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Approach used in computer science
Naive semantics is an approach used in computer science for representing basic knowledge about a specific domain, and has been used in applications such
Naive_semantics
Declarative logic programming language
until a fixpoint is reached. This algorithm is called naïve evaluation. The proof-theoretic semantics defines the meaning of a Datalog program to be the
Datalog
Subtopic of natural language processing in artificial intelligence
basis of computer-automated semantic interpretation. These range from naive semantics or stochastic semantic analysis to the use of pragmatics to derive
Natural language understanding
Natural_language_understanding
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
Class of formal logics
first-order logic, as opposed to the other forms of classical logic. Most semantics of classical logic are bivalent, meaning all of the possible denotations
Classical_logic
Formal semantics of logic programming languages
including Datalog and Prolog. This article describes the syntax and semantics of the purely declarative subset of these languages. Confusingly, the
Syntax and semantics of logic programming
Syntax_and_semantics_of_logic_programming
List of concepts in artificial intelligence
on applying Bayes' theorem with strong (naive) independence assumptions between the features. naive semantics An approach used in computer science for
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
Transitive Uncountable Universal Theories Alternative Axiomatic Constructive Naive Cantor's theorem Zermelo General Principia Mathematica New Foundations Zermelo–Fraenkel
Gödel_logic
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)
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
Overview of and topical guide to natural language processing
METEOR – Minimal recursion semantics – Morphological pattern – Multi-document summarization – Multilingual notation – Naive semantics – Natural language – Natural-language
Outline of natural language processing
Outline_of_natural_language_processing
Relationship in which one statement follows from another
deductive system for L {\displaystyle {\mathcal {L}}} or by formal intended semantics for language L {\displaystyle {\mathcal {L}}} . The Polish logician Alfred
Logical_consequence
Informal set theories
Naive set theory is any of several set theories used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are defined
Naive_set_theory
In mathematics, a statement that has been proven
since the theory that contains it may be unsound relative to a given semantics, or relative to the standard interpretation of the underlying language
Theorem
Branch of mathematics that studies sets
during this early stage go under the name of naive set theory. After the discovery of paradoxes within naive set theory (e.g. Russell's paradox, Cantor's
Set_theory
Evolution of a word's meaning
change can be seen as part of etymology, onomasiology, semasiology, and semantics. Awful – Literally "full of awe", originally meant "inspiring wonder (or
Semantic_change
Structure of a formal language
found in theoretical computer science, theoretical linguistics, formal semantics, mathematical logic, and other areas. A formal grammar is a set of rules
Formal_grammar
Logical connective OR
is warm". In classical logic, disjunction is given a truth functional semantics according to which a formula ϕ ∨ ψ {\displaystyle \phi \lor \psi } is
Logical_disjunction
Hypothesis of language influencing thought
"The Semiotic Aspect of Alfred Korzybski's General Semantics" (PDF). ETC: A Review of General Semantics. 1. 40 (1). JSTOR: 16–21. doi:10.5840/cpsem19828
Linguistic_relativity
Mathematical model for deduction or proof systems
of possible expressions that are valid utterances in the language) the semantics are what the utterances of the language mean (which is formalized in various
Formal_system
Truth. Cambridge University Press. Herzberger, H. G. (1982). Notes on naive semantics. Journal of Philosophical Logic, 11(1):61–102. Reprinted in Martin
Revision_theory
Philosophical view that some states of mind, as commonly understood, do not exist
Consciousness, which asserts that "formal argumentation from precise semantics" dissolves the hard problem because of the contradiction between precision
Eliminative_materialism
Alternative to Tarskian semantics
In formal semantics, truth-value semantics is an alternative to Tarskian semantics. It has been primarily championed by Ruth Barcan Marcus, H. Leblanc
Truth-value_semantics
Function, homomorphism, or morphism
Theory. Cambridge University Press. p. 2. ISBN 978-1-139-50332-7. Halmos, Paul R. (1970). Naive Set Theory. Springer-Verlag. ISBN 978-0-387-90092-6.
