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Assignment of meaning to the symbols of a formal language
An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer
Interpretation_(logic)
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
Area of physical and philosophical debate
1016/1355-2198(95)00019-4. Rudolf Carnap, 1939, "The interpretation of physics", in Foundations of Logic and Mathematics of the International Encyclopedia
Interpretations of quantum mechanics
Interpretations_of_quantum_mechanics
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
Assigning meanings to concepts, symbols, objects
constitutional documents and legislation (see statutory interpretation). In logic, an interpretation is an assignment of meaning to the symbols of a language
Interpretation_(philosophy)
Symbol representing a property or relation in logic
depending on the interpretation given to them. While first-order logic only includes predicates that apply to individual objects, other logics may allow predicates
Predicate_(logic)
Interpretation of intuitionistic logic
mathematical logic, the Brouwer–Heyting–Kolmogorov interpretation, or BHK interpretation, is an explanation of the meaning of proof in intuitionistic logic, proposed
Brouwer–Heyting–Kolmogorov interpretation
Brouwer–Heyting–Kolmogorov_interpretation
System of resource-aware logic
of simple denotational models, linear logic may be seen as refining the interpretation of intuitionistic logic by replacing cartesian (closed) categories
Linear_logic
Using inconsistent arguments
peculiarities of the logic of the dream-work can be seen taking place almost from the beginning of The Interpretation of Dreams. [...] This "kettle logic," as Derrida
Kettle_logic
Topics referred to by the same term
directly Interpretation function, in mathematical logic a function that assigns functions and relations to the symbols of a signature Interpretations of quantum
Interpretation
Study of the semantics, or interpretations, of formal and natural languages
In logic, the semantics or formal semantics is the study of the meaning and interpretation of formal languages, formal systems, and (idealizations of)
Semantics_(logic)
Mapping of mathematical formulas to a particular meaning
as "interpretations", whereas the term "interpretation" generally has a different (although related) meaning in model theory; see interpretation (model
Structure (mathematical logic)
Structure_(mathematical_logic)
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
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)
Various systems of symbolic logic
classical logic. The standard explanation of intuitionistic logic is the BHK interpretation. Several systems of semantics for intuitionistic logic have been
Intuitionistic_logic
Relationship between programs and proofs
propositions- or formulae-as-types interpretation. It is a generalization of a syntactic analogy between systems of formal logic and computational calculi that
Curry–Howard_correspondence
the International Financial Reporting Standards (IFRSs) and official interpretations, as set out by the IFRS Foundation. It includes accounting standards
List of International Financial Reporting Standards
List_of_International_Financial_Reporting_Standards
Argument whose conclusion must be true if its premises are
truth, in some systems of logic like in modal logic if the statement is true in all interpretations. In Aristotelian logic statements are not valid per
Validity_(logic)
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
Rules used for constructing, or transforming the symbols and words of a language
in a programming language. As in mathematical logic, it is independent of semantics and interpretation. A symbol is an idea, abstraction or concept, tokens
Syntax_(logic)
Simple logical interpretation
In mathematical logic, a Herbrand interpretation is an interpretation in which all constants and function symbols are assigned very simple meanings. Specifically
Herbrand_interpretation
Arithmetical concept
In proof theory, the Dialectica interpretation is a proof interpretation of intuitionistic logic (Heyting arithmetic) into a finite type extension of primitive
Dialectica_interpretation
Theoretical framework
the knowable, and the believed and the believable. In logic, a model is a type of interpretation under which a particular statement is true. Logical models
Conceptual_model
Branch of logic using category theory to study mathematical structures
science. In broad terms, categorical logic represents both syntax and semantics by a category, and an interpretation by a functor. The categorical framework
Categorical_logic
Mathematical use of "for all" and "there exists"
In mathematical logic, quantifiers are formal counterparts of natural-language adjectives like all, some, most, few, etc. which indicate the number of
Quantifier_(logic)
Works by Aristotle on logic
well-structured system. Indeed, parts of them seem to be a scheme of a lecture on logic. The arrangement of the works was made by Andronicus of Rhodes around 40
Organon
Logical connective OR
In logic, disjunction (also known as logical disjunction, logical or, logical addition, or inclusive disjunction) is a logical connective typically notated
Logical_disjunction
Syntactically correct logical formula
of an interpretation. Two key uses of formulas are in propositional logic and predicate logic. A key use of formulas is in propositional logic and predicate
Well-formed_formula
Study of the properties of logical systems
formal systems, and their interpretations. The study of interpretation of formal systems is the branch of mathematical logic that is known as model theory
Metalogic
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
