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Mathematical logic concept
logic, an atomic formula (also known as an atom or a prime formula) is a formula with no deeper propositional structure, that is, a formula that contains
Atomic_formula
Syntactically correct logical formula
R(t1,...,tn) is an atomic formula Finally, the set of formulas is defined to be the smallest set containing the set of atomic formulas such that the following
Well-formed_formula
Mass per amount of substance
and ma(X) is the mass of each entity of the substance (atomic mass, molecular mass, or formula mass), then the mass of the sample is m(X) = N(X) ⋅ ma(X)
Molar_mass
Term in logic
which any variables are bound. An atomic sentence is an atomic formula containing no variables. It follows that an atomic sentence contains no logical connectives
Atomic_sentence
Type of logical system
bound variable occurrences in a formula are defined inductively as follows. Atomic formulas If φ is an atomic formula, then x occurs free in φ if and
First-order_logic
Formula for spectral line wavelengths in alkali metals
In atomic physics, the Rydberg formula calculates the wavelengths of a spectral line in many chemical elements. The formula was primarily presented as
Rydberg_formula
Index of articles associated with the same name
works equally well if all integers are used) in such a way that any atomic formula x ∈ y {\displaystyle x\in y} appearing in ϕ {\displaystyle \phi } satisfies
Stratification_(mathematics)
In mathematical logic, a well-formed formula with no free variables
quantifiers in them are known as atomic sentences; by analogy to atomic formula. Sentences are then built up out of atomic sentences by applying connectives
Sentence_(mathematical_logic)
Components of a mathematical or logical formula
applying a predicate symbol to an appropriate number of terms is called an atomic formula, which evaluates to true or false in bivalent logics, given an interpretation
Term_(logic)
mathematical logic, an atomic model is a model such that the complete type of every tuple is axiomatized by a single formula. Such types are called principal
Atomic model (mathematical logic)
Atomic_model_(mathematical_logic)
Branch of logic
propositional formulas. Because of this, the propositional variables are called atomic formulas of a formal propositional language. While the atomic propositions
Propositional_logic
Formula to approximate nuclear mass based on nucleon counts
over the years, the structure of the formula remains the same today. The formula gives a good approximation for atomic masses and thereby other effects.
Semi-empirical_mass_formula
Topics referred to by the same term
basic building blocks of reality Atomic City (disambiguation) Atomic formula, a formula without subformulas Atomic number, the number of protons found
Atomic
Symbol representing a property or relation in logic
logic, a predicate is a non-logical relation symbol, which forms an atomic formula when applied to an appropriate number of terms. In set theory with the
Predicate_(logic)
Assignment of meaning to the symbols of a formal language
known as the set of σ-formulas. Each σ-formula is built up out of atomic formulas by means of logical connectives; atomic formulas are built from terms
Interpretation_(logic)
In mathematical logic, an atomic formula or its negation
In mathematical logic, a literal is an atomic formula (also known as an atom or prime formula) or its negation. The definition mostly appears in proof
Literal_(mathematical_logic)
Branch of metaphysics
formula begins with an atomic formula followed by the biconditional, the subformula to the right of the biconditional is a definition of the atomic formula
Mereotopology
Atomic model introduced by Niels Bohr in 1913
of the atom should account for the many atomic spectral lines. These lines were summarized in empirical formulas by Johann Balmer and Johannes Rydberg.
