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logic and computer science, two-variable logic is the fragment of first-order logic where formulae can be written using only two different variables.
Two-variable_logic
Type of logical system
science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables. Rather than propositions
First-order_logic
In logic, a statement which is always true
propositional logic, where a tautology is defined as a propositional formula that is true under any possible Boolean valuation of its propositional variables. A
Tautology_(logic)
Variable that can either be true or false
mathematical logic, a propositional variable (also called a sentence letter, sentential variable, or sentential letter) is an input variable (that can either
Propositional_variable
System for reasoning about vagueness
Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept
Fuzzy_logic
Mathematical use of "for all" and "there exists"
In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal
Quantifier_(logic)
Symbol representing a mathematical object
arguments, sets and their elements, vectors, spaces, etc. In mathematical logic, a variable is a symbol that either represents an unspecified constant of the
Variable_(mathematics)
Mathematical logical term
are interesting in the context of logics such as two-variable logic with counting that restrict the number of variables in formulas. Also, generalized counting
Counting_quantification
Method of deriving conclusions
of deriving conclusions from premises. They are integral parts of formal logic, serving as the logical structure of valid arguments. If an argument with
Rule_of_inference
Assignment of meaning to the symbols of a formal language
All of these types of variables can be quantified. There are two kinds of interpretations commonly employed for higher-order logic. Full semantics require
Interpretation_(logic)
Form of logic that allows quantification over predicates
logic. Second-order logic is in turn extended by higher-order logic and type theory. First-order logic quantifies only variables that range over individuals
Second-order_logic
Family of formal knowledge representation
Logic Complexity Navigator for examples). Many DLs are decidable fragments of first-order logic (FOL) and are usually fragments of two-variable logic
Description_logic
Logical formalism using combinators instead of variables
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell
Combinatory_logic
Concept in logic
propositional logic, ψ is a substitution instance of φ if and only if ψ may be obtained from φ by substituting formulas for propositional variables in φ, replacing
Substitution_(logic)
Reasoning about equations with free variables
logic, algebraic logic is the reasoning obtained by manipulating equations with free variables. What is now usually called classical algebraic logic focuses
Algebraic_logic
Graphical method to simplify Boolean expressions
can even wrap beyond the edge of the chart for variable minimization. This is because each logic variable corresponds to each vertical column and horizontal
Karnaugh_map
System of formal deduction in logic
In logic, more specifically proof theory, a Hilbert system, sometimes called Hilbert calculus, Hilbert-style system, Hilbert-style proof system, Hilbert-style
Hilbert_system
System for representing and reasoning about time
In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example
Temporal_logic
Algebraic manipulation of "true" and "false"
mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth
Boolean_algebra
Variable that stores data about other variables or program structure
In logic, a metavariable (also metalinguistic variable or syntactical variable) is a symbol or symbol string which belongs to a metalanguage and stands
Metavariable
Branch of logic
Propositional logic is a branch of classical logic. It is also called statement logic, sentential calculus, propositional calculus, sentential logic, or sometimes
Propositional_logic
Syntactically correct logical formula
first-order logic. In those contexts, a formula is a string of symbols φ for which it makes sense to ask "is φ true?", once any free variables in φ have
Well-formed_formula
Romanian-German mathematical logician
scientist known for her work on formal verification, model checking, and two-variable logic. She is a researcher at the Laboratoire bordelais de recherche en
Anca_Muscholl
Overview of and topical guide to logic
Classical logic Computability logic Deontic logic Dependence logic Description logic Deviant logic Doxastic logic Epistemic logic First-order logic Formal
Outline_of_logic
Process in digital electronics and integrated circuit design
represent the required logical function by a diagram representing the logic variables and value of the function. By manipulating or inspecting a diagram
Logic_optimization
Logic gate implementing negation
In digital logic, an inverter or NOT gate is a logic gate which implements logical negation. It outputs a bit whose value is opposite of the input bit's