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
Concept in mathematics
Conservative extension Interpretation (logic) Interpretation (model theory) Interpretability logic Japaridze, G., and De Jongh, D. (1998) "The logic of provability"
Interpretability
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
Existence of values making formula true
In mathematical logic, a formula is satisfiable if it is true under some assignment of values to its variables. For example, the formula x + 3 = y {\displaystyle
Satisfiability
Family of modal logics that extend provability logic
Interpretability logics comprise a family of modal logics that extend provability logic to describe interpretability or various related metamathematical
Interpretability_logic
Set of sentences in a formal language
In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios a deductive system is first
Theory_(mathematical_logic)
Interpretation of quantum mechanics
The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wave function is objectively real, and
Many-worlds_interpretation
Branch of logic
"Informal logic designates that branch of logic whose task is to develop non-formal2 standards, criteria, procedures for the analysis, interpretation, evaluation
Informal_logic
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
Form of logic that allows quantification over predicates
In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic
Second-order_logic
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
Programming paradigm
into a set of probabilistic facts and a logic program. It defines a probability distribution on interpretations of the Herbrand universe of the program
Probabilistic logic programming
Probabilistic_logic_programming
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
(mathematical logic) Interpretation (logic) Substructure (mathematics) Elementary substructure Skolem hull Non-standard model Atomic model (mathematical logic) Prime
List of mathematical logic topics
List_of_mathematical_logic_topics
logic is to be interpreted in a computational way. Probably the first formal treatment of logic for computability is the realizability interpretation
Logics_for_computability
In mathematical logic, a well-formed formula with no free variables
In mathematical logic, a sentence (or closed formula) of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can
Sentence_(mathematical_logic)
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
Mathematical model for deduction or proof systems
first order logic) together with additional non-logical axioms. According to model theory, a logical system may be given interpretations which describe
Formal_system
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
formulas with those variables. In first-order logic and higher-order logics, a structure, (the interpretation) and the corresponding assignment of a truth
Valuation_(logic)
Interpretation of quantum mechanics
The Copenhagen interpretation is a collection of views about the meaning of quantum mechanics, stemming from the work of Niels Bohr, Werner Heisenberg
Copenhagen_interpretation
Symbol connecting formulas in logic
classical logic, these connectives are interpreted as truth functions, though they receive a variety of alternative interpretations in nonclassical logics. Their
Logical_connective
Concept in model theory
mathematical logic, the term "interpretation" may refer to a structure, rather than being used in the sense defined here. These two notions of "interpretation" are
Interpretation_(model_theory)
Israeli computer scientist (born 1959)
areas including static program analysis, shape analysis, abstract interpretation, logic, theorem proving, programming languages, formal methods, data-flow
Shmuel_Sagiv
Characteristic of some logical systems
In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can
Completeness_(logic)
Country in East Asia
1080/09557570220126298. Chan, Steve (2020). Thucydides's Trap? Historical Interpretation, Logic of Inquiry, and the Future of Sino-American Relations. University
China
Formal semantics of logic programming languages
Logic programming is a programming paradigm that includes languages based on formal logic, including Datalog and Prolog. This article describes the syntax
Syntax and semantics of logic programming
Syntax_and_semantics_of_logic_programming
Formal system of logic
In mathematics and logic, a higher-order logic (abbreviated HOL) is a form of logic that is distinguished from first-order logic by additional quantifiers
Higher-order_logic
Work by Georg Wilhelm Friedrich Hegel
Science of Logic (German: Wissenschaft der Logik), first published between 1812 and 1816, is the work in which Georg Wilhelm Friedrich Hegel outlined
Science_of_Logic
Description of non-logical symbols
In mathematical logic, a signature is a description of the non-logical symbols of a formal language. In universal algebra, a signature lists the operations
Signature_(logic)
Work by Aristotle
the Western tradition to deal with the relationship between language and logic in a comprehensive, explicit, and formal way. The work begins by analyzing
On_Interpretation
Approach to static program analysis
Abstract Interpretation" (PDF). In Bruynooghe, Maurice; Wirsing, Martin (eds.). Proc. 4th Int. Symp. on Programming Language Implementation and Logic Programming
Abstract_interpretation
Type of abstract object
the free dictionary. Domain of a function Domain theory Interpretation (logic) Quantifier (logic) Term algebra Universe (mathematics) Corcoran, John. Universe
Domain_of_discourse
Study of the scope and nature of logic
Philosophy of logic is the branch of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as
Philosophy_of_logic
Symbols requiring interpretation
