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The concept of a stable model, or answer set, is used to define a declarative semantics for logic programs with negation as failure. This is one of several
Stable_model_semantics
Formal semantics of logic programming languages
the game. The stable model semantics define a condition for calling certain Herbrand models of a program stable. Intuitively, stable models are the "possible
Syntax and semantics of logic programming
Syntax_and_semantics_of_logic_programming
American computer scientist
Lifschitz: The Stable Model Semantics for Logic Programming. ICLP/SLP 1988: 1070-1080 Victor Marek and Miroslaw Truszczynski. Stable models and an alternative
Vladimir_Lifschitz
the semantics of disjunctive Datalog: Minimal model semantics Perfect model semantics Disjunctive stable model semantics, which generalizes the stable model
Disjunctive_Datalog
Reasoning of knowledge about knowledge
knowledge and lack of knowledge about facts. The stable model semantics, which is used to give a semantics to logic programming with negation as failure
Autoepistemic_logic
Programming paradigm focused on difficult search problems
is based on the stable model (answer set) semantics of logic programming. In ASP, search problems are reduced to computing stable models, and answer set
Answer_set_programming
Semantics for logic programming
have the truth value unknown. In the two-valued stable model semantics, there are two stable models, one in which a is true and b is false, and one in
Well-founded_semantics
Inference rule treating non-provability as falsity
ISBN 978-0-934613-42-2. Gelfond, M.; Lifschitz, V. (1988). "The Stable Model Semantics for Logic Programming". In Kowalski, R.; Bowen, K. (eds.). Proc
Negation_as_failure
Programming paradigm based on formal logic
alternative stable model semantics, there may be no intended models or several intended models, all of which are minimal and two-valued. The stable model semantics
Logic_programming
American computer scientist
Lifschitz: The Stable Model Semantics for Logic Programming. ICLP/SLP 1988: 1070-1080 Victor Marek and Miroslaw Truszczynski. Stable models and an alternative
Michael_Gelfond
Programming paradigm
which may use negation but have no recursive dependencies. The stable model semantics underlying answer set programming gives meaning to unstratified
Probabilistic logic programming
Probabilistic_logic_programming
Declarative logic programming language
have no impact on the semantics of the program. There are three widely-used approaches to the semantics of Datalog programs: model-theoretic, fixed-point
Datalog
Assumption that what is not known to be true is false
Negation as failure Non-monotonic logic Operational design domain Stable model semantics Unique name assumption Reiter, Raymond (1978). "On Closed World
Closed-world_assumption
Type of logical formula
only if P is true in M. The minimal model semantics of Horn clauses is the basis for the stable model semantics of logic programs. Constrained Horn clauses
Horn_clause
Logic programming using abductive reasoning
to simulate abduction in ALP using negation as failure with the stable model semantics. This can be done by adding, for every abducible predicate p, an
Abductive_logic_programming
Formal logic whose entailment relation is not monotonic
logic. Philosophy portal Logic programming Negation as failure Stable model semantics Rational consequence relation Strasser, Christian; Antonelli, G
Non-monotonic_logic
Interchange format for rule systems
is, declarative logic programming based on the answer set semantics (stable model semantics). Example: Document( Prefix(ex <http://example.com/concepts#>)
Rule_Interchange_Format
Study of meaning in language
Semantics is the study of linguistic meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends
Semantics
1933 book by Alfred Korzybski
and General Semantics is a 1933 philosophy book written by Alfred Korzybski (1879–1950). Published by the Institute of General Semantics, it remains in
Science_and_Sanity
Model of concurrent computation
systems in the actor model. These include: Operational semantics Laws for actor systems Denotational semantics Transition semantics There are also formalisms
Actor_model
Formal model in concurrency theory
algebraic semantics, and operational semantics. The three major denotational models of CSP are the traces model, the stable failures model, and the failures/divergences
Communicating sequential processes
Communicating_sequential_processes
Action semantics is a framework for the formal specification of semantics of programming languages invented by David Watt and Peter D. Mosses in the 1990s
Action_semantics
Software engineering visualization
information model in software engineering is a representation of concepts and the relationships, constraints, rules, and operations to specify data semantics for
Information_model
Various systems of symbolic logic
uses Heyting algebras in place of Boolean algebras. Another semantics uses Kripke models. These, however, are technical means for studying Heyting’s deductive
Intuitionistic_logic
Concerned with the notion of stability in model theory
mathematical field of model theory, a theory is called stable if it satisfies certain combinatorial restrictions on its complexity. Stable theories are rooted
