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Theoretical framework in linguistics
Minimal recursion semantics (MRS) is a framework for computational semantics. It can be implemented in typed feature structure formalisms such as head-driven
Minimal_recursion_semantics
Meaning represented by natural language
on computational semantics, SIGSEM. Discourse representation theory Formal semantics (natural language) Minimal recursion semantics Natural-language understanding
Computational_semantics
Omission of feature values in linguistic representations
immediate explosion of fully resolved readings. Frameworks such as Minimal recursion semantics encode constraints on scope without forcing a choice among all
Underspecification
Subfield of linguistic semantics
Lexical chain Lexicalization Lexical markup framework Lexical verb Minimal recursion semantics Ontology Polysemy Semantic primes Semantic satiation SemEval
Lexical_semantics
Concept in situation theory
framework "started out with situation semantics (Barwise & Perry 1983)" before later adopting Minimal Recursion Semantics as a more underspecified semantic
Situation_semantics
Language for controlling a computer
the first functional programming language. Unlike Fortran, it supported recursion and conditional expressions, and it also introduced dynamic memory management
Programming_language
Framework for describing natural languages' syntax
Tokyo in Japan. Lexical-functional grammar Minimal recursion semantics Relational grammar Situation semantics Syntax Transformational grammar Type Description
Head-driven phrase structure grammar
Head-driven_phrase_structure_grammar
Research program in theoretical linguistics
kicked by John"). Cognitive revolution Generative linguistics Minimal recursion semantics Origin of language Origin of speech Newmeyer, Frederick, J. (1986)
Generative_semantics
Process of repeating items in a self-similar way
mathematical or logical recursion. Recursion plays a crucial role not only in syntax, but also in natural language semantics. The word and, for example
Recursion
Mathematical concept
chosen. More formally, we can state the Transfinite Recursion Theorem as follows: Transfinite Recursion Theorem (version 1). Given a class function G: V
Transfinite_induction
Collaborative linguistics project
analysis, viz. head-driven phrase structure grammar (HPSG) and minimal recursion semantics (MRS). All tools under the DELPH-IN collaboration are developed
DELPH-IN
Scholar and Scopus her most cited publications include papers on minimal recursion semantics, multiword expressions, polysemy, named-entity recognition and
Ann_Copestake
Framework for exploring meaning
Combinatory categorial grammar Donkey pronoun Montague grammar Minimal recursion semantics Segmented discourse representation theory Kamp, Hans and Reyle
Discourse representation theory
Discourse_representation_theory
Proof method in mathematical logic
recursive function: "base cases" handle each minimal structure and a rule for recursion. Structural recursion is usually proved correct by structural induction;
Structural_induction
Mathematical-logic system based on functions
calculus may be used to model arithmetic, Booleans, data structures, and recursion, as illustrated in the following sub-sections i, ii, iii, and § iv. There
Lambda_calculus
Topics referred to by the same term
Society Medical Research Society Melbourne Rectangular Stadium Minimal recursion semantics Modified Rankin Scale, to measure disability after stroke Station
MRS
Type of binary relation
and recursion on S gives primitive recursion. If we consider the order relation (N, <), we obtain complete induction, and course-of-values recursion. The
Well-founded_relation
Natural language processing task
Class (philosophy) Formal semantics (linguistics) Information extraction Information retrieval Minimal recursion semantics Process philosophy Question
Semantic_parsing
function Set theory Forcing (mathematics) Boolean-valued model Kripke semantics General frame Predicate logic First-order logic Infinitary logic Many-sorted
List of mathematical logic topics
List_of_mathematical_logic_topics
Study of computable functions and Turing degrees
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated
Computability_theory
Subfield of mathematics
mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical
Mathematical_logic
Programming language
Although the design of most languages concentrates on innovations in syntax, semantics, or typing, Go is focused on the software development process itself.