In mathematical logic, especially model theory, non-logical symbols are elements of a formal language whose interpretation may change depending on the
Non-logical_symbol
Value indicating the relation of a proposition to truth
Brouwer–Heyting–Kolmogorov interpretation and Intuitionistic logic § Semantics. Multi-valued logics (such as fuzzy logic and relevance logic) allow for more than
Truth_value
Branch of mathematical logic
type. This interpretation is commonly known as the Dialectica interpretation. Together with the double-negation interpretation of classical logic in intuitionistic
Proof_theory
Gödel (1933) showed that intuitionistic logic can be embedded into modal logic S4. (other systems) Interpretation (Gödel): ◻ P {\displaystyle \Box P} means
Constructive_logic
functions called t-norms for permissible interpretations of conjunction. They are mainly used in applied fuzzy logic and fuzzy set theory as a theoretical
T-norm_fuzzy_logics
Relationship where one statement follows from another
models of interpretation. A sentence is said to be a logical consequence of a set of sentences, for a given language, if and only if, using only logic (i.e
Logical_consequence
Non-contradiction of a theory
there exists an interpretation under which all axioms in the theory are true. This is what consistent meant in traditional Aristotelian logic, although in
Consistency
In mathematics, a statement that has been proven
In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses
Theorem
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
Type of logic diagram
In term logic (a branch of philosophical logic), the square of opposition is a diagram representing the relations between the four basic categorical propositions
Square_of_opposition
Faulty deductive reasoning due to a logical flaw
under at least one interpretation of the predicates it is not validity preserving. People often have difficulty applying the rules of logic. For example, a
Formal_fallacy
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
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
Theory of logic to account for observations from quantum theory
with the Copenhagen interpretation of quantum mechanics, a school of researchers had now sprung up, either hoping that quantum logic would provide a viable
Quantum_logic
Book by George Boole
Mathematical Theories of Logic and Probabilities by George Boole, published in 1854, is the second of Boole's two monographs on algebraic logic. Boole was a professor
The_Laws_of_Thought
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
Probabilistic logic
A Markov logic network (MLN) is a probabilistic logic which applies the ideas of a Markov network to first-order logic, defining probability distributions
Markov_logic_network
Logical operation
In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P {\displaystyle P} to another proposition
Negation
Application of logical methods to philosophical problems
in classical logic. Relevance logic is a prominent form of paraconsistent logic. It rejects the purely truth-functional interpretation of the material
Philosophical_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
Framework for a family of logic languages
Common Logic (CL) is a framework for a family of logic languages, based on first-order logic, intended to facilitate the exchange and transmission of
Common_Logic
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
Ancient philosophy
acceptance of Porphyry's interpretation led to their being accepted by Scholastic philosophy. As a result the Stoic writings on logic did not survive, and
Stoicism
Sequence of words formed by specific rules
In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet".
Formal_language
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
Model in mathematical logic not isomorphic to the standard model
theory, non-standard analysis and non-standard models of arithmetic. Interpretation (logic) Roman Kossak, 2004 Nonstandard Models of Arithmetic and Set Theory
Non-standard_model
American political scientist
S2CID 211436877. Chan, Steve (2020). Thucydides's Trap?: Historical Interpretation, Logic of Inquiry, and the Future of Sino-American Relations. Ann Arbor
Graham_Allison
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
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
Logical principles
In logic and philosophy, "laws of thought" is a dated expression referring to three logical principles: the law of identity (LOI), the law of non-contradiction
Law_of_thought
Family of formal knowledge representation
Description logics (DL) are a family of formal knowledge representation languages. Many DLs are more expressive than propositional logic but less expressive
Description_logic
The study of the methodological principles of interpretation
(/ˌhɜːrməˈnjuːtɪks/) is the study of the methodological principles of interpretation, especially the interpretation of biblical texts, wisdom literature, and philosophical
Hermeneutics
Logical formalism using combinators instead of variables
Combinatory logic can be given a variety of interpretations. Many early papers by Curry showed how to translate axiom sets for conventional logic into combinatory
Combinatory_logic
Logical principle
or to deny everything of everything." [Hamilton LECT. V. LOGIC. 65] Yet in On Interpretation, Book 9, Aristotle seems to deny the law of excluded middle
Law_of_excluded_middle
Limitative results in mathematical logic
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Topics referred to by the same term
literature and rhetoric Tautology (logic), in formal logic, a statement that is true in every possible interpretation Tautology (rule of inference), a rule
Tautology
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