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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)
Study of meaning in language
Formal semantics relies on logic and mathematics to provide precise frameworks of the relation between language and meaning. Cognitive semantics examines
Semantics
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
Type of formal logic
◻P can be read as "necessarily P". In the standard relational semantics for modal logic, formulas are assigned truth values relative to a possible world
Modal_logic
Mathematical study of the meaning of programming languages
programming language theory, semantics is the rigorous mathematical logic study of the meaning of programming languages. Semantics assigns computational meaning
Semantics (programming languages)
Semantics_(programming_languages)
Formal semantics for non-classical logic systems
Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical
Kripke_semantics
Form of logic that allows quantification over predicates
two different semantics that are commonly used for second-order logic: standard semantics and Henkin semantics. In each of these semantics, the interpretations
Second-order_logic
Formal semantics based on algebras
mathematical logic, algebraic semantics is a formal semantics based on algebras studied as part of algebraic logic. For example, the modal logic S4 is characterized
Algebraic semantics (mathematical logic)
Algebraic_semantics_(mathematical_logic)
Formal system of logic
additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more expressive, but their model-theoretic
Higher-order_logic
Formal study of linguistic meaning
Formal semantics is the scientific study of linguistic meaning through formal tools from logic and mathematics. It is an interdisciplinary field, sometimes
Formal semantics (natural language)
Formal_semantics_(natural_language)
Branch of logic using category theory to study mathematical structures
theoretical computer science. In broad terms, categorical logic represents both syntax and semantics by a category, and an interpretation by a functor. The
Categorical_logic
Approach to formal semantics
including dialogical logic (developed by Paul Lorenzen and Kuno Lorenz in Germany starting in the 1950s) and game-theoretical semantics (developed by Jaakko
Game_semantics
Type of logical system
first-order logic, but aside from requiring the axiom of choice, game semantics agree with Tarskian semantics for first-order logic, so game semantics will not
First-order_logic
Logic for proving computer program correctness
Axiomatic semantics is an approach based on mathematical logic for proving the correctness of computer programs. It is closely related to Hoare logic. Axiomatic
Axiomatic_semantics
Framework in logic and natural language semantics
Dynamic semantics is a framework in logic and natural language semantics that treats the meaning of a sentence as its potential to update a context. In
Dynamic_semantics
Family of formal knowledge representation
and concept languages. Frames and semantic networks lack formal (logic-based) semantics. DL was first introduced into knowledge representation (KR) systems
Description_logic
Rules used for constructing, or transforming the symbols and words of a language
expressions in a programming language. As in mathematical logic, it is independent of semantics and interpretation. A symbol is an idea, abstraction or
Syntax_(logic)
Bearer of truth values
emergence of possible worlds semantics and renewed interest in the internal structure and ontological category of propositions. Logic is the study of correct
Proposition
System of resource-aware logic
such as programming languages, game semantics, and quantum physics (because linear logic can be seen as the logic of quantum information theory), as well
Linear_logic
Formal semantics of logic programming languages
article describes the syntax and semantics of the purely declarative subset of these languages. Confusingly, the name "logic programming" also refers to a
Syntax and semantics of logic programming
Syntax_and_semantics_of_logic_programming
Class of formal logics
propositional and first-order logic, as opposed to the other forms of classical logic. Most semantics of classical logic are bivalent, meaning all of the
Classical_logic
Reformulation of Floyd-Hoare logic
transformer semantics are a reformulation of Floyd–Hoare logic. Whereas Hoare logic is presented as a deductive system, predicate transformer semantics (either
Predicate transformer semantics
Predicate_transformer_semantics
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
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
Approach to the semantics of logic
Proof-theoretic semantics is a branch of proof theory and an approach to the semantics of logic in which the meaning of propositions and logical connectives
Proof-theoretic_semantics
Programming paradigm based on formal logic
