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Value indicating the relation of a proposition to truth
logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic
Truth_value
Mathematical table used in logic
of the operation for those values. A proposition's truth table is a graphical representation of its truth function. The truth function can be more useful
Truth_table
Conformity to reality
and about the possibility of truth value gaps—statements that have no truth value. Philosophers distinguish types of truth by domain, content, and epistemic
Truth
Study of correct reasoning
both proposed ternary logics which have a third truth value representing that a statement's truth value is indeterminate. These logics have been applied
Logic
System including an indeterminate value
many-valued logic systems in which there are three truth values indicating true, false, and some third value. This is contrasted with the more commonly known
Three-valued_logic
Statement that is true regardless of the truth or falsity of its constituent propositions
that logical truths are necessary truths. Instead he posits that the truth-value of any statement can be changed, including logical truths, given a re-evaluation
Logical_truth
Mathematical object in category theory
subobject classifier is used to interpret truth values, hence the alternative name “object of truth values”. Let X {\displaystyle X} be a set. A subset
Subobject_classifier
truth-value links is a concept in metaphysics discussed in debates between philosophical realism and anti-realism. Philosophers who appeal to truth-value
Truth-value_link
Branch of logic
classical truth-functional propositional logic, in which formulas are interpreted as having precisely one of two possible truth values, the truth value of true
Propositional_logic
Theory of truth in the philosophy of language
truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences.[vague] The semantic conception of truth,
Semantic_theory_of_truth
Function in logic
output of a truth function are all truth values; a truth function will always output exactly one truth value, and inputting the same truth value(s) will always
Truth_function
Bearer of truth values
meanings of declarative sentences, objects of beliefs, and bearers of truth values. They explain how different sentences, such as the English "Snow is white"
Proposition
Logical paradox from vague predicates
indeterminate and not-heap. The third truth-value can be understood either as a truth-value gap or as a truth-value glut. Alternatively, fuzzy logic offers
Sorites_paradox
Possessing negative truth value
negative truth value and is a nullary logical connective. In a truth-functional system of propositional logic, it is one of two postulated truth values, along
False_(logic)
Propositional calculus in which there are more than two truth values
Many-valued logic (also multi- or multiple-valued logic) is a propositional calculus in which there are more than two truth values. Traditionally, in
Many-valued_logic
Assignment of meaning to the symbols of a formal language
quantifiers) are truth-functional connectives that represent truth functions — functions that take truth values as arguments and return truth values as outputs
Interpretation_(logic)
Mathematical logic concept
then I don't wear my coat." Unlike the contrapositive, the inverse's truth value is not at all dependent on whether or not the original proposition was
Contraposition
Alternative to Tarskian semantics
In formal semantics, truth-value semantics is an alternative to Tarskian semantics. It has been primarily championed by Ruth Barcan Marcus, H. Leblanc
Truth-value_semantics
Paradoxical assertion
assign to this statement, the strengthened liar, a classical binary truth value leads to a contradiction. Assume that "this sentence is false" is true
Liar_paradox
Classical logic of two values, either true or false
inspection) has exactly one truth value, either true or false. A logic satisfying this principle is called a two-valued logic or bivalent logic. In formal
Principle_of_bivalence
Philosophical principle that perspectives and epistemology are always linked
interpretation is of equal truth or value. Rather than determining truth by correspondence, perspectivism generally determines truth through comparing and
Perspectivism
Approach to handling inferred information
information to compute the truth value of the stored derived facts and to restore consistency if an inconsistency is derived. A truth maintenance system, or
Reason_maintenance
Conditional statement which is true because the antecedent cannot be satisfied
no representatives. Vacuous truths most commonly appear in classical logic with two truth values. However, vacuous truths can also appear in, for example