Go_(programming_language)
American philosopher and logician (1940–2022)
and recursion theory. Kripke made influential and original contributions to logic, especially modal logic. His principal contribution is a semantics for
Saul_Kripke
Class of formal logics
first-order logic, as opposed to the other forms of classical logic. Most semantics of classical logic are bivalent, meaning all of the possible denotations
Classical_logic
Type of logical system
semantics. What follows is a description of the standard or Tarskian semantics for first-order logic. (It is also possible to define game semantics for
First-order_logic
Form of logic that allows quantification over predicates
two different semantics that are commonly used for second-order logic: standard semantics and Henkin semantics. In each of these semantics, the interpretations
Second-order_logic
Overview of and topical guide to natural language processing
Conference – METEOR – Minimal recursion semantics – Morphological pattern – Multi-document summarization – Multilingual notation – Naive semantics – Natural language
Outline of natural language processing
Outline_of_natural_language_processing
Overview of and topical guide to logic
Presupposition Probability Quantification Reason Reasoning Reference Semantics Strict conditional Syntax (logic) Truth Truth value Validity Affine logic
Outline_of_logic
Declarative logic programming language
semantics define the least fixed point of T to be the meaning of the program; this coincides with the minimal Herbrand model. The fixpoint semantics suggest
Datalog
Shading language for WebGPU
web security constraints (extensive static validation and well-defined semantics). Portability across diverse GPU backends via an abstract resource model
WebGPU_Shading_Language
Set of rules defining correctly structured programs
line to always be executed, even when x is 0, resulting in an endless recursion. While both space and tab characters are accepted as forms of indentation
Python_syntax_and_semantics
Mathematical set that can be enumerated
then there is a minimal standard model (see Constructible universe). The Löwenheim–Skolem theorem can be used to show that this minimal model is countable
Countable_set
Research tradition in linguistics
language. Generative linguistics includes work in core areas such as syntax, semantics, phonology, psycholinguistics, and language acquisition, with additional
Generative_grammar
Term that does not contain any variables
contains no variables. Ground terms may be defined by logical recursion (formula-recursion): Elements of C {\displaystyle C} are ground terms; If f ∈ F
Ground_expression
Reasoning for mathematical statements
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Mathematical_proof
Function computable with bounded loops
composition h ∘ g 1 {\displaystyle h\circ g_{1}} is obtained. Primitive recursion operator ρ {\displaystyle \rho } : Given the k-ary function g ( x 1 ,
Primitive_recursive_function
Linguistic research program proposed by Noam Chomsky
Noam Chomsky. Following Imre Lakatos's distinction, Chomsky presents minimalism as a program, understood as a mode of inquiry that provides a conceptual
Minimalist_program
Branch of mathematical logic
arithmetical transfinite recursion as recursive comprehension is to weak Kőnig's lemma. It has the hyperarithmetical sets as minimal ω-model. Arithmetical
Reverse_mathematics
Thesis on the nature of computability
functions (with arbitrarily many arguments) that is closed under composition, recursion, and minimization, and includes zero, successor, and all projections.
Church–Turing_thesis
Process calculus
emphasises the dialogue nature of computation, drawing connections with game semantics. Extensions of the π-calculus, such as the spi calculus and applied π
Π-calculus
Mathematical function that can be computed by a program
and projection functions, and is closed under composition, primitive recursion, and the μ operator. Equivalently, computable functions can be formalized
Computable_function
Limitative results in mathematical logic
theorem is closely related to several results about undecidable sets in recursion theory. Kleene (1943) presented a proof of Gödel's incompleteness theorem
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Mathematical_object
Branch of mathematical logic
structural proof theory, ordinal analysis, provability logic, proof-theoretic semantics, reverse mathematics, proof mining, automated theorem proving, and proof
Proof_theory
Mathematical theory of data types
influenced by them. Type theory is also widely used in formal theories of semantics of natural languages, especially Montague grammar and its descendants
Type_theory
Value indicating the relation of a proposition to truth
algebraic semantics. The algebraic semantics of intuitionistic logic is given in terms of Heyting algebras, compared to Boolean algebra semantics of classical
Truth_value
Logical principle
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Law_of_excluded_middle
Function that preserves distinctness
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Injective_function
Logical connective
unless its first argument is true and its second argument is false. This semantics can be shown graphically in the following truth table: One can also consider
Material_conditional
Mathematical use of "for all"
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Universal_quantification
One-to-one correspondence
problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing machine Type theory Related Abstract logic Algebraic
Bijection
Area of mathematical logic
First-order theories Hyperreal number Institutional model theory Kripke semantics Löwenheim–Skolem theorem Model-theoretic grammar Proof theory Saturated
Model_theory
Mathematical model for deduction or proof systems
