Search references for EXTENSIONAL AND-INTENSIONAL-DEFINITIONS. Phrases containing EXTENSIONAL AND-INTENSIONAL-DEFINITIONS
See searches and references containing EXTENSIONAL AND-INTENSIONAL-DEFINITIONS!EXTENSIONAL AND-INTENSIONAL-DEFINITIONS
Classification of definitions in mathematics, philosophy, and logic
In logic, extensional and intensional definitions are two key ways in which the objects, concepts, or referents a term refers to can be defined. They
Extensional and intensional definitions
Extensional_and_intensional_definitions
Statement that attaches a meaning to a term
classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects
Definition
According to an extensional definition, they are abstract groups, sets, or collections of objects. According to an intensional definition, they are abstract
Class (knowledge representation)
Class_(knowledge_representation)
Property or quality connoted by a word, phrase, or another symbol
language is intensional if it contains intensional statements, and extensional otherwise. All natural languages are intensional. The only extensional languages
Intension
Approach to predicate logic
distinction between intensional and extensional entities is parallel to the distinction between sense and reference. Logic is the study of proof and deduction as
Intensional_logic
Topics referred to by the same term
mathematical logic: see intensional statement. See also extensionality, and also intensional definition versus extensional definition Intensional logic embraces
Intensional
Logic principle
the concept of intensionality, which is concerned with whether the internal definitions of objects are the same. The extensional definition of function equality
Extensionality
Part of an ontology
logic § Modeling Metadata Web Ontology Language Extensional and intensional definitions Gruber, Thomas R. (June 1993). "A translation approach to portable
Abox
Definition by example
free dictionary. Comprehension Enumerative definition Exemplification Extensional and intensional definitions Intension Ostension Wittgenstein, Ludwig.
Ostensive_definition
1899 William Hughes Mearns poem
there") and the titular figure. The Coen Brothers film, The Man Who Wasn't There, was given its title based on the poem. Extensional and intensional definitions
Antigonish_(poem)
Example of a paradoxical argument
philosophy of language Extensional and intensional definitions – Classification of definitions in mathematics, philosophy, and logic Meinong's jungle –
Plato's_beard
Extensions with context
of the original sentence. De dicto and de re Extension (semantics) Extensional definition Extensionalism Intensional logic Opaque context Propositional
Extensional_context
Definition by exhaustively listing all of the objects a term applies to
An enumerative definition of a concept or term is a special type of extensional definition that gives an explicit and exhaustive listing of all the objects
Enumerative_definition
phenomenology Experience Experience machine Explanation Extensional and intensional definitions Fact Fairness False Felicific calculus Fidelity Final anthropic
List of philosophical concepts
List_of_philosophical_concepts
Totality of intensions of an object
both the composite and the primitive ideas. Extension Extensional definition Intension Intensional definition "Logical inferences and comprehension: How
Comprehension_(logic)
Programming language feature
implements function equality as extensional equality. Intensional equality Under intensional equality, two functions f and g are considered equal if they
First-class_function
Alternative foundation of mathematics
versions of the type theory: Martin-Löf proposed both intensional and extensional variants of the theory and early impredicative versions, shown to be inconsistent
Intuitionistic_type_theory
Group of things derived from extensional or intensional definition
similarly to a set defined by its members. The class is extensional. A set defined intensionally is a set of things that meet some requirement to be a member
Class_(philosophy)
Axiom used in set theory
'axiom of extensionality' has its roots in logic. An intensional definition describes the necessary and sufficient conditions for a term to apply to an object
Axiom_of_extensionality
Distinguishing objects and classes of objects
280-1. Class (philosophy) – Group of things derived from extensional or intensional definition Formalism (philosophy) – Concept of focusing on form over
Type–token_distinction
Mathematical-logic system
f = N in M By chaining such definitions, one can write a lambda calculus "program" as zero or more function definitions, followed by one lambda-term
Lambda_calculus
Type theory in logic and mathematics