field of logic programming has been concerned with trying to develop a logical semantics for negation as failure and with developing other semantics and other
Logic_programming
Framework in formal semantics and logic
Alternative semantics (or Hamblin semantics) is a framework in formal semantics and logic. In alternative semantics, expressions denote alternative sets
Alternative_semantics
Overview of and topical guide to logic
Reference Semantics Strict conditional Syntax (logic) Truth Truth value Validity Affine logic Alethic logic Aristotelian logic Boolean logic Buddhist logic Bunched
Outline_of_logic
Framework in logic and natural language semantics
Inquisitive semantics is a framework in logic and natural language semantics. In inquisitive semantics, the semantic content of a sentence captures both
Inquisitive_semantics
Extension of a concept, idea, or sign
that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — the extension of a
Extension_(semantics)
Study of programming languages via mathematical objects
In computer science, denotational semantics (initially known as mathematical semantics or Scott–Strachey semantics) is an approach of formalizing the meanings
Denotational_semantics
Symbol representing a property or relation in logic
relation. In the semantics of logic, predicates are interpreted as relations. For instance, in a standard semantics for first-order logic, the formula R
Predicate_(logic)
Application of logical methods to philosophical problems
Possible worlds semantics is a very influential formal semantics in modal logic that brings with it system S5. A formal semantics of a language characterizes
Philosophical_logic
Logical connective OR
(Unicode U+22C1 ⋁ N-ARY LOGICAL OR): ⋁i=1nai=a1∨a2∨…an−1∨an In the semantics of logic, classical disjunction is a truth functional operation which returns
Logical_disjunction
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)
Framework for a family of logic languages
semantics of these dialects are defined in the Standard by their translation to the abstract syntax and semantics of Common Logic. Many other logic-based
Common_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
1947 book by Rudolf Carnap
and Necessity: A Study in Semantics and Modal Logic (1947; enlarged edition 1956) is a book about semantics and modal logic by the philosopher Rudolf
Meaning_and_Necessity
declarative semantics for logic programs with negation as failure. This is one of several standard approaches to the meaning of negation in logic programming
Stable_model_semantics
Value indicating the relation of a proposition to truth
interpretation and Intuitionistic logic § Semantics. Multi-valued logics (such as fuzzy logic and relevance logic) allow for more than two truth values
Truth_value
Language for controlling a computer
language Scripting language Semantics (logic) Software engineering and List of software engineering topics Syntax (logic) Computer programming portal
Programming_language
Mathematical model for deduction or proof systems
regarding equality used in first order logic. The two main types of deductive systems are proof systems and formal semantics. Formal proofs are sequences of
Formal_system
Phenomenon whereby language is used to discuss possible situations
Linguistic modality has been one of the central concerns in formal semantics and philosophical logic. Research in these fields has led to a variety of accounts
Modality_(semantics)
Reasoning of knowledge about knowledge
autoepistemic logic can express knowledge and lack of knowledge about facts. The stable model semantics, which is used to give a semantics to logic programming
Autoepistemic_logic
2019 book by John Newell Martin
The Cartesian Semantics of the Port-Royal Logic is a Philosophy book by John N. Martin, first published in 2019 by Routledge. This book provides an analysis
The Cartesian Semantics of the Port Royal Logic
The_Cartesian_Semantics_of_the_Port_Royal_Logic
Mathematical use of "for all" and "there exists"
higher-order properties used e.g. as standard semantics of quantified noun phrases. Term logic, also called Aristotelian logic, treats quantification in a manner
Quantifier_(logic)
Approach to predicate logic
calculi often preceded the finding of their corresponding formal semantics. Intensional logic is not alone in that: also Gottlob Frege accompanied his (extensional)
Intensional_logic
Programming paradigm
programming are based on the distribution semantics, which splits a program into a set of probabilistic facts and a logic program. It defines a probability distribution
Probabilistic logic programming
Probabilistic_logic_programming
Topics referred to by the same term
may also refer to: Semantics (computer science), the mathematical study of the meaning of programming languages Semantics of logic, the study of the interpretations
Semantics_(disambiguation)
Family of logics for natural-language and counterfactual conditionals
gives rise to well-known paradoxes. Conditional logics are used in philosophical logic, formal semantics of natural language, artificial intelligence, and
