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Fragment of first-order logic
logic, the monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic (also called predicate calculus) in which
Monadic_predicate_calculus
Form of second-order logic
complexity theory Monadic predicate calculus Second-order logic Courcelle, Bruno; Engelfriet, Joost (2012-01-01). Graph Structure and Monadic Second-Order
Monadic_second-order_logic
Type of logical system
First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a type of formal system used in mathematics, philosophy
First-order_logic
Form of logic that allows quantification over predicates
sometimes called full second-order logic to distinguish it from the monadic version. Monadic second-order logic is particularly used in the context of Courcelle's
Second-order_logic
Number of arguments required by a function
Abraham Robinson follows Quine's usage. In philosophy, the adjective monadic is sometimes used to describe a one-place relation such as 'is square-shaped'
Arity
Syntactically correct logical formula
In mathematical logic, propositional logic, and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence
Well-formed_formula
Symbol representing a mathematical concept
only if Y = F(X). Many treatments of predicate logic don't allow functional predicates, only relational predicates. This is useful, for example, in the
Function_symbol
Paradox in set theory
following contradiction. Let w be the predicate: to be a predicate that cannot be predicated of itself. Can w be predicated of itself? From each answer its
Russell's_paradox
Topics referred to by the same term
a chemical valence Monadic, in theology, a religion or philosophy possessing a concept of a divine Monad Monadic predicate calculus, in logic Monad (disambiguation)
Monadic
Symbol representing a property or relation in logic
In logic, a predicate is a non-logical symbol that represents a property or a relation, though, formally, does not need to represent anything at all.
Predicate_(logic)
Logical connective AND
Logical graph Negation Operation Peano–Russell notation Propositional calculus "2.2: Conjunctions and Disjunctions". Mathematics LibreTexts. 2019-08-13
Logical_conjunction
Impossible task in computing
3.15), thus undecidable. The monadic predicate calculus is the fragment where each formula contains only 1-ary predicates and no function symbols. Its
Entscheidungsproblem
Sequence of words formed by specific rules
expressed in a formal language. A formal system (also called a logical calculus, or a logical system) consists of a formal language together with a deductive
Formal_language
Limitative results in mathematical logic
to replace "not provable" with "false" in a Gödel sentence because the predicate "Q is the Gödel number of a false formula" cannot be represented as a
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Mathematical set formed from two given sets
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Cartesian_product
All-encompassing set or class
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Universe_(mathematics)
Subfield of automated reasoning and mathematical logic
Begriffsschrift (1879) introduced both a complete propositional calculus and what is essentially modern predicate logic. His Foundations of Arithmetic, published in
Automated_theorem_proving
Infinite cardinal number
the infinity ( ∞ {\displaystyle \infty } ) commonly found in algebra and calculus, in that the alephs measure the sizes of sets, while infinity is commonly
Aleph_number
Function computable with bounded loops
primitive recursive in ψ. #C: A predicate P obtained by substituting functions χ1,..., χm for the respective variables of a predicate Q is primitive recursive
Primitive_recursive_function
Problem in computer science
Church published his proof of the undecidability of a problem in the lambda calculus. Turing's proof was published later, in January 1937. Since then, many
Halting_problem
Mathematical use of "for all"
It expresses that a predicate can be satisfied by every member of a domain of discourse. In other words, it is the predication of a property or relation
Universal_quantification
Branch of mathematical logic
these can give a complete and axiomatic formalization of propositional or predicate logic of either the classical or intuitionistic flavour, almost any modal
Proof_theory
Mathematical-logic system based on functions
In mathematical logic, the lambda calculus (also written as λ-calculus) is a formal system for expressing computation based on function abstraction and
Lambda_calculus
Infinite set that is not countable
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Uncountable_set
Non-contradiction of a theory
propositional calculus was proved by Paul Bernays in 1918[citation needed] and Emil Post in 1921, while the completeness of (first order) predicate calculus was
Consistency
Assignment of meaning to the symbols of a formal language
semantics. The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard ways of
Interpretation_(logic)
Reasoning about equations with free variables