a field is in rapid flux. At one time,[when?] the idea that types in intensional type theory with their identity types could be regarded as groupoids
Homotopy_type_theory
Formal study of linguistic meaning
Frege's and Tarski's ideas. To overcome problems associated with extensional definitions of meaning, Carnap pioneered the study of intensional semantics
Formal semantics (natural language)
Formal_semantics_(natural_language)
Mathematical construction of a set with an equivalence relation
identity and equivalence must be maintained, often with an interpretation of intensional equality (the equality on the original set) and extensional equality
Setoid
Notion of equality in type theory
Intuitionistic Type Theory (PDF). Streicher, Thomas (1993). Investigations into intensional type theory (PDF). Hofmann, Martin; Streicher, Thomas (July 1994). "The
Identity_type
Type whose definition depends on a value
whether the type theory is intensional or extensional. In 1934, Haskell Curry noticed that the types used in typed lambda calculus, and in its combinatory logic
Dependent_type
Cultural or emotional association
dictionary. Context as Other Minds Double entendre Extension Extensional definition Intension Intensional definition Implicature Loaded language Metacommunicative
Connotation
Mathematics and computer science concept
functional extensionality, UIP and K in fact sufficient to capture the differences between intensional and extensional Martin-Löf type theory: extensional MLTT
Uniqueness_of_identity_proofs
Terms to describe a conditional relationship between two statements
extensional, while contexts in which extension is not enough are intensional. Mathematics is typically extensional throughout." Stanford University primer
Necessity_and_sufficiency
Data type in type theory
2013-03-12. Retrieved 2023-09-13. Hofmann, Martin (1997). Extensional Constructs in Intensional Type Theory. doi:10.1007/978-1-4471-0963-1. ISBN 978-1-4471-1243-3
Quotient_type
Mathematical constructs and creation rules
finality) corresponds directly to the appropriate induction principle. In intensional type theories with the univalence axiom, this correspondence holds up
Inductive_type
Ordered listing of items in collection
offer enumerations as an extensional method for defining concepts, providing a contrast and alternative to intensional definitions, allowed by most programming
Enumeration
be obtained by repeatedly adding 1 to 0. *120 intensional function A function that is not extensional. logical 1. The logical sum of two propositions
Glossary of Principia Mathematica
Glossary_of_Principia_Mathematica
Model or diagram describing interrelated things
2, November 1978 "The Role of Intensional and Extensional Interpretation in Semantic Representations". Kent in "Data and Reality" : "One thing we ought
Entity–relationship_model
Study of meaning in language
such as quantification, intensionality, noun phrases, plurals, mass terms, tense, and modality. Montague semantics is an early and influential theory in
Semantics
properties have the same "values" (i.e., the same property extension), but may have different intensional meaning (i.e., denote different concepts). Property
Property_equivalence
Bearer of truth values
challenges arise for the truth values of extensional and intensional sentences. A sentence is extensional if its truth value does not change when a term is replaced
Proposition
3-volume treatise on mathematics, 1910–1913
restricted to definite orders". This change from a quasi-intensional stance to a fully extensional stance also restricts predicate logic to the second order
Principia_Mathematica
Type of formal logic
base-extension semantics for the classical propositional systems. In this case, the validity of a formula can be shown by an inductive definition generated
Modal_logic
Basic notion of sameness in mathematics
term extensionality, as used in 'Axiom of Extensionality' has its roots in logic and grammar (cf. Extension (semantics)). In grammar, an intensional definition
Equality_(mathematics)
Higher-order function which returns some fixed point of the input function
Talcott, Carolyn (1985). The Essence of Rum: A theory of the intensional and extensional aspects of Lisp-type computation (Ph.D. thesis). Stanford University
Fixed-point_combinator
Differentiating and characterizing feature
quality, feature, characteristic, type, exemplifiable, predicate, and intensional entity. Generally speaking, an object is said to exemplify, instantiate
Property_(philosophy)
Kind of proof calculus
either typechecking is undecidable (extensional type theory), or extensional reasoning is more difficult (intensional type theory). For this reason, some
Natural_deduction