Vacuous_truth
System for reasoning about vagueness
many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where
Fuzzy_logic
In logic, a statement which is always true
contradiction; in any symbolism, a tautology may be substituted for the truth value "true", as symbolized, for instance, by "1". Tautologies are a key concept
Tautology_(logic)
Study of meaning in language
particular, at their truth value. A conclusion follows semantically from a set of premises if the truth of the premises ensures the truth of the conclusion
Semantics
Concept in mathematical logic
the truth values of all variables are reversed, so is the truth value these connectives return, e.g. ¬ {\displaystyle \neg } , maj(p, q, r). The truth-preserving
Functional_completeness
Mathematical logic concept
same truth value in each of the members of that class. One can also speak of absoluteness of a formula between two structures, if it has the same truth value
Absoluteness_(logic)
Type of logical system
Then the truth value of a sentence is defined to be its truth value under any variable assignment, and it is proved that this truth value does not depend
First-order_logic
logic A three-valued logic where the third truth value is the truth-value gap "neither true nor false" ("N"), and the designated values are "true" and
Glossary_of_logic
Symbol connecting formulas in logic
truth-value of the operation or it never makes a difference. E.g., ¬, ↔, ↮ {\displaystyle \nleftrightarrow } , ⊤, ⊥. Duality To read the truth-value assignments
Logical_connective
Yes-or-no question that cannot ever be solved by a computer
Gödel's First Incompleteness Theorem is completely unconcerned with the truth value of a statement, but only concerns the issue of whether it is possible
Undecidable_problem
Concept in the philosophy of language
Bertrand Russell's theory of truth,[clarification needed] there is only one actual world, and a statement's truth value depends on whether the statement
Failure_to_refer
Logical connective OR
c) → (b ∨ c)) Truth-preserving: The interpretation under which all variables are assigned a truth value of 'true', produces a truth value of 'true' as
Logical_disjunction
3-volume treatise on mathematics, 1910–1913
terms of truth-values for the behaviour of the symbols "⊢" (assertion of truth), "∾" (logical not), and "V" (logical inclusive OR). Truth-values: PM embeds
Principia_Mathematica
Algebraic manipulation of "true" and "false"
First, the values of the variables are the truth values true and false, usually denoted by 1 and 0, whereas in elementary algebra the values of the variables
Boolean_algebra
Topics referred to by the same term
realism Subtle realism Theological critical realism Transcendental realism Truth-value link realism Realist approaches in the social sciences include: Ethnographic
Realism
Type of connective in logic
connective introduced by Church. Given operands p, q, and r, which represent truth-valued propositions, the meaning of the conditioned disjunction [p, q, r] is
Conditioned_disjunction
propositional logic, an assignment of truth values to propositional variables, with a corresponding assignment of truth values to all propositional formulas with
Valuation_(logic)
Concept in logic
{\displaystyle q} are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of p {\displaystyle p} and q
Logical_equivalence
Notion in mathematics
complex values. Value function Value (computer science) Value (physics) Absolute value Truth value Collins, Joseph Victor (1893). Text-book of Algebra: Through
Value_(mathematics)
In mathematical logic, a well-formed formula with no free variables
have concrete, fixed truth values: as the free variables of a (general) formula can range over several values, the truth value of such a formula may
Sentence_(mathematical_logic)
Study of the semantics, or interpretations, of formal and natural languages
The truth conditions for quantified formulas are given purely in terms of truth with no appeal to domains whatsoever (and hence its name truth-value semantics)
Semantics_(logic)
Symbol representing a property or relation in logic
or set indicator functions (i.e., functions from a set element to a truth value). Set-builder notation makes use of predicates to define sets. In autoepistemic
Predicate_(logic)
Formal study of linguistic meaning
output is a truth value. Simple intransitive verbs without objects are functions that take an entity as input and produce a truth value as output. The
Formal semantics (natural language)
Formal_semantics_(natural_language)
Set theory concept
Boolean-valued model is a generalization of the ordinary Tarskian notion of structure from model theory. In a Boolean-valued model, the truth values of propositions