Inverter_(logic_gate)
Concept in mathematics or computer science
mathematical logic and computer science, a variable may be said to be either free or bound. Some older books use the terms real variable and apparent variable for
Free variables and bound variables
Free_variables_and_bound_variables
Argument whose conclusion must be true if its premises are
In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true
Validity_(logic)
Inference rule in logic, proof theory, and automated theorem proving
theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution rule acts
Resolution_(logic)
Mathematical table used in logic
gives definitions of each of the 6 possible 2-input logic gate functions of two Boolean variables P and Q: For binary operators, a condensed form of truth
Truth_table
Term that does not contain any variables
In mathematical logic, a ground term of a formal system is a term that does not contain any variables. Similarly, a ground formula is a formula that does
Ground_expression
System that manages the behavior of other systems
combinational logic, software logic, such as in a programmable logic controller, is used.[clarification needed] Fundamentally, there are two types of control
Control_system
Computer programming paradigm
features, like logical variables and backtracking. Today most Prolog implementations include one or more libraries for constraint logic programming. The difference
Constraint_programming
Concept in mathematical logic
In logic, a functionally complete set of logical connectives or Boolean operators is one that can be used to express all possible truth tables by combining
Functional_completeness
In mathematical logic, an atomic formula or its negation
proof theory (of classical logic), e.g. in conjunctive normal form and the method of resolution. Literals can be divided into two types: A positive literal
Literal_(mathematical_logic)
Logic programming with constraint satisfaction
Constraint logic programming is a form of constraint programming, in which logic programming is extended to include concepts from constraint satisfaction
Constraint_logic_programming
Programming paradigm based on formal logic
Logic programming is a programming, database, and knowledge representation paradigm based on formal logic. A logic program is a set of sentences in logical
Logic_programming
List of symbols used to express logical relations
contains logic symbols. Without proper rendering support, you may see question marks, boxes, or other symbols instead of logic symbols. In logic, a set
List_of_logic_symbols
Various systems of symbolic logic
logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by
Intuitionistic_logic
Approach to logic
In logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to
Term_logic
School of thought in philosophy of mathematics
is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Bertrand Russell and
Logicism
Logical incompatibility between two or more propositions
In traditional logic, a contradiction involves a proposition conflicting either with itself or established fact. It is often used as a tool to detect
Contradiction
Logic that allows infinitely long proofs
of free and bound variables apply in the same manner to infinite formulae. Just as in finitary logic, a formula all of whose variables are bound is referred
Infinitary_logic
3-volume treatise on mathematics, 1910–1913
logic and to minimise the number of primitive notions, axioms, and inference rules; to precisely express mathematical propositions in symbolic logic using
Principia_Mathematica
Form of second-order logic
In mathematical logic, monadic second-order logic (MSO) is the fragment of second-order logic where the second-order quantification is limited to quantification
Monadic_second-order_logic
Formal system of logic
First-order logic quantifies only variables that range over individuals; second-order logic, also quantifies over sets; third-order logic also quantifies
Higher-order_logic
System including an indeterminate value
three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which
Three-valued_logic
Family of digital circuits
PMOS or pMOS logic, from p-channel metal–oxide–semiconductor, is a family of digital circuits based on p-channel, enhancement mode metal–oxide–semiconductor
PMOS_logic
Mathematical theory
In mathematics and logic, plural quantification is the theory that an individual variable x may take on plural, as well as singular, values. As well as
Plural_quantification
Mathematical-logic system based on functions
are related to lambda calculus: Combinatory logic – A notation for mathematical logic without variables SKI combinator calculus – A computational system
Lambda_calculus
Basic notion of sameness in mathematics
of symbolic logic. There are generally two ways that equality is formalized in mathematics: through logic or through set theory. In logic, equality is
Equality_(mathematics)
Logical formulation of recursion