this assignment is only truly functorial in extensional type theories (see #Properties). In intensional type theories, such functions are not truly functors
Polynomial functor (type theory)
Polynomial_functor_(type_theory)
Approximation of a mathematical set
the key definitions. More formal properties and boundaries of rough sets can be found in Pawlak (1991) and cited references. The initial and basic theory
Rough_set
Something that exists
the same entities. Intensional entities contrast with extensional entities, such as mathematical sets, which obey extensionality. This is articulated
Entity
School of thought in philosophy of mathematics
can only be defined intensionally, i.e. as the objects denoted by such and such concepts ... logically; the extensional definition appears to be equally
Logicism
Branch of mathematics that studies sets
students to logical operators (NOT, AND, OR), and semantic or rule description (technically intensional definition) of sets (e.g. "months starting with
Set_theory
Study of the semantics, or interpretations, of formal and natural languages
logic. James Garson has given some results in the areas of adequacy for intensional logics outfitted with such a semantics. The truth conditions for quantified
Semantics_(logic)
Fundamental unit of cognition
Procedural Semantics for Hyperintensional Logic: Foundations and Applications of Transparent Intensional Logic. Springer Science & Business Media. ISBN 978-90-481-8812-3
Concept
Assignment of meaning to the symbols of a formal language
rather with the extension of that property (or relation). In other words, these first-order interpretations are extensional not intensional. An example of
Interpretation_(logic)
Representation of data of various types in lambda calculus
using intensional equality. There are potential problems with the interpretation of results because of the difference between the intensional and extensional
Church_encoding
Study of programming languages via mathematical objects
semantics in more intensional models, such as the actor model and process calculi, there are different notions of equivalence within each model, and so the concepts
Denotational_semantics
Logical formalism using combinators instead of variables
is not equal to I {\displaystyle I} . We say the terms are extensionally equal. Extensional equality captures the mathematical notion of the equality of
Combinatory_logic
by a leader in the field of computer science 'a treatise on extensionality'. The extensional is treated in mathematics as ambient—it is not something about
History_of_topos_theory
1960 book by Willard Van Orman Quine
epistemology, physicalism as against phenomenalism and mind-body dualism, and extensionality as against intensionality. He also develops a behavioristic conception
Word_and_Object
or term, as opposed to its extension, which refers to the range of things it applies to. intensional definition A definition that specifies the essential
Glossary_of_logic
Swedish logician, philosopher, and mathematical statistician
was extensional while the type theory presented in the book by Nordström et al. in 1990, which was heavily influenced by his later ideas, intensional, and
Per_Martin-Löf
About mathematical infinity
belief in infinities arises from confusing the intensional nature of mathematical laws with the extensional nature of sets, sequences, symbols etc. A series
Controversy over Cantor's theory
Controversy_over_Cantor's_theory
Overview of and topical guide to logic
logic Fuzzy logic Higher-order logic Infinitary logic Informal logic Intensional logic Intermediate logic Interpretability logic Intuitionistic logic
Outline_of_logic
Relationship between programs and proofs
Interpretation of Modal Necessity", in de Rijke, Maarten (ed.), Advances in Intensional Logic, Applied Logic Series, vol. 7, Springer-Verlag, pp. 61–91, ISBN 978-0-7923-4711-8
Curry–Howard_correspondence
System of resource-aware logic
Logic and Computation: A Rosetta Stone" (PDF). New Structures of Physics. Bimbó, Katalin (13 September 2015). "The decidability of the intensional fragment
Linear_logic
Allowing for partial definitions reduces the amount of work needed as the algorithm need not generate these partial definitions for itself, and the incorrect
First-order_inductive_learner
Form of type polymorphism
of values. The set can be described extensionally by listing all the values, or it can be described intensionally by stating the membership of the set
Subtyping
About mathematical functions
with classes." By 1910–1913 and Principia Mathematica Russell had given up on the requirement for an intensional definition of a relation, stating that
History of the function concept
History_of_the_function_concept
Field of philosophical logic
