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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
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
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
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
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
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
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
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
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
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
Natural language processing task
Class (philosophy) Formal semantics (linguistics) Information extraction Information retrieval Minimal recursion semantics Process philosophy Question
Semantic_parsing
Scholar and Scopus her most cited publications include papers on minimal recursion semantics, multiword expressions, polysemy, named-entity recognition and
Ann_Copestake
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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)
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
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
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Mathematical_object
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
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
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
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
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
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
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
Dialect of Lisp
iteration construct, do, but it is more idiomatic in Scheme to use tail recursion to express iteration. Standard-conforming Scheme implementations are required
Scheme_(programming_language)
Infinite cardinal number
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Aleph_number
Logical incompatibility between two or more propositions
order on truth values. Minimal logic + GD yields Gödel-Dummett logic. Peirce's rule entails but is not entailed by GD over minimal logic. Law of the excluded
Contradiction
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
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
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
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
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
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
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
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)
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 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
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)
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
One-to-one correspondence
problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing machine Type theory Related Abstract logic Algebraic
Bijection
Fundamental theorem in mathematical logic
completeness theorem for its standard semantics (though does have the completeness property for Henkin semantics), and the set of logically valid formulas
Gödel's_completeness_theorem
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)
Existence and cardinality of models of logical theories
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Löwenheim–Skolem_theorem
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
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
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
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
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)
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
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)
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
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
Impossible task in computing
and a discussion of, his proof. Soare, Robert I., "Computability and recursion", Bull. Symbolic Logic 2 (1996), no. 3, 284–321. Toulmin, Stephen, "Fall
Entscheidungsproblem
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
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
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
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
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
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
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
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
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
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
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
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)
Technique for defining number-theoretic functions by recursion
course-of-values recursion is a technique for defining number-theoretic functions by recursion. In a definition of a function f by course-of-values recursion, the
Course-of-values_recursion
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
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)
Proposition in mathematical logic
sketch, but this was also incorrect, although it influenced later ideas in recursion theory. In 1906, Kőnig revised part of his attempted CH disproof and established
Continuum_hypothesis
Additional mathematical object
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Mathematical_structure
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
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
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
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
Axioms for the natural numbers
computability". In Maurice Nivat and John C. Reynolds (ed.). Algebraic Methods in Semantics (PDF). Cambridge: Cambridge University Press. pp. 459–541. ISBN 978-0-521-26793-9
Peano_axioms
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
Non-contradiction of a theory
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Consistency
Measure of algorithmic complexity
minimal length (i.e., using the fewest bits), it is called a minimal description of s, and the length of d(s) (i.e. the number of bits in the minimal
Kolmogorov_complexity
Assignment of meaning to the symbols of a formal language
general study of interpretations of formal languages is called formal semantics. The most commonly studied formal logics are propositional logic, predicate
Interpretation_(logic)
Every set is smaller than its power set
problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing machine Type theory Related Abstract logic Algebraic
Cantor's_theorem
Standard system of axiomatic set theory
Its omission here can be justified in two ways. First, in the standard semantics of first-order logic in which ZFC is typically formalized, the domain
Zermelo–Fraenkel_set_theory
MINIMAL RECURSION-SEMANTICS
MINIMAL RECURSION-SEMANTICS
Girl/Female
Indian
Pray of Lord Shiva
Girl/Female
Arabic, Muslim
Pleasure Trip; Excursion Spot
Girl/Female
Indian, Tamil
Sweet
Girl/Female
Arabic, Muslim
Beautiful Flowers
Boy/Male
Hindu
Girl/Female
Hindu
Full of jewel
Girl/Female
Arabic, Australian, Muslim
To Reach Your Destination
Girl/Female
Muslim
Pleasure trip, Excursion spot
Girl/Female
Danish, German, Nigerian
Calmness
Girl/Female
Gujarati, Hindu, Indian, Kannada, Tamil
Fish Eyes; Lighting
Girl/Female
Hindu, Indian
Knowledge
Girl/Female
Arabic, Hindu, Indian, Kannada, Marathi, Muslim, Sindhi
Pleasure Trip; Excursion Spot
Girl/Female
Muslim/Islamic
To reach your destination
Girl/Female
Muslim/Islamic
Excursion spot
Boy/Male
Hindu, Indian, Punjabi, Sikh, Tamil
Great Speech
Girl/Female
Muslim
To reach your destination
Girl/Female
Hindu, Indian
Mineral
Boy/Male
Gujarati, Hindu, Indian
Rich; Maladar
Girl/Female
English, Hindu, Indian, Marathi
Small Daughter
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Tamil, Telugu, Traditional
A String of Pearls
MINIMAL RECURSION-SEMANTICS
MINIMAL RECURSION-SEMANTICS
Female
Hebrew
(×Ö´×™×œÖ¸× Ö¸×”) Feminine form of Hebrew Ilan, ILANA means "tree."
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Oriya, Sanskrit, Sindhi, Tamil, Telugu
Cloud; Rain
Surname or Lastname
English
English : nickname for a fortunate person, from Middle English (i)blescede, blissed ‘blessed’ (from Old English blētsian ‘to bless’). The word also appears to have been in use in the Middle Ages as a female personal name, and some cases of the surname may be derived from this.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Marathi, Tamil
Beautiful
Girl/Female
Hindu, Indian
Happy Mood
Boy/Male
Hindu
Lord Vishnu or Lord Krishna
Boy/Male
Hindu, Indian
Brave
Female
Hungarian
Hungarian form of Greek Magdalēnē, MAGDOLNA means "of Magdala."
Boy/Male
Hindu, Indian
Visited; Reflection; Seen; Display
Boy/Male
Shakespearean
Twelfth Night', also called 'What You Will' A clown, servant to Olivia.
MINIMAL RECURSION-SEMANTICS
MINIMAL RECURSION-SEMANTICS
MINIMAL RECURSION-SEMANTICS
MINIMAL RECURSION-SEMANTICS
MINIMAL RECURSION-SEMANTICS
n.
An excursion.
a.
Of or pertaining to minerals; consisting of a mineral or of minerals; as, a mineral substance.
n.
Anything very minute; as, the minims of existence; -- applied to animalcula; and the like.
v. t.
Causing revulsion; revulsive.
n.
Same as Occursion.
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.
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.
pl.
of Minimum
a.
Of or pertaining to a sine; employing, or founded upon, sines; as, a sinical quadrant.
n.
The act of recurring; return.
a.
Of or relating to animals; as, animal functions.
a.
Consisting of the flesh of animals; as, animal food.
a.
Impregnated with minerals; as, mineral waters.
n.
Reversion.
n.
A flowing; also, a hostile incursion.
n.
An excursion.
n.
The act of ceding back; restoration; repeated cession; as, the recession of conquered territory to its former sovereign.
pl.
of Minimus