obtained by matrix multiplication using Boolean arithmetic. An example of calculus of relations arises in erotetics, the theory of questions. In the universe
Algebraic_logic
Complexity class used to classify decision problems
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
NP_(complexity)
Statement that is taken to be true
schemata are also used in the predicate calculus, but additional logical axioms are needed to include a quantifier in the calculus. Axiom of equality. Let L
Axiom
System of formal deduction in logic
as follows: Postulates for the propostional calculus #1-8, Additional postulates for the predicate calculus #9-12, and Additional postulates for number
Hilbert_system
Formalization of the natural numbers
\varphi (S(x))} , deduce φ ( y ) {\displaystyle \varphi (y)} , for any predicate φ . {\displaystyle \varphi .} In first-order arithmetic, the only primitive
Primitive recursive arithmetic
Primitive_recursive_arithmetic
Fundamental theorem in mathematical logic
[citation needed] We first fix a deductive system of first-order predicate calculus, choosing any of the well-known equivalent systems. Gödel's original
Gödel's_completeness_theorem
Approach to logic
with the advent of new logic, remaining dominant until the advent of predicate logic in the late nineteenth century. However, even if eclipsed by newer
Term_logic
Mathematical model for deduction or proof systems
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Formal_system
Argument whose conclusion must be true if its premises are
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Validity_(logic)
Class of formal logics
Orman Quine believed that a formal system that allows quantification over predicates (higher-order logic) didn't meet the requirements to be a logic, saying
Classical_logic
Logical principle
"the law of excluded middle and related theorems of the propositional calculus". He proposed his "system Σ … and he concluded by mentioning several applications
Law_of_excluded_middle
Attempt to persuade or to determine the truth of a conclusion
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Argument
Algebraic manipulation of "true" and "false"
propositional calculus have an equivalent expression in Boolean algebra. Thus, Boolean logic is sometimes used to denote propositional calculus performed
Boolean_algebra
Study of the semantics, or interpretations, of formal and natural languages
introduced, and that made it impossible to perform the kind of subject–predicate analysis in Aristotle's logic. Term logic is an attempt to modernize Aristotle's
Semantics_(logic)
Term that does not contain any variables
particular, predicates cannot be ground terms). Roughly speaking, the Herbrand universe is the set of all ground terms. A ground predicate, ground atom
Ground_expression
Logical incompatibility between two or more propositions
outside the formula calculus. Therefore, the procedure mentioned in the text in effect offers an interpretation of the calculus, by supplying a model
Contradiction
Mathematical set containing no elements
or if Cantor merely used ≡ O {\displaystyle \equiv O} as an emptiness predicate. Zermelo accepted O {\displaystyle O} itself as a set, but considered
Empty_set
Formal system of logic
term "higher-order logic" is commonly used to mean higher-order simple predicate logic. Here, "simple" indicates that the underlying type theory is the
Higher-order_logic
Standard system of axiomatic set theory
common. The signature has a single predicate symbol, usually denoted ∈ {\displaystyle \in } , which is a predicate symbol of arity 2 (a binary relation
Zermelo–Fraenkel_set_theory
Rules used for constructing, or transforming the symbols and words of a language
an inconsistency. Truth-functional propositional logic and first-order predicate logic are semantically complete, but not syntactically complete (for example
Syntax_(logic)
Set of all things that may be the input of a mathematical function
Propositional calculus Propositional formula Truth tables Many-valued logic 3 finite ∞ Predicate First-order list Second-order Monadic Higher-order Fixed-point
Domain_of_a_function
Logical connective
propositional calculus Laws of Form Logical graph Logical equivalence Material implication (rule of inference) Peirce's law Propositional calculus Sole sufficient
Material_conditional
Propositional calculus Propositional formula Truth tables Many-valued logic 3 finite ∞ Predicate First-order list Second-order Monadic Higher-order Fixed-point
Mathematical_object
One-to-one correspondence
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Bijection
Computation model defining an abstract machine
or simply a universal machine). Another mathematical formalism, lambda calculus, with a similar "universal" nature was introduced by Alonzo Church. Church's
Turing_machine
Symbol representing a mathematical object
and Gottfried Wilhelm Leibniz independently developed the infinitesimal calculus, which essentially consists of studying how an infinitesimal variation
Variable_(mathematics)
System including an indeterminate value