Conditional_logic
Assignment of meaning to the symbols of a formal language
formal languages is called formal semantics. The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and
Interpretation_(logic)
Category of formal programming language semantics
Operational semantics is a category of formal programming language semantics in which certain desired properties of a program, such as correctness, safety
Operational_semantics
Classical logic of two values, either true or false
intended semantics of classical logic is bivalent, but this is not true of every semantics for classical logic. In Boolean-valued semantics (for classical
Principle_of_bivalence
Extension of classical first-order logic
team semantics, such as dependence logic, dependence-friendly logic, exclusion logic and independence logic; with the exception of the latter, IF logic is
Independence-friendly_logic
Phenomenon in natural language
nonclassical frameworks such as dynamic semantics, linear logic, alternative semantics, and inquisitive semantics. Others have proposed ways of deriving
Free_choice_inference
Branch of logic
of bunched logic has been given a game semantics. The algebraic semantics of bunched logic is a special case of its categorical semantics, but is simple
Bunched_logic
Semantics for logic programming
well-founded semantics is a three-valued semantics for logic programming, which gives a precise meaning to general logic programs. The well-founded semantics was
Well-founded_semantics
American logician (born 1932)
of Kripke semantics for modal and tense logic, called Scott-Montague semantics (Scott 1970). John Lemmon and Scott began work on a modal-logic textbook
Dana_Scott
Academic discipline
language semantics. Logic programming is a programming, database and knowledge representation paradigm that is based on formal logic. A logic program is
Logic_in_computer_science
Boolean-valued model Kripke semantics General frame Predicate logic First-order logic Infinitary logic Many-sorted logic Higher-order logic Lindström quantifier
List of mathematical logic topics
List_of_mathematical_logic_topics
Truth-based approach to semantics
Tarski's semantic theory of truth achieves for the semantics of logic. Truth-conditional theories of semantics attempt to define the meaning of a given proposition
Truth-conditional_semantics
Subfield of mathematics
higher-order logics, which include a portion of set theory directly in their semantics. The most well studied infinitary logic is Lω1,ω. In this logic, quantifiers
Mathematical_logic
Syntax-semantics interface
meaning languages in glue semantics analyses include versions of discourse representation theory, intensional logic, first-order logic, and natural semantic
Glue_semantics
Ontology language
offers a declarative, compact and simple syntax, and the well-defined semantics of a logic programming language. Features include, among others, object identity
F-logic
System of logic in mathematics and philosophy
real-valued semantics determined by the Łukasiewicz t-norm is not the only possible semantics of Łukasiewicz logic. General algebraic semantics of propositional
Łukasiewicz_logic
Topics referred to by the same term
Algebraic semantics may refer to: Algebraic semantics (computer science) Algebraic semantics (mathematical logic) This disambiguation page lists articles
Algebraic_semantics
Alternative to Tarskian semantics
between truth-value semantics and the standard semantics for predicate logic is that there are no domains for truth-value semantics. Only the truth clauses
Truth-value_semantics
Translation of a text into a logical system
Logic translation is the process of representing a text in the formal language of a logical system. If the original text is formulated in ordinary language
Logic_translation
Logical operation
pseudocomplementation in a Heyting algebra. These algebras provide a semantics for classical and intuitionistic logic. The negation of a proposition p is notated in different
Negation
Type of formal logic
logics. Ross Brady (Australia) Bryson Brown (Canada) Walter Carnielli (Brazil). The developer of the possible-translations semantics, a new semantics
Paraconsistent_logic
Extension of first-order logic with atoms expressing variable dependencies
(IF logic): in other words, its game-theoretic semantics can be obtained from that of first-order logic by restricting the availability of information
Dependence_logic
Formal systems of logic that significantly differ from standard logical systems
logic. The precise nature of the relation between dialectical and formal logic was hotly debated within the Soviet Union and China. Dynamic semantics
Non-classical_logic
logic, a relation that describes which worlds are accessible from other worlds in the semantics of possible world models. actual world In modal logic
Glossary_of_logic
Mathematical theory of data types