Bohr_model
Term that does not contain any variables
ground terms. A ground predicate, ground atom or ground literal is an atomic formula all of whose argument terms are ground terms. If p ∈ P {\displaystyle
Ground_expression
Processing of natural language by a computer
grammar Formation rule Well-formed formula Automata theory Regular expression Production Ground expression Atomic formula Applications Formal methods Propositional
Natural_language_processing
Type of formal logic
is an atomic formula, then ϕ {\displaystyle \phi } is a formula of L {\displaystyle {\mathcal {L}}} . If ϕ {\displaystyle \phi } is a formula of L {\displaystyle
Modal_logic
Programming language that uses first order logic
(depending on the context) a term or an atomic formula of logic. An atom in a standard logic terminology means an atomic formula; an atom of Prolog (depending on
Prolog
Type of logical formula
that every set of definite clauses D has a unique minimal model M. An atomic formula A is logically implied by D if and only if A is true in M. It follows
Horn_clause
Form of logic that allows quantification over predicates
expression t ∈ S (also written S(t), or St to save parentheses) is an atomic formula. Sets of individuals can also be viewed as unary relations on the domain
Second-order_logic
Extension of first-order logic with atoms expressing variable dependencies
{\mbox{Free}}(\phi )} are defined as follows: Any atomic formula ϕ {\displaystyle \phi } is a formula, and Free ( ϕ ) {\displaystyle {\mbox{Free}}(\phi
Dependence_logic
System for representing and reasoning about time
\;|\;\lnot \phi \;|\;\phi \lor \phi \;|\;G\phi \;|\;H\phi } where a is some atomic formula. Kripke models are used to evaluate the truth of sentences in TL. A
Temporal_logic
System of resource-aware logic
atomic formula, then φ {\displaystyle \varphi } is a formula of L {\displaystyle {\mathcal {L}}} . If φ {\displaystyle \varphi } is an atomic formula
Linear_logic
Core of an atom composed of nucleons
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford at the
Atomic_nucleus
Inference rule in logic, proof theory, and automated theorem proving
{\displaystyle p} the non-atomic formula a → e {\displaystyle a\rightarrow e} in step (12). Using Murray's rules, the semantically equivalent formula e ∨ ¬ a ∨ ¬ a
Resolution_(logic)
Programming paradigm based on formal logic
The atomic formula holds(Fact, Time) expresses that the Fact holds at the Time. Such time-varying facts are also called fluents. The atomic formula happens(Event
Logic_programming
completeness of atomic initial sequents states that initial sequents A ⊢ A (where A is an arbitrary formula) can be derived from only atomic initial sequents
Completeness of atomic initial sequents
Completeness_of_atomic_initial_sequents
Mathematical study of the meaning of programming languages
semantics makes no distinction between a phrase's meaning and the logical formulas that describe it; its meaning is exactly what can be proven about it in
Semantics (programming languages)
Semantics_(programming_languages)
Moving charge energy loss formula found by Hans Bethe
Bethe formula or Bethe–Bloch formula describes the mean energy loss per distance travelled of swift charged particles (protons, alpha particles, atomic ions)
Bethe_formula
Metabolic redox process producing energy in the absence of oxygen
converted into glucose and galactose (both six-carbon sugars with the same atomic formula): C12H22O11 + H2O → 2 C6H12O6 Heterolactic fermentation is in a sense
Fermentation
Claimed as largest named number
x_{i}=x_{j}} are atomic formulas. If θ {\displaystyle \theta } is a formula, then ( ¬ θ ) {\displaystyle (\neg \theta )} is a formula (the negation of
Rayo's_number
Probabilistic logic
particular event, given by an atomic formula (marginal inference), possibly conditioned by another atomic formula. Marginal inference can be performed