which. Similarly, Stephen Cole Kleene used a third value to represent predicates that are "undecidable by [any] algorithms whether true or false" As with
Three-valued_logic
Mathematical function that can be computed by a program
proposed, the major ones being Turing machines, register machines, lambda calculus and general recursive functions. Although these four are of a very different
Computable_function
Method of deriving conclusions
analyzing how the internal structure of propositions, like names and predicates, influences reasoning. Other logical systems explore inferential patterns
Rule_of_inference
Target set of a mathematical function
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Codomain
Theory of truth in the philosophy of language
used in his incompleteness theorems. Roughly, this states that a truth-predicate satisfying Convention T for the sentences of a given language cannot be
Semantic_theory_of_truth
Mathematical logic concept
to the predicate of the inferred proposition, it is permissible that it could be the original subject or its contradictory, and the predicate term of
Contraposition
Symbolic description of a mathematical object
(contracted) within a term. One of the most common systems involves lambda calculus. A polynomial consists of variables and coefficients, that involve only
Expression_(mathematics)
Mathematical set that can be enumerated
141. ISBN 978-0-8247-7915-3. Apostol, Tom M. (June 1969), Multi-Variable Calculus and Linear Algebra with Applications, vol. 2 (2nd ed.), New York: John
Countable_set
Logical operation
\neg \exists xP(x)\equiv \forall x\neg P(x)} ). For example, with the predicate P as "x is mortal" and the domain of x as the collection of all humans
Negation
Branch of logic
predicate calculus]. Kibernetika. 5 (2): 17–27. Also available as;"Range and degree of realizability of formulas in the restricted predicate calculus"
Finite_model_theory
Set that is not a finite set
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Infinite_set
Logic theorem
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Law_of_noncontradiction
Proof in set theory
a bijection between their underlying sets, Cantor also defines binary predicate of cardinalities | S | {\displaystyle |S|} and | T | {\displaystyle |T|}
Cantor's_diagonal_argument
Term in logic and deductive reasoning
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Soundness
Collection of sets in mathematics that can be defined based on a property of its members
{\displaystyle \phi (x)} holds; thus, the class can be described as the set of all predicates equivalent to ϕ {\displaystyle \phi } (which includes ϕ {\displaystyle
Class_(set_theory)
In logic, a statement which is always true
unsatisfiable). The definition of tautology can be extended to sentences in predicate logic, which may contain quantifiers—a feature absent from sentences of
Tautology_(logic)
Reasoning for mathematical statements
Propositional calculus Propositional formula Truth tables Many-valued logic 3 finite ∞ Predicate First-order list Second-order Monadic Higher-order Fixed-point
Mathematical_proof
Obsolete theories in natural history and natural philosophy
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
List of superseded scientific theories
List_of_superseded_scientific_theories
Function that preserves distinctness
other methods of proving that a function is injective. For example, in calculus if f {\displaystyle f} is a differentiable function defined on some interval
Injective_function
Proposition in mathematical logic
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Continuum_hypothesis
Value indicating the relation of a proposition to truth
algebras, compared to Boolean algebra semantics of classical propositional calculus. Philosophy portal Psychology portal Bayesian probability Circular reasoning
Truth_value
Type of logical argument that applies deductive reasoning
some academic contexts, syllogism has been superseded by first-order predicate logic following the work of Gottlob Frege, in particular his Begriffsschrift
Syllogism
Hilbert-style deductive systems for propositional logics. Classical propositional calculus is the standard propositional logic. Its intended semantics is bivalent
List of axiomatic systems in logic
List_of_axiomatic_systems_in_logic
Logic concept
In formal theories of truth, a truth predicate is a fundamental concept based on the sentences of a formal language as interpreted logically. That is
Truth_predicate
Variable that can either be true or false
as x and y attached to predicate letters such as Px and xRy, having instead individual constants a, b, ... attached to predicate letters are propositional
Propositional_variable
Set of elements common to all of some sets
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Intersection_(set_theory)
Mathematical function such that every output has at least one input
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Surjective_function
Symbol connecting formulas in logic
topics Logical conjunction Logical constant Modal operator Propositional calculus Term logic Tetralemma Truth function Truth table Truth values Chao, C.