In mathematical logic, fixed-point logics are extensions of classical predicate logic that have been introduced to express recursion. Their development
Fixed-point_logic
Rules to verify computer program correctness
Hoare logic (also known as Floyd–Hoare logic or Hoare rules) is a formal system with a set of logical rules for reasoning rigorously about the correctness
Hoare_logic
Mathematical use of "for all"
In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any", "for all", "for every"
Universal_quantification
Impossible task in computing
extension is EXPTIME-complete (Theorem 2.24). The first-order logic fragment where the only variable names are x , y {\displaystyle x,y} is NEXPTIME-complete
Entscheidungsproblem
Problem of determining if a Boolean formula could be made true
automatic theorem proving. A propositional logic formula, also called Boolean expression, is built from variables, operators AND (conjunction, also denoted
Boolean satisfiability problem
Boolean_satisfiability_problem
Symbol connecting formulas in logic
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is an operator that combines or modifies
Logical_connective
Number of arguments required by a function
that accepts a variable number of arguments is called variadic. In logic and philosophy, predicates or relations accepting a variable number of arguments
Arity
Input where a function output does not matter
Incomplete opcode decoding Logic redundancy Undefined behaviour Undefined variable Uninitialized variable Four-valued logic Nine-valued logic Examples of encoding
Don't-care_term
Placeholder term used in computer science
Microsoft and Oracle. Metavariable (logic) xyzzy Alice and Bob John Doe Fnord Free variables and bound variables Gadget Lorem ipsum Nonce word Placeholder
Metasyntactic_variable
Logic theorem
In logic, the law of noncontradiction (LNC; also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction)
Law_of_noncontradiction
Term in logic
In logic and analytic philosophy, an atomic sentence is a type of declarative sentence which is either true or false (may also be referred to as a proposition
Atomic_sentence
Logical principle
In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is
Law_of_excluded_middle
Graphical language for PLC design
language for programmable logic controller design, that can describe the function between input variables and output variables. A function is described
Function_block_diagram
Whether a decision problem has an effective method to derive the answer
effectively determined. Zeroth-order logic (propositional logic) is decidable, whereas first-order and higher-order logic are not. A theory (set of sentences
Decidability_(logic)
Subfield of mathematics
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory
Mathematical_logic
Symbolic description of a mathematical object
texts outside of mathematical logic, for an individual expression it is not always possible to identify which variables are free and bound. For example
Expression_(mathematics)
Fundamental theorem in mathematical logic
theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic. The completeness theorem
Gödel's_completeness_theorem
Measure of algorithmic complexity
Springer. ISBN 978-0-387-33998-6. Yu, Manin (1977). A Course in Mathematical Logic. Springer-Verlag. ISBN 978-0-7204-2844-5. Sipser, Michael (1997). Introduction
Kolmogorov_complexity
Non-contradiction of a theory
In deductive logic, a consistent theory is one that does not lead to a logical contradiction. A theory T {\displaystyle T} is consistent if there is no
Consistency
Logical formulation of graph properties
can be used in these sentences. The first-order logic of graphs concerns sentences in which the variables and predicates concern individual vertices and
Logic_of_graphs
Formalization of the natural numbers
is just an equation between two terms. In this setting a term is a primitive recursive function of zero or more variables. Curry (1941) gave the first
Primitive recursive arithmetic
Primitive_recursive_arithmetic
Algebraization of first-order logic
In mathematical logic, predicate functor logic (PFL) is one of several ways to express first-order logic (also known as predicate logic) by purely algebraic
Predicate_functor_logic
Class of formal logics
Classical logic (or standard logic) or Frege–Russell logic is the intensively studied and most widely used class of deductive logic. Classical logic has had
Classical_logic
Attempt to persuade or to determine the truth of a conclusion
through the logical, the dialectical, and the rhetorical perspective. In logic, an argument is usually expressed not in natural language but in a symbolic
Argument
Statement that is taken to be true
well-established, that it is accepted without controversy or question. In modern logic, an axiom is a premise or starting point for reasoning. In mathematics,
Axiom
Mathematical function such that every output has at least one input