Markov_logic_network
Overview of and topical guide to logic
connective Logical matrix Product term True quantified Boolean formula Truth table Atomic formula Atomic sentence Domain of discourse Empty domain Extension (predicate
Outline_of_logic
Algebraization of first-order logic
algebraizes the fragment of first-order logic consisting of formulas having no atomic formula lying in the scope of more than three quantifiers. That fragment
Predicate_functor_logic
that every measurable subset has the same measure or measure 0 atomic An atomic formula (in set theory) is one of the form x=y or x∈y axiom Aczel's anti-foundation
Glossary_of_set_theory
1:2:4, Dalton deduced that the formulas for the oxides of nitrogen are N2O, NO, and NO2. In 1804, Dalton explained his atomic theory to his friend and fellow
History_of_atomic_theory
Branch of mathematics that studies sets
include rough set theory and fuzzy set theory, in which the value of an atomic formula embodying the membership relation is not simply True or False. The Boolean-valued
Set_theory
Mathematical model for deduction or proof systems
components, as a minimum: Formal language, which is a set of well-formed formulas, which are strings of symbols from an alphabet, formed by a formal grammar
Formal_system
Freely generated algebraic structure over a given signature
consists of all ground terms: terms that have no variables in them. An atomic formula or atom is commonly defined as a predicate applied to a tuple of terms;
Term_algebra
Fragment of first-order logic
argument), and there are no function symbols. In other words, all atomic formulas are of the form P ( t ) {\displaystyle P(t)} , where P {\displaystyle
Monadic_predicate_calculus
Extension of classical first-order logic
terms and atomic formulas are defined exactly as in first-order logic with equality. Formulas of IF logic are defined as follows: Any atomic formula φ {\displaystyle
Independence-friendly_logic
Symbol connecting formulas in logic
given formula with parentheses. The order of precedence determines which connective is the "main connective" when interpreting a non-atomic formula. The
Logical_connective
The atomic radius of a chemical element is the distance from the center of the nucleus to the outermost shell of an electron. Since the boundary is not
Atomic radii of the elements (data page)
Atomic_radii_of_the_elements_(data_page)
Sequence of words formed by specific rules
of the formula can be derived from the interpretation of its terms; a model for a formula is an interpretation of terms such that the formula becomes
Formal_language
Style of formal logical argumentation
on the right. The root of the tree is the formula we wish to prove; the leaves consist of atomic formulas only. The tree is known as a reduction tree
Sequent_calculus
Important atomic emission spectra
emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given by the Rydberg formula. These observed spectral
Hydrogen_spectral_series
System of mathematical set theory
step-by-step construction of the formula with classes. Since all set-theoretic formulas are constructed from two kinds of atomic formulas (membership and equality)
Von Neumann–Bernays–Gödel set theory
Von_Neumann–Bernays–Gödel_set_theory
Principal energy levels in atomic physics
shells. So when Bohr outlined his electron shell atomic theory in 1922, there was no mathematical formula for the theory. So Rutherford said he was hard
Electron_shell
Base set of symbols with which a language is formed
grammar Formation rule Well-formed formula Automata theory Regular expression Production Ground expression Atomic formula Applications Formal methods Propositional
Alphabet_(formal_languages)
Hydrogen spectral series
The Balmer series, or Balmer lines in atomic physics, is one of a set of six named series describing the spectral line emissions of the hydrogen atom.