Logical_connective
Mathematical set containing all objects
{\displaystyle A} , with φ ( x ) {\displaystyle \varphi (x)} defined as the predicate x ∉ x {\displaystyle x\notin x} , it would state the existence of Russell's
Universal_set
Collection of mathematical objects
mathematical induction, which is called transfinite induction. Given a property (predicate) P ( n ) {\displaystyle P(n)} depending on a natural number, mathematical
Set_(mathematics)
Characteristic of some logical systems
an inconsistency. Truth-functional propositional logic and first-order predicate logic are semantically complete, but not syntactically complete (for example
Completeness_(logic)
Set theory concept
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Von_Neumann_universe
Finite collection of distinct objects
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Finite_set
Mathematical set of all subsets of a set
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Power_set
Set whose elements all belong to another set
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Subset
Size of a possibly infinite set
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Cardinal_number
Function, homomorphism, or morphism
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Map_(mathematics)
Any one of the distinct objects that make up a set in set theory
predication of x called membership that is equivalent to the statement ‘x is a member of y if and only if, for all objects x, the general predication
Element_of_a_set
Type of logic diagram
simple proposition containing two terms, subject (S) and predicate (P), in which the predicate is either asserted or denied of the subject. Every categorical
Square_of_opposition
Set theory concept
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Large_cardinal
Pair of mathematical objects
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Ordered_pair
This can be seen in the development of analysis from reexamination of the calculus of Leibniz and Newton. They argue further that finished mathematics is
Philosophy_of_mathematics
Property that assigns truth values to k-tuples of individuals
statistics, it is common to refer to a Boolean-valued function as an n-ary predicate. From the more abstract viewpoint of formal logic and model theory, the
Finitary_relation
Mathematical use of "there exists"
In predicate logic, an existential quantification is a type of quantifier which asserts the existence of an object with a given property. It is usually
Existential_quantification
Structure of a formal language
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Formal_grammar
Theorem that arithmetical truth cannot be defined in arithmetic
metalanguage capable of expressing the semantics of some object language (e.g. a predicate is definable in Zermelo–Fraenkel set theory for whether formulae in the
Tarski's undefinability theorem
Tarski's_undefinability_theorem
In mathematics, a statement that has been proven
in a completely symbolic form (e.g., as propositions in propositional calculus), they are often expressed informally in a natural language such as English
Theorem
Theorem in set theory
Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus Set theory Set hereditary Class (Ur-)Element Ordinal number
Schröder–Bernstein_theorem
MONADIC PREDICATE-CALCULUS
MONADIC PREDICATE-CALCULUS
Boy/Male
Hindu, Indian, Tamil
Sun; Moon; Dedicate
Girl/Female
Indian
Dedicate, Presenting
Girl/Female
Tamil
Arpitha | à®…à®°à¯à®ªà®¿à®¤à®¾
Dedicate, Presenting
Arpitha | à®…à®°à¯à®ªà®¿à®¤à®¾
Boy/Male
American, Australian, British, English, Latin
Servant of the Priory; Monastic Leader
Boy/Male
Arabic, Muslim