Boolean-valued_model
Method to analyze non-binary inputs
turn (heater is "high") This rule uses the truth value of the "temperature" input, which is some truth value of "cold", to generate a result in the fuzzy
Fuzzy_control_system
Distinction in the philosophy of language
sentence – its truth value – appear. This early theory of meaning explains how the significance or reference of a sentence (its truth value) depends on the
Sense_and_reference
Philosophical doctrine on the subjugation of all events to fate
overcome logical fatalism. The third truth value view says that future contingents can have a third value which is beyond truth or falsity. The all-false view
Fatalism
Logical operator in propositional calculus
compares two truth values, or more generally, two formulas, such that it gives the value True if both arguments have the same truth value, and False if
Logical_equality
Logical incompatibility between two or more propositions
B\implies A} , whose most simple reading is that there is a linear order on truth values. Minimal logic + GD yields Gödel-Dummett logic. Peirce's rule entails
Contradiction
Many-valued logic in which truth values comprise a continuous range
logic, an infinite-valued logic (or real-valued logic or infinitely-many-valued logic) is a many-valued logic in which truth values comprise a continuous
Infinite-valued_logic
Type of formal logic
formula must be assigned at least one truth value, but there is no requirement that it be assigned at most one truth value. The semantic clauses for negation
Paraconsistent_logic
Possible truths which are not necessary
while the truth values of contingent past- and present-tense statements can be expressed in pairs of contradictions to represent their truth or falsity
Contingency_(philosophy)
Logic formula
which is well formed. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may
Propositional_formula
Semantics for dealing with irreferential singular terms and vagueness
logic in cases where truth values are undefined. According to supervaluationism, a proposition can have a definite truth value even when its components
Supervaluationism
Systematic study of values
Lead section, § Are Value Claims Truth Evaluable?, § Value Realism by Degrees: a Flow Chart Oddie 2013, § Are Value Claims Truth Evaluable?, § Quasi-Realism
Value_theory
Logical operation
notions, truth values, or semantic values more generally. In classical logic, negation is normally identified with the truth function that takes truth to falsity
Negation
Any logic with four truth values
A four-valued logic is any logic with four truth values. Several types of four-valued logic have been advanced. The most common, particularly in electronics
Four-valued_logic
Type of formal logic
formulas are assigned truth values relative to a possible world. A formula's truth value at one possible world can depend on the truth values of other formulas
Modal_logic
Formula that contains at least one free variable
not have a truth value assigned to it, in contrast with a closed formula which constitutes a proposition and thus can have a truth value like true or
Open_formula
System for representing and reasoning about time
am hungry". Though its meaning is constant in time, the statement's truth value can vary in time. Sometimes it is true, and sometimes false, but never
Temporal_logic
Variant of a linguistic expression
there is also an inference of truth value. Either the truth value is True for a person who is tall, or the truth value is False. Each of the examples
Logical_form_(linguistics)
Relation between sets of properties or facts
Examples of supervenience, in which case the truth values of some propositions cannot vary unless the truth values of some other propositions vary, include:
Supervenience
Method of deriving conclusions
logical operators are truth-functional, meaning that the truth value of a compound proposition depends only on the truth values of the simple propositions
Rule_of_inference
Philosophical study of morality
are truth-apt, meaning that they all have a truth value: they are either true or false. Cognitivism claims that moral statements have a truth value but
Ethics
Logical operator in modal logic
non-truth-functional in the following sense: The truth-value of composite formulae sometimes depend on factors other than the actual truth-value of their
Modal_operator
Moral virtue and practice
the truth that value judgments, including the command "Thou shalt not kill," are merely subjective assertions. — Zuckert and Zuckert, The truth about
Integrity
Logical principles
least one truth value. There are no truth gaps. The law of non contradiction says no proposition has more than one truth value. There are no truth gluts.