B\Rightarrow \ \vdash {\mathsf {O}}A\to {\mathsf {O}}B.} If we introduce an intensional conditional operator then we can say that the starving ought to be fed
Deontic_logic
Axiomatization of arithmetic
{\displaystyle \Pi _{1}^{0}} -formulas. Early on, also variants with intensional equality and Brouwerian choice sequence have been investigated. Reverse mathematics
Heyting_arithmetic
Declarative logic programming language
called the extensional database or EDB of the Datalog program. The set of tuples computed by evaluating the Datalog program is called the intensional database
Datalog
German-American philosopher (1891–1970)
of definitions and conventions about the use of certain concepts. In contrast, scientific propositions are empirical statements that describe and explain
Rudolf_Carnap
Informal set theories
all objects for which the condition P holds (known as defining a set intensionally). For example, {x | x ∈ R} denotes the set of real numbers, {x | x has
Naive_set_theory
be given in intensional definition, as in: int[String] age = { "Stephan" -> 37, "Lynda" -> 29 }; or can be given in extensional definition, as in: int[String]
OptimJ
names additive, extensional, or comparative conjunction are sometimes used for lattice conjunction. In the logic BL and its extensions (though not in t-norm
T-norm_fuzzy_logics
Type of logical system
ISBN 978-3-030-73838-9. Gamut, L. T. F. (1990). Logic, Language, and Meaning. Vol. 2: Intensional Logic and Logical Grammar. University of Chicago Press. ISBN 978-0-226-28086-8
First-order_logic
Theory in philosophy of language
determine, referential or extensional properties but that it should be defined in terms of, and determined by, all and only the intensional properties of names
Descriptivist_theory_of_names
Globalization meta-process
the same function in the untyped lambda calculus. See also intensional versus extensional equality. The reverse operation to lambda lifting is lambda
Lambda_lifting
Family of formalisms in natural language syntax
value of a function at an argument. With some modifications to handle intensionality and quantification, this approach can be used to cover a wide variety
Categorial_grammar
2010 book by Jerry Fodor and Massimo Piattelli-Palmarini
formulated) is correct, then it is a paradigm example of intensional causation. Intensional causation requires either (1) there be a mind involved in
What_Darwin_Got_Wrong
thesis" as written here, but surely Gandy meant the latter, at least intensionally, because Turing did not prove anything in 1936 or anywhere else about
History of the Church–Turing thesis
History_of_the_Church–Turing_thesis
Axiom in Russell's ramified theory of types
excluded impredicative definitions by his ramified theory of types (1908, 1910). Kleene observes that "to exclude impredicative definitions within a type, the
Axiom_of_reducibility
ISSN 1611-3349. Hofmann, Martin (1997). "Syntax and semantics of dependent types". Extensional constructs in intensional type theory. London: Springer. pp. 13–54
Semantics_of_type_theory
Philosophical thesis about the mind–body relationship
which are an extensional matter and not influenced by the way they are described, from law-like relations, which are intensional and dependent on the
Anomalous_monism
American philosopher and logician (1908–2000)
included in logic was not logic for Quine. Formal systems involving intensional notions, especially modality. Quine was especially hostile to modal logic
Willard_Van_Orman_Quine
executive organ" multiple times but provides neither an intensional nor an extensional definition. Article 19 of the Federal Constitutional Law contains
Supreme_executive_organ
Philosophical tradition of the British people
worked in Britain and pioneered the A-theory of time. Prior was also influential for his contributions to tense logic and intensional logic. Hugh Mellor
British_philosophy
Actor event diagrams. The set is defined extensionally using power domain semantics rather than intensionally using causal axioms. The behaviors of individual
Denotational semantics of the Actor model
Denotational_semantics_of_the_Actor_model
intension are properties, and the extension is a set of individual real-world objects. If n > 1, the attributes are n-place intensional relations between real-world
Integrational theory of language
Integrational_theory_of_language
travel, tourism, insurance
EXTENSIONAL AND-INTENSIONAL-DEFINITIONS
EXTENSIONAL AND-INTENSIONAL-DEFINITIONS
EXTENSIONAL AND-INTENSIONAL-DEFINITIONS
EXTENSIONAL AND-INTENSIONAL-DEFINITIONS
EXTENSIONAL AND-INTENSIONAL-DEFINITIONS
EXTENSIONAL AND-INTENSIONAL-DEFINITIONS
EXTENSIONAL AND-INTENSIONAL-DEFINITIONS
EXTENSIONAL AND-INTENSIONAL-DEFINITIONS
EXTENSIONAL AND-INTENSIONAL-DEFINITIONS
travel, tourism, insurance