Balmer_series
the following form: H, G => B where H is an atomic formula, G and B are two sequences of atomic formulas. H is called the head, G the guard, and B the
B-Prolog
Structure of a formal language
framework L-system Lojban Post canonical system Shape grammar Well-formed formula Meduna, Alexander (2014), Formal Languages and Computation: Models and
Formal_grammar
Standard unit of mass for atomic-scale entities
The dalton (symbol: Da), or unified atomic mass unit (symbol: u), is a unit of mass defined as 1/12 of the mass of an unbound neutral atom of carbon-12
Dalton_(unit)
Study of the semantics, or interpretations, of formal and natural languages
logics outfitted with such a semantics. The truth conditions for quantified formulas are given purely in terms of truth with no appeal to domains whatsoever
Semantics_(logic)
by C ∨ B. For purposes of the translation, ⊥ is considered to be an atomic formula as well; hence it is replaced with ⊥ ∨ B (which is equivalent to B)
Friedman_translation
Topics referred to by the same term
Atom (measure theory), a minimal measurable set Atom (order theory) Atomic formula, a single predicate in first-order logic Atom, an urelement in set theory
Atom_(disambiguation)
Existence of values making formula true
atomic formula is satisfiable if there is a collection of elements of a structure that render the formula true. If A is a structure, φ is a formula,
Satisfiability
Symbols requiring interpretation
used to combine one or more (depending on the arity) terms into an atomic formula. For example a signature could consist of a binary function symbol +
Non-logical_symbol
Rules used for constructing, or transforming the symbols and words of a language
semantics of a language, which is concerned with its meaning. The symbols, formulas, systems, theorems and proofs expressed in formal languages are syntactic
Syntax_(logic)
Standard system of axiomatic set theory
as one that could be formulated as a well-formed formula in a first-order logic whose atomic formulas were limited to set membership and identity. They
Zermelo–Fraenkel_set_theory
Variable that can either be true or false
connectives, and some logical quantifiers. Propositional variables are the atomic formulas of propositional logic, and are often denoted using capital roman letters
Propositional_variable
Rest mass of an atom in its ground state
Atomic mass (ma or m) is the mass of a single atom. The atomic mass mostly comes from the combined mass of the protons and neutrons in the nucleus, with
Atomic_mass
Technique in mathematical logic
Gentzen) associates with each formula φ in a first-order language another formula φN, which is defined inductively: If φ is atomic, then φN is ¬¬φ as above
Double-negation_translation
function symbols, and a collection of relation symbols. Formulas are built out of atomic formulas using logical connectives and quantifiers. A structure
Valuation_(logic)
Arithmetical concept
of A {\displaystyle A} as follows, where P {\displaystyle P} is an atomic formula: ( P ) D ≡ P ( A ∧ B ) D ( x , v ; y , w ) ≡ A D ( x ; y ) ∧ B D ( v
Dialectica_interpretation
Branch of mathematics
polynomials with real coefficients. These formulas are thus the formulas which may be constructed from the atomic formulas by the logical operators and (∧), or
Algebraic_geometry
Smallest unit of a chemical element
Martin, W.C.; Wiese, W.L. (May 2007). "Atomic Spectroscopy: A Compendium of Basic Ideas, Notation, Data, and Formulas". National Institute of Standards and
Atom
Mathematical methods
n and formulas A in the language of Heyting arithmetic, known as Kleene's 1945-realizability relation: Any number n realizes an atomic formula s=t if
Realizability
Method of symbol substitution
grammar Formation rule Well-formed formula Automata theory Regular expression Production Ground expression Atomic formula Applications Formal methods Propositional
Production_(computer_science)
Type of database query
{\displaystyle \{x,y\}} between two variables if and only if there is an atomic formula R ( x , y ) {\displaystyle R(x,y)} or R ( y , x ) {\displaystyle R(y
Conjunctive_query
In logic, defining a new symbol
{\displaystyle f} . Let ψ {\displaystyle \psi } be any atomic formula of T ′ {\displaystyle T'} . We define formula ψ ∗ {\displaystyle \psi ^{\ast }} of T {\displaystyle
Extension_by_definition
British chemist and physicist (1766–1844)
molecular formula in order to calculate relative atomic weights. Dalton's "rule of greatest simplicity" caused him to assume that the formula for water
John_Dalton
f(t_{1},\dots ,t_{k})^{I}:=f^{I}(t_{1}^{I},\dots ,t_{k}^{I})} . For each atomic formula R ( t 1 , … , t k ) {\displaystyle R(t_{1},\dots ,t_{k})} , its interpreted
Gödel_logic
Rule defining the correct structure of expressions in formal grammar
meaning. A formal grammar determines which symbols and sets of symbols are formulas in a formal language. A formal system (also called a logical calculus,
Formation_rule
Area of mathematical logic
understanding the geometry of definable sets. A first-order formula is built out of atomic formulas such as R ( f ( x , y ) , z ) {\displaystyle R(f(x,y),z)}
Model_theory
Substance composed of chemically identical molecular entities
ionic species, with its formula being NO3−. The term "chemical species" is also applied to a set of chemically identical atomic or molecular structures
Chemical_species
Compact notation for chemical compounds
A chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule
Chemical_formula
Alternative to Tarskian semantics
clauses for atomic and for quantificational formulas differ from those of the standard semantics. Whereas in standard semantics atomic formulas like P b
Truth-value_semantics
Set theory concept
an element of M to the term f(a0,...,an-1). Interpretation of the atomic formulas of L is more complicated. To each pair a and b of elements of M, the
Boolean-valued_model
Algorithm in modal logic
{\displaystyle ST_{x}(p)\equiv P(x)} , where p {\displaystyle p} is an atomic formula; P(x) is true when p {\displaystyle p} holds in world x {\displaystyle
Standard_translation
extends the semantics and syntax usage rules of the HiLog and HiLog atomic formulas to extend SWSL-FOL. The combination of SWSL-FOL + Equality and SWSL-FOL
Semantic Web Services Language
Semantic_Web_Services_Language
Approximate atomic number calculated for materials with many elements
often dubious - sort of method is employed. One such proposed formula for the effective atomic number, Zeff, is as follows: Z eff = f 1 × ( Z 1 ) 2.94 + f
Effective atomic number (compounds and mixtures)
Effective_atomic_number_(compounds_and_mixtures)
Kind of proof calculus
schemata, which range over formulas rather than only over atomic propositions. The name of a rule is given to the right of its formula tree. For instance, the
Natural_deduction
Logical formula with NOT only on variables
negation normal form can increase the size of a formula only linearly: the number of occurrences of atomic formulas remains the same, the total number of occurrences
Negation_normal_form
Theory in computer science
}}\phi ]\end{aligned}}} where p {\displaystyle p} ranges over a set of atomic formulas. It is not necessary to use all connectives – for example, { ¬ , ∧
Computation_tree_logic
Chemical compound
Atomic carbon, systematically named carbon and λ0-methane, is a colourless gaseous inorganic chemical with the chemical formula C (also written [C]).
