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Rules used for constructing, or transforming the symbols and words of a language
In logic, syntax is an arrangement of well-structured entities in the formal languages or formal systems that express something. Syntax is concerned with
Syntax_(logic)
System responsible for combining morphemes into complex structures
offer unique perspectives on syntax, reflecting its complexity and centrality to understanding human language. In logic, syntax is the study of how strings
Syntax
Overview of and topical guide to logic
Syntax (logic) Truth Truth value Validity Affine logic Alethic logic Aristotelian logic Boolean logic Buddhist logic Bunched logic Categorical logic Classical
Outline_of_logic
Study of the semantics, or interpretations, of formal and natural languages
semantics Formal semantics (natural language) Semantics (computer science) Syntax (logic) Jaakko Hintikka (2007), Socratic Epistemology: Explorations of Knowledge-Seeking
Semantics_(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
Framework for a family of logic languages
the Standard by their translation to the abstract syntax and semantics of Common Logic. Many other logic-based languages could also be defined as subsets
Common_Logic
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name
List_of_logic_symbols
Topics referred to by the same term
following: Syntax (journal), a Blackwell Publishing journal devoted to natural language syntax. Syntax (logic) Syntax (programming languages) Syntax (band)
Syntax_(disambiguation)
Formal semantics of logic programming languages
This article describes the syntax and semantics of the purely declarative subset of these languages. Confusingly, the name "logic programming" also refers
Syntax and semantics of logic programming
Syntax_and_semantics_of_logic_programming
Token in a mathematical or logical formula
A formal symbol is a fundamental concept in logic, tokens of which may be marks or a configuration of marks which form a particular pattern.[citation
Symbol_(formal)
Bug in a program that causes incorrect operation, but not termination
recognized as such. Logic errors occur in both compiled and interpreted languages. Unlike a program with a syntax error, a program with a logic error is a valid
Logic_error
Formal systems of logic that significantly differ from standard logical systems
Non-classical logics (sometimes alternative logics) are formal systems that differ in a significant way from standard logical systems such as propositional
Non-classical_logic
Form of reasoning
invalid deductive reasoning is a form of deductive reasoning. Deductive logic studies under what conditions an argument is valid. According to the semantic
Deductive_reasoning
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
American company
LSI's own. In November 2000, LSI Logic acquired Syntax Systems, and in August 2001 the groups merged to become LSI Logic Storage Systems, and later Engenio
LSI_Logic
Relationship in which 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
Theories in architecture and urban planning
Space syntax is a set of theories and techniques for the analysis of spatial configurations. It was conceived by Bill Hillier, Julienne Hanson, and colleagues
Space_syntax
Branch of logic using category theory to study mathematical structures
to theoretical computer science. In broad terms, categorical logic represents both syntax and semantics by a category, and an interpretation by a functor
Categorical_logic
units of knowledge representation in Arden syntax are Medical Logic Modules (MLMs), which contain the logic necessary to make a single medical decision
Arden_syntax
Establishment of a theorem using inference from the axioms
In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (known as well-formed formulas when relating to formal language)
Formal_proof
Family of formal knowledge representation
fact. Like first-order logic (FOL), a syntax defines which collections of symbols are legal expressions in a description logic, and semantics determine
Description_logic
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
Academic discipline
Logic in computer science covers the overlap between the field of logic and that of computer science. The topic can essentially be divided into three
Logic_in_computer_science
Text for clarification; one of four rhetorical modes
(natural language) Inference Philosophy of logic Proof Semantics of logic Syntax Logics Classical Informal Critical thinking Reason Mathematical Non-classical
Description
Symbol with a fixed meaning in logic
In logic, a logical constant or constant symbol of a language L {\displaystyle {\mathcal {L}}} is a symbol that has the same semantic value under every
Logical_constant
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
Set of rules defining correctly structured C++ program
The syntax of C++ is the set of rules defining how a C++ program is written and compiled. C++ syntax is largely inherited from the syntax of its ancestor
C++_syntax
Sequence of words formed by specific rules
limited computational power. In logic and the foundations of mathematics, formal languages are used to represent the syntax of axiomatic systems, and mathematical
Formal_language
One or more words used to refer to something
Stanford Encyclopedia of Philosophy (SEP), a philosophical dissertation on the syntax and semantics of names Pilcher, Jane (2017). "Names, Bodies and Identities"
Name
System for representing and reasoning about time
the first positional logic that, as a framework, was used later for Łoś's inventions in epistemic logic. The logic itself has syntax very different than
Temporal_logic
In logic, a statement which is always true
In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula that is true regardless of the interpretation of its component terms
Tautology_(logic)
Inference seeking the simplest and most likely explanation
first-order logic, without requiring any preliminary reduction of formulae into normal forms. These methods have also been extended to modal logic. Abductive