35. Goldblatt, Robert (2006) [1984]. Topoi, the Categorial Analysis of Logic (Revised ed.). Dover Publications. ISBN 978-0-486-45026-1. Retrieved 2009-11-25
Surjective_function
Components of a mathematical or logical formula
value of x. Besides in logic, terms play important roles in universal algebra, and rewriting systems. Given a set V of variable symbols, a set C of constant
Term_(logic)
Set of elements in any of some sets
org/10.1093/OED/1665274057 "Earliest Uses of Symbols of Set Theory and Logic". Maths History. Archived from the original on 2025-04-26. Retrieved 2025-04-10
Union_(set_theory)
Reasoning for mathematical statements
frequently used as an assumption for further mathematical work. Proofs employ logic expressed in mathematical symbols, along with natural language that usually
Mathematical_proof
Phenomenon resulting from the superposition of two waves
In physics, interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration
Wave_interference
Standard system of axiomatic set theory
{\displaystyle x} and y {\displaystyle y} be metavariables for any variables. These are the two ways to build atomic formulae (the simplest wffs): x = y {\displaystyle
Zermelo–Fraenkel_set_theory
Named container for a particular type of data
generally be accessed or changed at any time. In pure functional and logic languages, variables are bound to expressions and keep a single value during their
Variable (high-level programming language)
Variable_(high-level_programming_language)
Form of mathematical proof
that "the two sets overlap" is false for { 1 } {\textstyle \left\{1\right\}} and { 2 } {\textstyle \left\{2\right\}} . In second-order logic, one can write
Mathematical_induction
Mathematical set formed from two given sets
Drake, Set Theory: An Introduction to Large Cardinals, p. 24. Studies in Logic and the Foundations of Mathematics, vol. 76 (1978). ISBN 0-7204-2200-0.
Cartesian_product
Mathematical logic concept
In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent
Contraposition
Function that preserves distinctness
graphical approach for a real-valued function f {\displaystyle f} of a real variable x {\displaystyle x} is the horizontal line test. If every horizontal line
Injective_function
Diagram that shows all possible logical relations between a collection of sets
set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science. A Venn diagram uses simple
Venn_diagram
Bearer of truth values
determine the truth values of compound propositions. First-order logic extends propositional logic with additional devices to analyze the internal structure
Proposition
Study of correct reasoning
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical
Logic
aimed to express all of arithmetic in terms of logic. Frege's work laid the groundwork for much of modern logic and was highly influential, though it encountered
Mathematical_object
Variables that are measurable, whether directly or indirectly
In statistics, latent variables (from Latin: present participle of lateo 'lie hidden'[citation needed]) are variables that can only be inferred indirectly
Latent and observable variables
Latent_and_observable_variables
Model that describes the programmable interface of a computer processor
instructions have variable length, typically integral multiples of a byte or a halfword. Some, such as the ARM with Thumb-extension have mixed variable encoding
Instruction_set_architecture
Programming language for industrial controllers
Ladder logic was originally a written method to document the design and construction of relay racks as used in manufacturing and process control. Each
Ladder_logic
Mathematical model for deduction or proof systems
arithmetic. Early logic systems includes Indian logic of Pāṇini, syllogistic logic of Aristotle, propositional logic of Stoicism, and Chinese logic of Gongsun
Formal_system
Mathematical theory of data types
In mathematical logic, and theoretical computer science, type theory is the study of formal systems that classify expressions or mathematical objects
Type_theory
Look up Appendix:Glossary of logic in Wiktionary, the free dictionary. This is a glossary of logic. Logic is the study of the principles of valid reasoning
Glossary_of_logic
Probabilistic logic
approximation via pseudolikelihood. The class of Markov logic networks which use only two variables in any formula allows for polynomial time exact inference
Markov_logic_network
Relationship between programs and proofs
following table. Typed combinatory logic can be formulated using a similar syntax: let Γ be a finite collection of variables, annotated with their types. A
Curry–Howard_correspondence
Relationship where one statement follows from another
consequence (also entailment or logical implication) is a fundamental concept in logic which describes the relationship between statements that hold true when
Logical_consequence
TWO VARIABLE-LOGIC
TWO VARIABLE-LOGIC
Girl/Female
Tamil
Valuable
Male
Polish
Polish form of Latin Ivo, IWO means "yew tree."