Map_(mathematics)
Mathematical-logic system
questions about the semantics of the lambda calculus. Could a sensible meaning be assigned to lambda calculus terms? The natural semantics was to find a set
Lambda_calculus
Symbol representing a property or relation in logic
property or relation. In the semantics of logic, predicates are interpreted as relations. For instance, in a standard semantics for first-order logic, the
Predicate_(logic)
In artificial intelligence, a condition that varies over time
2011.6094743. Jakob Suchan and Mehul Bhatt (2017). Commonsense Scene Semantics for Cognitive Robotics: Towards Grounding Embodied Visuo-Locomotive Interactions
Fluent (artificial intelligence)
Fluent_(artificial_intelligence)
Syntactically correct logical formula
ISBN 978-1-4471-3657-6. Agler, David W. (2013). Symbolic Logic: Syntax, Semantics, and Proof. Rowman & Littlefield. p. 41. ISBN 978-1-4422-1742-3. Simpson
Well-formed_formula
Theorem in set theory
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Kőnig's_theorem_(set_theory)
Reasoning for mathematical statements
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Mathematical_proof
Value indicating the relation of a proposition to truth
algebraic semantics. The algebraic semantics of intuitionistic logic is given in terms of Heyting algebras, compared to Boolean algebra semantics of classical
Truth_value
Theorem in set theory
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Schröder–Bernstein_theorem
Symbolic logic system
QED. There are semantics of minimal logic that mirror the frame-semantics of intuitionistic logic, see the discussion of semantics in paraconsistent
Minimal_logic
Mathematical use of "for all" and "there exists"
n·2 = n + n, where N is the set of all natural numbers. Mathematical semantics is the application of mathematics to study the meaning of expressions
Quantifier_(logic)
Mathematical game
playing at level 0, responding to an assumed average of 50 in relation to naive play, and thus their guess would be 33 (2/3 of 50). At k-level 2, a player
Guess_2/3_of_the_average
Rule defining the correct structure of expressions in formal grammar
language. It does not describe anything else about a language, such as its semantics (i.e. what the strings mean). (See also formal grammar). A formal language
Formation_rule
Recovery algorithm
In computer science, Algorithms for Recovery and Isolation Exploiting Semantics, or ARIES, is a recovery algorithm designed to work with a no-force, steal
Algorithms for Recovery and Isolation Exploiting Semantics
Algorithms_for_Recovery_and_Isolation_Exploiting_Semantics
Complexity class used to classify decision problems
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
NP_(complexity)
Type of logical system
semantics. What follows is a description of the standard or Tarskian semantics for first-order logic. (It is also possible to define game semantics for
First-order_logic
Concept in linguistics
Index General linguistics Diachronic Morphology Phonology Pragmatics Semantics Syntax Typology Applied linguistics Acquisition Anthropological Applied
Model-theoretic_grammar
Italian-born philosopher (born 1958)
philosophical logic (mainly vagueness, supervaluationism, paraconsistency, formal semantics) and metaphysics (mainly mereology and mereotopology, causation, events
Achille_Varzi_(philosopher)
Syntactically well-formed, semantically incongruous phrase
derived from it, which demonstrates the distinction between syntax and semantics, and the idea that a syntactically well-formed sentence is not guaranteed
Colorless green ideas sleep furiously
Colorless_green_ideas_sleep_furiously
Axiom of set theory proposed by Peter Aczel in 1988
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Aczel's_anti-foundation_axiom
Logic theorem
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Law_of_noncontradiction
Mathematical theory of data types
on dependent type theory. Type theory was created to avoid paradoxes in naive set theory and formal logic, such as Russell's paradox which demonstrates
Type_theory
Guatemalan-American philosopher (1924–1991)
the Government of Guatemala in 1991. "On the Semantics of the Ought-to-Do", Synthese, 21, 3/4, Semantics of Natural Language, 1970, pp. 449–468. "Intentions
Héctor-Neri_Castañeda
Whether a decision problem has an effective method to derive the answer
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Decidability_(logic)
Philosophical terms
of these two theses.[citation needed] Externalism and internalism in semantics is closely tied to the distinction in philosophy of mind concerning mental
Internalism_and_externalism
American media theorist and cultural critic (1931–2003)
He was the editor of the quarterly journal ETC: A Review of General Semantics from 1976 to 1986. In 1976, Postman taught a course at NYU on CBS-TV's
Neil_Postman
Function that preserves distinctness
Wiley & Sons, ISBN 978-0-471-05464-1, p. 17 ff. Halmos, Paul R. (1974), Naive Set Theory, New York: Springer, ISBN 978-0-387-90092-6, p. 38 ff. Wikimedia
Injective_function
Logical operation
pseudocomplementation in a Heyting algebra. These algebras provide a semantics for classical and intuitionistic logic. The negation of a proposition
Negation
Property that assigns truth values to k-tuples of individuals
Axiomatic Set Theory, Dover Publications Tarski, A. (1983) [1956], Logic, Semantics, Metamathematics, Papers from 1923 to 1938, translated by J.H. Woodger
Finitary_relation
Technique used in mathematical logic
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Back-and-forth_method
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Institutional_model_theory
Area of mathematical logic
First-order theories Hyperreal number Institutional model theory Kripke semantics Löwenheim–Skolem theorem Model-theoretic grammar Proof theory Saturated
Model_theory
Description of non-logical symbols
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Signature_(logic)
Term in logic
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Atomic_sentence
Process of repeating items in a self-similar way
plays a crucial role not only in syntax, but also in natural language semantics. The word and, for example, can be construed as a function that can apply
Recursion
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)
Yes-or-no question that cannot ever be solved by a computer
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Undecidable_problem
Symbol representing a mathematical object