Theory". Journal of Logic and Computation. 15 (2): 99–112. doi:10.1093/logcom/exi004. Cooper, Robin (2010). Type theory and semantics in flux. Handbook
Type_theory
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
Approach to semantics in analytic philosophy
Two-dimensionalism is an approach to semantics in analytic philosophy. It is a theory of how to determine the sense and reference of a word and the truth-value
Two-dimensionalism
Principle in linguistics about meaning
In semantics, mathematical logic and related disciplines, the principle of compositionality (also known as semantic compositionalism) is the principle
Principle_of_compositionality
Dialogical logic (German: dialogische Logik, also known as the logic of dialogues) is a pragmatic approach to the semantics of logic developed in the
Dialogical_logic
Technique in natural language processing
Juliana (1997), "XSB: A system for efficiently computing well-founded semantics", Logic Programming And Nonmonotonic Reasoning, Berlin, Heidelberg: Springer
Tabled_logic_programming
Framework for studying interactive computational tasks through logic
concepts of "intuitionistic truth", "linear-logic truth" and "IF-logic truth" can be derived from the semantics of CoL. CoL systematically answers the fundamental
Computability_logic
System for reasoning about vagueness
created from propositional logic, predicate fuzzy logics extend fuzzy systems by universal and existential quantifiers. The semantics of the universal quantifier
Fuzzy_logic
Term used to model separate circumstances that cannot exist together
since the advent of possible world semantics for modal logic, as well as world based semantics for non-classical logics, but have yet to find the ubiquitous
Impossible_world
Context-based approach to semantics
also bears a resemblance to accounts of proof-theoretic semantics in the semantics of logic, which associate meaning with the reasoning process. Abductive
Inferential_role_semantics
Reasoning about equations with free variables
appropriate for the study of various logics (in the form of classes of algebras that constitute the algebraic semantics for these deductive systems) and connected
Algebraic_logic
Semantic property of plurals
Predication (philosophy) Trivalent logic Križ, Manuel (2019). "Homogeneity effects in natural language semantics". Language and Linguistics Compass.
Homogeneity_(semantics)
Formal logic whose entailment relation is not monotonic
Model-theoretic formalization of a non-monotonic logic begins with restriction of the semantics of a suitable monotonic logic to some special models, for instance
Non-monotonic_logic
well as a semantics that explains how the logic is to be interpreted in a computational way. Probably the first formal treatment of logic for computability
Logics_for_computability
American philosopher and logician (1940–2022)
to logic, especially modal logic. His principal contribution is a semantics for modal logic involving possible worlds, now called Kripke semantics. He
Saul_Kripke
Topics referred to by the same term
models Formal semantics or semantics of logic, the mathematical study of the interpretations of formal languages Formal semantics or semantics (computer science)
Formal_semantics
Field of logic concerned with imperatives
and falsity play in their semantics. Thus, there is almost no consensus on any aspect of imperative logic. One of a logic's principal concerns is logical
Imperative_logic
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
formal semantics can be provided using the concept of a quasi-set. Schrödinger logics were introduced by da Costa and Krause. Schrödinger logic is not
Schrödinger_logic
School of thought on cognition and problem-solving
General semantics is a school of thought that incorporates philosophic and scientific aspects. Although it does not stand on its own as a separate school
General_semantics
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)
System for representing and reasoning about time
of Philosophy: "Temporal Logic"—by Anthony Galton. Temporal Logic by Yde Venema, formal description of syntax and semantics, questions of axiomatization
Temporal_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
Term in logic and deductive reasoning
logic, a logical system has the soundness property if every formula that can be proved in the system is logically valid with respect to the semantics
Soundness
Mapping of mathematical formulas to a particular meaning
the objects used to define the semantics of first-order logic, cf. also Tarski's theory of truth or Tarskian semantics. For a given theory in model theory
Structure (mathematical logic)
Structure_(mathematical_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
Resource-sensitive logic allowing each assumption to be used at most once
name as part of the geometry of interaction semantics of linear logic, which characterizes linear logic in terms of linear algebra; here he alludes to
Affine_logic
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