental.
a.
Following by consequence; consequent; deducible.