from?" (PDF). In Böttner, Michael; Thümmel, Wolf (eds.). Variable-Free Semantics. Osnabrück Secolo. pp. 46–65. ISBN 978-3-929979-53-4. Quine, Willard V
Variable_(mathematics)
Symbolic description of a mathematical object
Determining which value is assumed to be free depends on context and semantics. An expression is often used to define a function, or denote compositions
Expression_(mathematics)
Omission of operations and relations of a structure
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Reduct
Theorem of mathematical logic
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Robinson's joint consistency theorem
Robinson's_joint_consistency_theorem
Set whose elements all belong to another set
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Subset
Mathematical use of "there exists"
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Existential_quantification
One-to-one correspondence
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Bijection
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Łoś–Vaught_test
Field of artificial intelligence
resulting extended semantics of LP is a variation of the standard semantics of Horn clauses and FOL, and is a form of database semantics, which includes
Knowledge representation and reasoning
Knowledge_representation_and_reasoning
Logical quantifier
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Uniqueness_quantification
Written or spoken commentary for storytelling
Person Narration? The Case of Katherine Mansfield". Journal of Literary Semantics. 46 (1): 67–85. doi:10.1515/jls-2017-0005. S2CID 171741675. Rasley, Alicia
Narration
Hypothetical internal cognitive symbol that represents external reality
natural languages but on a much more abstract level, possess a syntax and semantics very much like those of natural languages. For the Portuguese logician
Mental_representation
Basic framework of mathematics
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Foundations_of_mathematics
Axiomatic logical system
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Robinson_arithmetic
Sentence that resists simple formalization
In semantics, a donkey sentence is a sentence containing a pronoun which is semantically bound but syntactically free. Their name comes from the example
Donkey_sentence
Theory that allows sets to be elements of themselves
in computer science (process algebra and final semantics), linguistics and natural language semantics (situation theory), philosophy (work on the liar
Non-well-founded_set_theory
Computer science researcher in artificial intelligence
community, contributing substantially (perhaps solely) to the revised semantics of RDF known as RDF-Core, one of the three designers (along with Peter
Pat_Hayes
Theorem about products in model theory
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Feferman–Vaught_theorem
Type of large language model
Retrieved April 28, 2023. Sterling, Bruce (February 13, 2020). "Web Semantics: Microsoft Project Turing introduces Turing Natural Language Generation
Generative pre-trained transformer
Generative_pre-trained_transformer
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Apartness_relation
Category of mathematical proof
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Proof_of_impossibility
Term in logic and deductive reasoning
be proven in the system is logically valid with respect to the logical semantics of the system. These two properties are different but closely related
Soundness
Symbols requiring interpretation
<. Structures over a signature, also known as models, provide formal semantics to a signature and the first-order language over it. A structure over
Non-logical_symbol
Proof by Alan Turing
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Turing's_proof
Mathematical logic concept
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Computably_enumerable_set
Extension of the Web to facilitate data exchange
is to make Internet data machine-readable. To enable the encoding of semantics with the data, technologies such as Resource Description Framework (RDF)
Semantic_Web
Axioms for the natural numbers
computability". In Maurice Nivat and John C. Reynolds (ed.). Algebraic Methods in Semantics (PDF). Cambridge: Cambridge University Press. pp. 459–541. ISBN 978-0-521-26793-9
Peano_axioms
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
C-minimal_theory
Search algorithm
theory Dynamic inconsistency Escalation of commitment Farsightedness Game semantics Hierarchy of beliefs Incomplete information Information set Move by nature
Alpha–beta_pruning
Subfield of automated reasoning and mathematical logic
analysis with boxer." Semantics in text processing. step 2008 conference proceedings. 2008. Muskens, Reinhard. "Combining Montague semantics and discourse representation
Automated_theorem_proving
System of mathematical set theory
identical if MK includes the strong form of Limitation of Size). But the semantics of second-order ZFC are quite different from those of MK. For example
Morse–Kelley_set_theory
Kind of transfinite induction
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Epsilon-induction
Proof method in mathematical logic
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Structural_induction
Form of computer memory management
The original method involves a naïve mark-and-sweep in which the entire memory set is touched several times. In the naive mark-and-sweep method, each object
Tracing_garbage_collection
American philosopher (1941–2001)
is most famous for his work in metaphysics, philosophy of language and semantics, in which his books On the Plurality of Worlds (1986) and Counterfactuals
David_Lewis_(philosopher)
Target set of a mathematical function
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
Codomain
Overview of and topical guide to logic
Presupposition Probability Quantification Reason Reasoning Reference Semantics Strict conditional Syntax (logic) Truth Truth value Validity Affine logic
Outline_of_logic
Problem in computer science
intended to finish. The fact that the halting problem is undecidable is often naively taken to mean that establishing whether a program halts is impossible.
Halting_problem
Testing device for logical soundness
General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence
T-schema
Comparison between two programming languages
they are not. C++ uses value semantics by default, while Java always uses reference semantics. To opt for reference semantics in C++, either a pointer or
Comparison_of_Java_and_C++
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