of possible expressions that are valid utterances in the language) the semantics are what the utterances of the language mean (which is formalized in various
Formal_system
Infinite cardinal number
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Aleph_number
Study of the semantics, or interpretations, of formal and natural languages
In logic, the semantics or formal semantics is the study of the meaning and interpretation of formal languages, formal systems, and (idealizations of)
Semantics_(logic)
Sequence of program instructions invokable by other software
source code that is compiled to machine code that implements similar semantics. There is a callable unit in the source code and an associated one in
Function (computer programming)
Function_(computer_programming)
Dialect of Lisp
implementations are now required to support Scheme's full numeric tower, and the semantics of numbers have been expanded, mainly in the direction of support for
Scheme_(programming_language)
In mathematics, a statement that has been proven
since the theory that contains it may be unsound relative to a given semantics, or relative to the standard interpretation of the underlying language
Theorem
In model theory, a weakly o-minimal structure is a model-theoretic structure whose definable sets in the domain are just finite unions of convex sets
Weakly_o-minimal_structure
Complexity class used to classify decision problems
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
NP_(complexity)
Symbol representing a property or relation in logic
property or relation. In the semantics of logic, predicates are interpreted as relations. For instance, in a standard semantics for first-order logic, the
Predicate_(logic)
Symbol representing a mathematical object
from?" (PDF). In Böttner, Michael; Thümmel, Wolf (eds.). Variable-Free Semantics. Osnabrück Secolo. pp. 46–65. ISBN 978-3-929979-53-4. Quine, Willard V
Variable_(mathematics)
recursive function call, it is no longer capable of full μ-recursion, but only primitive recursion. Ackermann's function is the canonical example of a recursive
Loop_variant
Branch of mathematics that studies sets
science (such as in the theory of relational algebra), philosophy, formal semantics, and evolutionary dynamics. Its foundational appeal, together with its
Set_theory
Structure of a formal language
found in theoretical computer science, theoretical linguistics, formal semantics, mathematical logic, and other areas. A formal grammar is a set of rules
Formal_grammar
Type of infinite structure
a minimal structure need not be a strongly minimal theory, that is, there may be an elementarily equivalent structure that is not minimal. O-minimal structures
O-minimal_theory
Set of elements in any of some sets
problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing machine Type theory Related Abstract logic Algebraic
Union_(set_theory)
Statement that is taken to be true
assignment of values. Usually one takes as logical axioms at least some minimal set of tautologies that is sufficient for proving all tautologies in the
Axiom
Relationship where one statement follows from another
deductive system for L {\displaystyle {\mathcal {L}}} or by formal intended semantics for language L {\displaystyle {\mathcal {L}}} . The Polish logician Alfred
Logical_consequence
Branch of logic
referred to by Colin Howson as the principle of composition. It is this recursion in the definition of a language's syntax which justifies the use of the
Propositional_logic
Theorem that arithmetical truth cannot be defined in arithmetic
in mathematical logic, the foundations of mathematics, and in formal semantics. Informally, the theorem states that "arithmetical truth cannot be defined
Tarski's undefinability theorem
Tarski's_undefinability_theorem
Formal system of logic
additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more expressive, but their model-theoretic
Higher-order_logic
Mathematical set containing no elements
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Empty_set
Functional programming language
main implementation is the Glasgow Haskell Compiler (GHC). Haskell's semantics are historically based on those of the Miranda programming language, which
Haskell
Theory of truth in the philosophy of language
formulated it, this theory applies only to formal languages, cf. also semantics of first-order logic. He gave a number of reasons for not extending his
Semantic_theory_of_truth
Establishment of a theorem using inference from the axioms
constitute well formed formulas. However, it does not describe their semantics (i.e. what they mean). A formal system (also called a logical calculus
Formal_proof
Form of mathematical proof
Mathematical induction in this extended sense is closely related to recursion. Mathematical induction is an inference rule used in formal proofs, and
Mathematical_induction
the semantics of modal logic, suggesting that objects in possible worlds have counterparts in other possible worlds. course of values recursion A principle
Glossary_of_logic
Paradox in set theory
problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing machine Type theory Related Abstract logic Algebraic
Russell's_paradox
Basis for Euclidean geometry
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Hilbert's_axioms
Set whose elements all belong to another set
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Subset
Set of all things that may be the input of a mathematical function
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Domain_of_a_function
Logical connective OR
is warm". In classical logic, disjunction is given a truth functional semantics according to which a formula ϕ ∨ ψ {\displaystyle \phi \lor \psi } is
Logical_disjunction
Yes/no problem in computer science
efficient algorithm for a certain problem. On the other hand, the field of recursion theory categorizes undecidable decision problems by Turing degree, which
Decision_problem
In logic, a statement which is always true