Abductive_reasoning
One of five systems of modal logic
In logic and philosophy, S5 is one of five systems of modal logic proposed by Clarence Irving Lewis and Cooper Harold Langford in their 1932 book Symbolic
S5_(modal_logic)
Type of formal logic
Modal logic is a kind of logic used to represent statements about necessity and possibility. In philosophy and related fields it is used as a tool for
Modal_logic
Subfield of mathematics
logics such as intuitionistic logic. First-order logic is a particular formal system of logic. Its syntax involves only finite expressions as well-formed
Mathematical_logic
Programming paradigm based on formal logic
constraints on the order in which operations are performed. Logic programming, with its current syntax of facts and rules, can be traced back to debates in the
Logic_programming
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
System of resource-aware logic
"LINEAR LOGIC: ITS SYNTAX AND SEMANTICS" (PDF). Linear Logic: Its Syntax and Semantics: 42. Troelstra, A. S. (Anne Sjerp) (1992). Lectures on linear logic. Internet
Linear_logic
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)
Mathematical use of "for all" and "there exists"
Philosophy: Shapiro, Stewart (2000). "Classical Logic" (Covers syntax, model theory, and metatheory for first order logic in the natural deduction style.) Westerståhl
Quantifier_(logic)
Family of knowledge representation languages
supports a variety of syntaxes. It is useful to distinguish high level syntaxes aimed at specification from exchange syntaxes more suitable for general
Web_Ontology_Language
Rule defining the correct structure of expressions in formal grammar
Peter (2005). Fundamentals of Mathematical Logic. A K Peters/CRC Press. Retrieved 2022-11-17. Specifying the syntax of any language L follows a common pattern
Formation_rule
System for reasoning about vagueness
Fuzzy logic with evaluated syntax (sometimes also called Pavelka's logic), denoted by EVŁ, is a further generalization of mathematical fuzzy logic. While
Fuzzy_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
Variable_(mathematics)
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
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
Game of symbolic logic
WFF 'N PROOF is a game of modern logic, developed to teach principles of symbolic logic. It was developed by Layman E. Allen in 1962 a former professor
WFF_'N_PROOF
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
The history of logic deals with the study of the development of the science of valid inference (logic). Formal logics developed in ancient times in India
History_of_logic
Placeholder term used in computer science
documentation from companies such as Microsoft and Oracle. Metavariable (logic) xyzzy Alice and Bob John Doe Fnord Free variables and bound variables Gadget
Metasyntactic_variable
German-American philosopher (1891–1970)
that its signs are governed by the rules of deductive logic. Moreover, the theory of logical syntax expounds a method with which one can talk about a language:
Rudolf_Carnap
Number measuring the chance an event occurs
meaning. These formal terms are manipulated by the rules of mathematics and logic, and any results are interpreted or translated back into the problem domain
Probability
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
Ontology language
languages, and offers a declarative, compact and simple syntax, and the well-defined semantics of a logic programming language. Features include, among others
F-logic
Form of logic that allows quantification over predicates
(n))} The syntax of second-order logic prescribes which expressions are well formed formulas. In addition to the syntax of first-order logic, second-order
Second-order_logic
Study of the scope and nature of logic
logic is based on whether the criteria of valid inference and logical truth are specified in terms of syntax or semantics. Different types of logic are
Philosophy_of_logic
Formal study of linguistic meaning
Languages at the Semantics/Syntax Interface" (PDF). 50 years of Linguistics at MIT. Retrieved 2025-06-21. Cable, Seth (2019). "From Logic To Montague Grammar
Formal semantics (natural language)
Formal_semantics_(natural_language)
Branch of logic
Informal logic encompasses the principles of logic and logical thought outside of a formal setting (characterized by the usage of particular statements)
Informal_logic
Form of text that defines C code
C syntax is the form that text must have in order to be C programming language code. The language syntax rules are designed to allow for code that is terse
C_syntax
Analysis of facts to form a judgment
beliefs and actions. Critical thinking allows people to deduct with more logic, to process sophisticated information and look at various sides of an issue
Critical_thinking
mathematical logic, Gödel logics, sometimes referred to as Dummett logics or Gödel–Dummett logics, is a family of finite- or infinite-valued logics in which
Gödel_logic
Logically self-contradictory statement
interdependent elements" leading to a lasting "unity of opposites". In logic, many paradoxes exist that are invalid arguments, yet are nevertheless valuable
Paradox
Language for controlling a computer
language Scripting language Semantics (logic) Software engineering and List of software engineering topics Syntax (logic) Computer programming portal Information
Programming_language
1956 computer program written by Allen Newell, Herbert A. Simon and Cliff Shaw
Logic Theorist is a computer program completed in 1956 by Allen Newell, Herbert A. Simon, and Cliff Shaw. It was the first program deliberately engineered
Logic_Theorist
Two types of knowledge, justification, or argument
priori justification is predominant are, for example, mathematics and formal logic; by contrast, most of the sciences generally involve a posteriori justification
A_priori_and_a_posteriori
Use of logic to perform or reason about computation
Computational logic is the use of logic to perform or reason about computation. It bears a similar relationship to computer science and engineering as