Fighter; Defender
Boy/Male
Arabic, Muslim
A Scholar of Baghdad who Wrote Books on the Quran and Related Subjects; Abu Al-hasan; Had this Name
Boy/Male
Bengali, Indian
Dear One
Boy/Male
Armenian, Australian
Nomadic Cart
Girl/Female
Arabic
Dark Night; Dedicate
Girl/Female
Tamil
Arpita | à®…à®°à¯à®ªà®¿à®¤à®¾
Dedicate, Presenting
Arpita | à®…à®°à¯à®ªà®¿à®¤à®¾
Biblical
respiration; conversion; taking captive;man sitting in Nob;dweller on the mount, he that predicts;
Boy/Male
Hindu
Girl/Female
Bengali, Indian
Dedicate
Girl/Female
American, Australian, British, Christian, English
Wanderer; A Bohemian Traveler; Fortune Telling; Nomadic
Girl/Female
Indian
Dedicate, Presenting
Girl/Female
Indian
Name of Godeess Durga
Girl/Female
Bengali, Indian
Dedicate
Girl/Female
Hindu, Indian, Malayalam, Marathi, Tamil, Telugu
Devotee of God; Daughter of God; Dedicated; Tribute; To Dedicate Something
Boy/Male
Christian, Hindu, Indian
Special Smile; Sweet Little Attitude
Girl/Female
Indian
One who Willingly Dedicate Herself
MONADIC PREDICATE-CALCULUS
MONADIC PREDICATE-CALCULUS
Female
English
Variant spelling of English Sharleen, SHARLENE means "man."
Girl/Female
Swedish American
Pure.
Boy/Male
Hindu
Boy/Male
British, English
Path
Boy/Male
Tamil
Jayaketan | ஜயாகேதந
Symbol of victory
Boy/Male
Gaelic Irish
Ardent.
Boy/Male
Hindu, Indian
Poison
Male
Iranian/Persian
(بابک) Variant spelling of Persian Babak, PAPAK means "little father."
Boy/Male
Indian, Marathi
Brightness
Boy/Male
American, Australian, British, Chinese, English, French, German, Greek, Irish, Swedish, Swiss
To Tame; Subdues; Spirit; Subdue; Variant of Damon One who Tames
MONADIC PREDICATE-CALCULUS
MONADIC PREDICATE-CALCULUS
MONADIC PREDICATE-CALCULUS
MONADIC PREDICATE-CALCULUS
MONADIC PREDICATE-CALCULUS
a.
Of or pertaining to Moses, the leader of the Israelites, or established through his agency; as, the Mosaic law, rites, or institutions.
a.
Pertaining to, or obtained from, vanadium; containing vanadium; specifically distinguished those compounds in which vanadium has a relatively higher valence as contrasted with the vanadious compounds; as, vanadic oxide.
n.
One who predicates, affirms, or proclaims; specifically, a preaching friar; a Dominican.
v. t.
To assert to belong to something; to affirm (one thing of another); as, to predicate whiteness of snow.
a.
Capable of being predicated or affirmed of something; affirmable; attributable.
a.
Of or pertaining to nomads, or their way of life; wandering; moving from place to place for subsistence; as, a nomadic tribe.
v. t.
To set apart and consecrate, as to a divinity, or for sacred uses; to devote formally and solemnly; as, to dedicate vessels, treasures, a temple, or a church, to a religious use.
a.
Predicated.
a.
Of, pertaining to, or like, a monad, in any of its senses. See Monad, n.
n.
A Sotadic verse or poem.
v. t.
To tell or declare beforehand; to foretell; to prophesy; to presage; as, to predict misfortune; to predict the return of a comet.
v. t.
To root out; to destroy utterly; to extirpate; as, to eradicate diseases, or errors.
imp. & p. p.
of Predict
imp. & p. p.
of Predicate
a.
Expressing affirmation or predication; affirming; predicating, as, a predicative term.
a.
Alt. of Monadical
p. pr. & vb. n.
of Predicate
v. t.
That which is affirmed or denied of the subject. In these propositions, "Paper is white," "Ink is not white," whiteness is the predicate affirmed of paper and denied of ink.
n.
A picture or design made in mosaic; an article decorated in mosaic.
n.
A surface decoration made by inlaying in patterns small pieces of variously colored glass, stone, or other material; -- called also mosaic work.