Girl/Female
Armenian
Valuable.
Boy/Male
Welsh
gift from God'.
Male
Welsh
Welsh form of English Tom, TWM means "twin."
Boy/Male
Vietnamese
Valuable.
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Valuable
Boy/Male
Hindu, Indian
Valuable
Boy/Male
Anglo, British, English
Variable
Boy/Male
Spanish
God. Abbreviation of names like Mateo and Teodor.
Boy/Male
Arabic, Bengali, Hindu, Indian, Kannada, Marathi, Muslim, Telugu
Valuable
Biblical
according to variable songs or tunes,
Boy/Male
Hawaiian
Valuable.
Surname or Lastname
English
English : from the feminine personal name Mirabel, equated in medieval records with Latin mirabilis ‘marvellous’, ‘wonderful’ (in the sense ‘extraordinary’).
Girl/Female
Biblical
According to variable songs or tunes.
Girl/Female
Gujarati, Hindu, Indian
Valuable
Boy/Male
Arabic, Indian, Muslim
Valuable
Surname or Lastname
English
English : perhaps, as Reaney proposes, a variant of Tough.
Girl/Female
Indian
Valuable
Boy/Male
Hindi
Valuable.
TWO VARIABLE-LOGIC
TWO VARIABLE-LOGIC
Boy/Male
Hindu
Melody
Male
Arthurian
, (Sir) knight of the Round Table (the servant).
Girl/Female
Christian, French, German, Greek
Angel; A Messenger from God
Boy/Male
Muslim
Best friend
Surname or Lastname
English
English : variant of Pearce.
Boy/Male
American, Anglo, Australian, British, English
Valley Ford; From the Hall by the Ford
Male
Celtic
, Lord of Belinus; war-lord.
Girl/Female
Tamil
Prestha | பà¯à®°à¯‡à®¸à¯à®¤à®¾
Dearest
Girl/Female
Indian, Marathi
Desire
Boy/Male
Australian, Lebanese
Choreographer
TWO VARIABLE-LOGIC
TWO VARIABLE-LOGIC
TWO VARIABLE-LOGIC
TWO VARIABLE-LOGIC
TWO VARIABLE-LOGIC
a.
Worthy; estimable; deserving esteem; as, a valuable friend; a valuable companion.
n.
A shifting wind, or one that varies in force.
v. t.
To represent by parable.
adv.
In a variable manner.
a.
Liable to undergo a judicial examination; properly coming under the cognizance of a court; as, a cause may be triable before one court which is not triable in another.
n.
A symbol representing two units, as 2, II., or ii.
n.
Arable land; plow land.
n.
The sum of one and one; the number next greater than one, and next less than three; two units or objects.
a.
Arable; tillable.
a.
Friendly; kindly; sweet; gracious; as, an amiable temper or mood; amiable ideas.
n.
That which is variable; that which varies, or is subject to change.
a.
Having value or worth; possessing qualities which are useful and esteemed; precious; costly; as, a valuable horse; valuable land; a valuable cargo.
a.
Invariable.
a.
Having the capacity of varying or changing; capable of alternation in any manner; changeable; as, variable winds or seasons; a variable quantity.
n.
An invariable quantity; a constant.
n.
Those parts of the sea where a steady wind is not expected, especially the parts between the trade-wind belts.
n.
A quantity which may increase or decrease; a quantity which admits of an infinite number of values in the same expression; a variable quantity; as, in the equation x2 - y2 = R2, x and y are variables.
a.
Possessing sweetness of disposition; having sweetness of temper, kind-heartedness, etc., which causes one to be liked; as, an amiable woman.
a.
Liable to vary; too susceptible of change; mutable; fickle; unsteady; inconstant; as, the affections of men are variable; passions are variable.
a.
Subject to change; changeable; variable.