Law_of_thought
Programming paradigm
facts in the bodies of its clauses. The probability of any assignment of truth values to the groundings of the formulas associated with probabilistic facts
Probabilistic logic programming
Probabilistic_logic_programming
Logic with discrete truth values
In logic, a finite-valued logic (also finitely many-valued logic) is a propositional calculus in which truth values are discrete. Traditionally, in Aristotle's
Finite-valued_logic
Type of search algorithm
basic backtracking algorithm runs by choosing a literal, assigning a truth value to it, simplifying the formula and then recursively checking if the simplified
DPLL_algorithm
Sequence of words formed by specific rules
algebra, which is a formal way of describing logical operations using truth values and set operators. In his work An Investigation of The Laws of Thought
Formal_language
Argument whose conclusion must be true if its premises are
validity. In truth-preserving validity, the interpretation under which all variables are assigned a truth value of 'true' produces a truth value of 'true'
Validity_(logic)
Symbols representing logical operations
it to another truth value. Similarly, a binary truth function maps ordered pairs of truth values to truth values, while a ternary truth function maps
Logic_alphabet
Function that outputs either true or false
true. A truth predicate may have additional domains beyond the formal language domain, if that is what is required to determine a final truth value. Bit
Boolean-valued_function
Immediate inference concept in logic
about the truth value of the I proposition. Similarly, if the E proposition is false, that will not tell us anything about the truth value of the O proposition
Subalternation
Data whose unit can take on only two possible states
by different names including bit (binary digit) in computer science, truth value in mathematical logic and related domains and binary variable in statistics
Binary_data
Logical paradox concerning truth values
Quine's paradox is a paradox concerning truth values, stated by Willard Van Orman Quine. It is related to the liar paradox as a problem, and it purports
Quine's_paradox
Logical condition in philosophy
condition by which two expressions may be interchanged without altering the truth-value of statements in which the expressions occur. Substitution salva veritate
Salva_veritate
Data having only values "true" or "false"
the Boolean is a data type that has one of two possible values representing the two truth values of logic: true and false. It is named after George Boole
Boolean_data_type
network, a data link may evaluate to a truth value, given a data input. A data link may also hold a data value that is subsequently transformed by mathematical
NetWeaver_Developer
Logical fallacy
arguments that assert a conclusion's truth value (true or false) without regard to the formal preservation of the truth from the premises; appeal to consequences
Appeal_to_consequences
Meta-ethical theory
not have any truth conditions. Hence, expressivists either do not allow that moral sentences have truth value, or rely on a notion of truth that does not
Expressivism
Theorem in formal logic
allow some contradictory statements to be proven without affecting the truth value of (all) other statements. In symbolic logic, the principle of explosion
Principle_of_explosion
Mathematician and philosopher (1906–1978)
axiomatic system satisfying certain technical conditions cannot decide the truth value of all statements about the natural numbers, and cannot prove that it
Kurt_Gödel
Immediate inference in logic
The quality of the inferred categorical proposition is changed but the truth value is the same to the original proposition. The immediately inferred proposition
Obversion
Gödel–Dummett logics, is a family of finite- or infinite-valued logics in which the sets of truth values V are closed subsets of the unit interval [0,1] containing
Gödel_logic
Properties of mathematical relationships
if one of the following holds for the function's truth table: In every row in which the truth value of the function is T, there are an odd number of Ts
Linearity
Incorrect proposition that forms the basis of an argument
validity of an argument is a function of its internal consistency, not the truth value of its premises. For example, consider this syllogism, which involves
False_premise
Topics referred to by the same term
and women's rights activist Truth Social, social media platform by Trump Media & Technology Group (TMTG) Truth value, value indicating the relation of
Truth_(disambiguation)
Logical principle
check that the sentence must receive at least one of the n truth values (and not a value that is not one of the n). Other systems reject the law entirely
Law_of_excluded_middle
Movement in Western philosophy
theology, ethics and aesthetics as cognitively meaningless in terms of truth value or factual content. Despite its ambition to overhaul philosophy by mimicking
Logical_positivism
Philosophical concept about vagueness
as other theories of vagueness might claim, lack a truth-value – even if the determinate truth-value is beyond our epistemological grasp. Epistemicism
Epistemicism
Various systems of symbolic logic
of any truth value besides 'true' or 'false'. In contrast, propositional formulae in intuitionistic logic are not assigned a definite truth value and are
Intuitionistic_logic
Variant of the liar paradox
"This sentence is false." Any attempts to assign a classical binary truth value to this statement lead to a contradiction, or paradox. This occurs because
Pinocchio_paradox
Standards and rules used to judge the accuracy of statements and claims
distinct belief), proves it is true. There is some value in the criterion if it means innate truth, such as the laws of logic and mathematics. If it merely
Criteria_of_truth
Unary truth function in many-valued logic
many-valued logic with linearly ordered truth values, cyclic negation is a unary truth function that takes a truth value n and returns n − 1 as value if
Cyclic_negation
Derivation of the laws of probability theory
presuming that the truth value of conjunction P ∧ Q {\displaystyle P\land Q} is a twice differentiable function f {\displaystyle f} of truth values of the two
Cox's_theorem
Extension of a concept, idea, or sign
Frege's "On Sense and Reference") as its truth value. So the extension of "Lassie is famous" is the logical value 'true', since Lassie is famous. Some concepts
Extension_(semantics)
travel, tourism, insurance
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travel, tourism, insurance