that shelf. If it's either a book or it's bound, it's on that shelf". A minimal tautology is a tautology that is not the instance of a shorter tautology
Tautology_(logic)
Programming language that uses first order logic
called tail call optimization for deterministic predicates exhibiting tail recursion or, more generally, tail calls: A clause's stack frame is discarded before
Prolog
Function, homomorphism, or morphism
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Map_(mathematics)
Sequence of words formed by specific rules
expresses only what they look like (their syntax), not what they mean (semantics). For instance, nowhere in these rules is there any indication that "0"
Formal_language
Diagram that shows all possible logical relations between a collection of sets
problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing machine Type theory Related Abstract logic Algebraic
Venn_diagram
Particular class of sets which can be described entirely in terms of simpler sets
z_{n}\in X{\Bigr \}}.} L {\displaystyle L} is defined by transfinite recursion as follows: L 0 := ∅ . {\textstyle L_{0}:=\varnothing .} L α + 1 := Def
Constructible_universe
Axiom of set theory
problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing machine Type theory Related Abstract logic Algebraic
Axiom_of_choice
Collection of mathematical objects
problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing machine Type theory Related Abstract logic Algebraic
Set_(mathematics)
Basic framework of mathematics
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Foundations_of_mathematics
Method of deriving conclusions
section, § 1. Combining Logic and Probability Theory, § 2.1 Probabilistic Semantics Boričić 2016, pp. 77–78 Nederpelt & Geuvers 2014, pp. 159–162 Sørensen
Rule_of_inference
Mathematical proposition equivalent to the axiom of choice
directly using transfinite recursion, still assuming the axiom of choice. For that, see for example Transfinite recursion theorem § Example: a basis construction
Zorn's_lemma
Logical connective AND
problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing machine Type theory Related Abstract logic Algebraic
Logical_conjunction
Result in mathematics and set theory
defined for any well-founded set-like relation R on X by well-founded recursion. It provides a homomorphism of R onto a (non-unique, in general) transitive
Mostowski_collapse_lemma
Mathematical logic concept
complexity class containing all computably enumerable sets is RE. In recursion theory, the lattice of c.e. sets under inclusion is denoted E {\displaystyle
Computably_enumerable_set
Whether a decision problem has an effective method to derive the answer
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Decidability_(logic)
Logic theorem
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Law_of_noncontradiction
MINIMAL RECURSION-SEMANTICS
MINIMAL RECURSION-SEMANTICS
Girl/Female
Arabic, Muslim
Beautiful Flowers
Girl/Female
Muslim/Islamic
To reach your destination
Girl/Female
Arabic, Australian, Muslim
To Reach Your Destination
Boy/Male
Gujarati, Hindu, Indian
Rich; Maladar
Girl/Female
Hindu, Indian
Mineral
Girl/Female
Hindu, Indian
Knowledge
Girl/Female
Indian, Tamil
Sweet
Girl/Female
Gujarati, Hindu, Indian, Kannada, Tamil
Fish Eyes; Lighting
Girl/Female
Hindu
Full of jewel
Girl/Female
Danish, German, Nigerian
Calmness
Boy/Male
Hindu, Indian, Punjabi, Sikh, Tamil
Great Speech
Girl/Female
English, Hindu, Indian, Marathi
Small Daughter
Boy/Male
Hindu
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Tamil, Telugu, Traditional
A String of Pearls
Girl/Female
Indian
Pray of Lord Shiva
Girl/Female
Muslim/Islamic
Excursion spot
Girl/Female
Arabic, Muslim
Pleasure Trip; Excursion Spot
Girl/Female
Muslim
Pleasure trip, Excursion spot
Girl/Female
Arabic, Hindu, Indian, Kannada, Marathi, Muslim, Sindhi
Pleasure Trip; Excursion Spot
Girl/Female
Muslim
To reach your destination
MINIMAL RECURSION-SEMANTICS
MINIMAL RECURSION-SEMANTICS
Boy/Male
Arabic, Celebrity, Gujarati, Indian, Muslim
Father of a Multitude; A Prophet's Name; Abraham; Earth
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Marathi, Oriya, Sanskrit, Telugu
Sound; Voice
Girl/Female
Arabic
Beautiful
Boy/Male
Welsh
August.
Female
Native American
Native American Sioux name ANPAYTOO means "radiant."
Boy/Male
American, British, English, German, Norse
Rule with Mercy
Girl/Female
Celtic American Gaelic Irish Scottish
Sorrowful.
Boy/Male
Indian
Trusted
Boy/Male
Indian
Lord Perumal
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Tamil, Telugu
Dear One; Beloved
MINIMAL RECURSION-SEMANTICS
MINIMAL RECURSION-SEMANTICS
MINIMAL RECURSION-SEMANTICS
MINIMAL RECURSION-SEMANTICS
MINIMAL RECURSION-SEMANTICS
a.
Of or relating to animals; as, animal functions.
n.
An excursion.
n.
Reversion.
v. t.
Causing revulsion; revulsive.
n.
Anything very minute; as, the minims of existence; -- applied to animalcula; and the like.
a.
Impregnated with minerals; as, mineral waters.
n.
The act of ceding back; restoration; repeated cession; as, the recession of conquered territory to its former sovereign.
v. i.
Anything which is neither animal nor vegetable, as in the most general classification of things into three kingdoms (animal, vegetable, and mineral).
n.
An excursion.
n.
A flowing; also, a hostile incursion.
a.
Of or pertaining to a sine; employing, or founded upon, sines; as, a sinical quadrant.
pl.
of Minimum
a.
Of or pertaining to minerals; consisting of a mineral or of minerals; as, a mineral substance.
a.
Consisting of the flesh of animals; as, animal food.
pl.
of Minimus
n.
Same as Occursion.
n.
The power, either inherent or due to some physical action, by which bodies, or the particles of bodies, are made to recede from each other, or to resist each other's nearer approach; as, molecular repulsion; electrical repulsion.
n.
The act of recurring; return.