Atomic_carbon
Electrically neutral group of two or more atoms
can have the same atomic composition while being different molecules. The empirical formula is often the same as the molecular formula but not always. For
Molecule
given formula, unprimed variables all have the same type, while primed variables ( x ′ {\displaystyle x'} ) range over the next higher type. The atomic formulas
ST_type_theory
Relational model
define the set of atomic formulas A[S,type] with the following rules: if v and w in V, a in type(v) and b in type(w) then the formula v.a = w.b is in A[S
Tuple_relational_calculus
Approach to the foundations of mathematics
iterative hierarchy. Scott began with an axiom he declined to name: the atomic formula x∈y implies that y is a set. In symbols: ∀x,y∃a[x∈y→y=a]. His axiom
Scott–Potter_set_theory
1989 studio album by Steve Stevens
their Formula One coverage throughout the early 1990s The title track features a quote by William H. P. Blandy, who originally said "I am not an atomic playboy"
Atomic_Playboys
d-constructible set is the set of solutions to a quantifier-free, or atomic, formula with parameters in K. Like the theory of algebraically closed fields
Differentially_closed_field
Decidable theory of equality
atomic formula is x = y {\displaystyle x=y} where x , y {\displaystyle x,y} are (possibly identical) variables. Syntactically more complex formulas can
Theory_of_pure_equality
Axiomatic set theory devised by W.V.O. Quine
value because j is an automorphism. Make such an application to each atomic formula in ϕ 1 {\displaystyle \phi _{1}} in such a way that each variable x
New_Foundations
Platonic philosophical analogy
that uses axioms which are universal negations of conjunctions of atomic formulas" (C. Chambers, The Axiomatic Structure of Empirical Content) Archived
Analogy_of_the_divided_line
Project for an open source artificial intelligence framework
database, dubbed the AtomSpace, that holds "atoms" (that is, terms, atomic formulas, sentences and relationships) together with their "values" (valuations
OpenCog
ATOMIC FORMULA
ATOMIC FORMULA
Male
Hungarian
Pet form of Hungarian Tamás, TOMI means "twin."
Boy/Male
Tamil
Atom
Male
Japanese
(富) Japanese name TOMIO means "treasured man."
Boy/Male
Hindu
Atom
Boy/Male
Tamil
Atom
Girl/Female
Tamil
Atom
Boy/Male
Gujarati, Hindu, Indian
Topic; Subject
Boy/Male
Hindu
Atom
Boy/Male
Hindu
The soul
Boy/Male
Czechoslovakian
Girl/Female
Tamil
Anu Keerthi | அநà¯Â கிரதீ Â
Atom
Anu Keerthi | அநà¯Â கிரதீ Â
Boy/Male
Anglo Saxon
Horrible.
Boy/Male
Indian
An Atom's Warrior
Boy/Male
African, Australian, Finnish, Japanese
The People; Twin; Happy Child
Girl/Female
British, English, French, Italian
Lovely
Boy/Male
Hindu, Indian
Relating to the Soul
Girl/Female
Gujarati, Hindu, Indian, Marathi, Telugu
Sunrise; Comic
Girl/Female
Hebrew
Strong as an oak.
Girl/Female
Indian
Atom
Girl/Female
Hindu
Atom
ATOMIC FORMULA
ATOMIC FORMULA
Boy/Male
Hindu, Indian, Marathi
Goddess
Girl/Female
Muslim
Best coquetry
Girl/Female
Muslim
A narrator of Hadith
Girl/Female
Hindu
Wearing red-color attire
Girl/Female
American, British, English, Gaelic, Irish
Variants of the Name Casey; Alert; Watchful
Boy/Male
English American
Derived from a surname meaning cleric or clerk. Famous people: American actor Clark Gable;...
Boy/Male
Indian
Crown, Pavitra, Pure
Boy/Male
Greek
Avenger.
Girl/Female
Assamese, Bengali, Hindu, Indian, Kannada, Marathi, Sanskrit, Telugu
The Capital
Girl/Female
Arthurian Legend
Arthur's burial place.
ATOMIC FORMULA
ATOMIC FORMULA
ATOMIC FORMULA
ATOMIC FORMULA
ATOMIC FORMULA
a.
Unaccented; as, an atonic syllable.
a.
Alt. of Atomical
n.
An Adonic verse.
a.
Having two replaceable atoms or radicals.
a.
Containing two atoms.
a.
Characterized by atony, or want of vital energy; as, an atonic disease.
n.
An atom; a mite; a pigmy.
v. t.
To reduce to atoms, or to fine spray.
v. t.
To reduce to atoms.
n.
The doctrine of atoms. See Atomic philosophy, under Atomic.
a.
Produced without sexual union; as, agamic or unfertilized eggs.
a.
Pertaining to azote, or nitrogen; formed or consisting of azote; nitric; as, azotic gas; azotic acid.
n.
Nomic spelling.
a.
Pertaining to, or characterized by, aptotes; uninflected; as, aptotic languages.
a.
Relating to the etymon; as, an etymic word.
n.
A tonic element or letter; a vowel or a diphthong.
a.
Of or pertaining to atoms; relating to atomism.
n.
One who holds to the atomic philosophy or theory.
a.
Of or pertaining to atoms.
a.
Aeolian, 1; as, the Aeolic dialect; the Aeolic mode.