Computational_logic
Math theory of strings of symbols
theory, also called string theory, character-string theory, or theoretical syntax, studies character strings over finite alphabets of characters, signs, symbols
Concatenation_theory
Type of logical system
first-order logic (FOL), also called predicate logic, predicate calculus, or quantificational logic, is a type of formal system. First-order logic uses quantified
First-order_logic
Application of logical methods to philosophical problems
Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often
Philosophical_logic
abstract syntax (abbreviated HOAS) is a technique for the representation of abstract syntax trees for languages with variable binders. An abstract syntax is
Higher-order_abstract_syntax
Concept of philosophy and logic used to express modal claims
used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic. Their metaphysical status
Possible_world
Logic formula
In propositional logic, a propositional formula is a type of syntactic formula which is well formed. If the values of all variables in a propositional
Propositional_formula
Method of logical reasoning
Schaum's Outlines, Logic, Second Edition. John Nolt, Dennis Rohatyn, Archille Varzi. McGraw-Hill, 1998. p. 223 Schaum's Outlines, Logic, p. 230 Johnson,
Inductive_reasoning
Tree in formal language theory
computational linguistics; in theoretical syntax, the term syntax tree is more common. Concrete syntax trees reflect the syntax of the input language, making them
Parse_tree
Various systems of symbolic logic
verified using Rocq. The syntax of formulas of intuitionistic logic is similar to propositional logic or first-order logic. However, intuitionistic connectives
Intuitionistic_logic
Statement that attaches a meaning to a term
logic definitions are usually introduced using extension by definition (so using a metalogic). On the other hand, lambda-calculi are a kind of logic where
Definition
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
Relationship between objects
In logic, a reference is a relationship between objects in which one object designates, or acts as a means by which to connect to or link to, another
Reference
Field of philosophical logic
Deontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a
Deontic_logic
Structure of a formal language
languages have the meanings of their strings structured according to their syntax—a practice known as compositional semantics. In these cases, the first step
Formal_grammar
Study of the properties of logical systems
Metalogic is the metatheory of logic. Whereas logic studies how logical systems can be used to construct valid and sound arguments, metalogic studies the
Metalogic
Set of rules defining correctly structured programs
The syntax of the SQL programming language is defined and maintained by ISO/IEC SC 32 as part of ISO/IEC 9075. This standard is not freely available. Despite
SQL_syntax
Terms to describe a conditional relationship between two statements
In logic and mathematics, necessity and sufficiency are concepts used to denote a conditional or implicational relationship between two statements. For
Necessity_and_sufficiency
Branch of mathematics that studies sets
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any
Set_theory
Term in philosophy
between two conclusions, both of which seem justified. It is a term used in logic and epistemology, particularly in the philosophy of Immanuel Kant. Antinomy
Antinomy
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
List of statements that appear to contradict themselves
a surprise. The surprise examination and Bottle Imp paradox use similar logic. These paradoxes, insolubilia (insolubles), have in common a contradiction
List_of_paradoxes
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
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
Symbol connecting formulas in logic
combine or negate arithmetic expressions. For instance, in the syntax of propositional logic, the binary connective ∨ {\displaystyle \lor } (meaning "or")
Logical_connective
Algebraic manipulation of "true" and "false"
topics Logic design Principia Mathematica Three-valued logic Łukasiewicz logic Vector logic Not all search engines support the same query syntax. Additionally
Boolean_algebra
Assignment of meaning to the symbols of a formal language
formal semantics. The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard
Interpretation_(logic)
Formal semantics for non-classical logic systems
the model theory of such logics was almost non-existent before Kripke (algebraic semantics existed, but were considered 'syntax in disguise').[citation
Kripke_semantics
Logic founded on unproven premises
In classical rhetoric and logic, begging the question or assuming the conclusion (Latin: petitio principii) is an informal fallacy that occurs when an
Begging_the_question
Precisely specified semantic version of a statement
In logic, the logical form of a statement is a precisely specified semantic version of that statement in a formal system. Informally, the logical form
Logical_form
Language to express rules and logic with semantic web
and F-Logic ontologies. [5] Archived 6 January 2006 at the Wayback Machine RacerPro, supports the processing of rules in a SWRL-based syntax by translating
Semantic_Web_Rule_Language
Steps in reasoning
or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular evidence to a universal conclusion
Inference
Logic used to describe behaviours of concurrent systems
Temporal logic of actions (TLA) is a logic developed by Leslie Lamport, which combines temporal logic with a logic of actions. It is used to describe
Temporal_logic_of_actions
Mathematics notation with operators preceding operands
notation is used as a syntax for mathematical expressions by programming language interpreters it is readily parsed into abstract syntax trees and can, in
Polish_notation
; Plotkin, G.; Turi, D. (1999). "Abstract syntax and variable binding". Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158). pp
Abstract_syntax
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