Stable_theory
Pairing where no unchosen pair prefers each other over their choice
mathematics, economics, and computer science, the stable matching problem is the problem of finding a stable matching between two equally sized sets of elements
Stable_matching_problem
Abstract model
1975: Conceptual data model: describes the semantics of a domain, being the scope of the model. For example, it may be a model of the interest area of
Data_model
Chart or model use to illustrate the nervous system
S. patent on May 26, 1925, it is used as a training device in general semantics. The device is intended to show that human "knowledge" of, or acquaintance
Structural_differential
Standard part function Set theory Forcing (mathematics) Boolean-valued model Kripke semantics General frame Predicate logic First-order logic Infinitary logic
List of mathematical logic topics
List_of_mathematical_logic_topics
Machine learning model
problem that stable diffusion models also struggle with. Examples include distorted hands and unreadable text. The deployment of text-to-video models raises
Text-to-video_model
Area of mathematical logic
number Institutional model theory Kripke semantics Löwenheim–Skolem theorem Model-theoretic grammar Proof theory Saturated model Skolem normal form Chang
Model_theory
Type of large language model
A generative pre-trained transformer (GPT) is a type of large language model (LLM) that is widely used in generative artificial intelligence chatbots
Generative pre-trained transformer
Generative_pre-trained_transformer
Concept in model theory
interpretation in N. Many model-theoretic properties are preserved under interpretability. For example, if the theory of N is stable and M is interpretable
Interpretation_(model_theory)
Economic Model
one models the residual demand – the demand faced by higher-priced firms given the sales of the lower-priced firms). Myopic Stable. The Myopic Stable Set
Bertrand–Edgeworth_model
Study of signs
branches are syntactics, which addresses formal relations between signs; semantics, which addresses the relation between signs and their meanings; and pragmatics
Semiotics
French computer scientist
Clark's completion. This result has shown useful for implementing stable model semantics with classical propositional satisfiability solvers. This theorem
François_Fages
Condition where selection restores genetic composition
noted that evolutionary stability can exist in either model, allowing for an evolutionarily stable state to exist even when multiple strategies are used
Evolutionarily_stable_state
extends his possible-world semantics to normal modal logics. 1965 - Michael D. Morley introduces the beginnings of stable theory in order to prove Morley's
Timeline of mathematical logic
Timeline_of_mathematical_logic
Programming paradigm based on modeling the logic of a computation
programming (ASP) evolved in the late 1990s, based on the stable model (answer set) semantics of logic programming. Like Datalog, it is a subset of Prolog;
Declarative_programming
Mathematical system
second-order arithmetic is formalized using the semantics of first-order logic (Henkin semantics) then any model includes a domain for the set variables to
Second-order_arithmetic
Fundamental unit of cognition
Semantics". Semantics. De Gruyter Mouton. doi:10.1515/9783110226614.688. ISBN 978-3-110-22661-4. Jacobson, Pauline I. (2014). Compositional Semantics:
Concept
Type of stable matching problem
combinatorial game theory and algorithms, the stable-roommate problem (SRP) is the problem of finding a stable matching for an even-sized set. A matching
Stable_roommates_problem
Computation which does not terminate or terminates in an exceptional state
divergent if it has no normal form. In denotational semantics an object function f : A → B can be modelled as a mathematical function f : A ∪ { ⊥ } → B ∪ {
Divergence_(computer_science)
Solution concept in game theory
An evolutionarily stable strategy (ESS) is a strategy (or set of strategies) that is impermeable when adopted by a population in adaptation to a specific
Evolutionarily stable strategy
Evolutionarily_stable_strategy
Open-source data infrastructure for AI
Ontologies using Artificial Intelligence (DRAGON-AI)", Journal of Biomedical Semantics, 15 (1): 19, arXiv:2312.10904, doi:10.1186/s13326-024-00320-3, PMC 11484368
ChromaDB
Model of conflict for two players in game theory
) In the two population model, this mixed point becomes unstable. In fact, the only stable states in the two population model correspond to the pure strategy
Chicken_(game)
Different models of collaborative tagging
account the semantics of the set of tags assigned to documents, the predictive value of tags on contents of documents is relatively stable. This finding
Models of collaborative tagging
Models_of_collaborative_tagging
Semantics of Business Vocabulary and Business Rules (SBVR) Other related frameworks are: POLDAT Zachman Framework Business framework Business model i*
Business_Motivation_Model
Search algorithm
theory Dynamic inconsistency Escalation of commitment Farsightedness Game semantics Hierarchy of beliefs Imperfect information Incomplete information Information
Alpha–beta_pruning
Model of humans as rational, self-interested agents
widens the discussion. In its standard formulation, the model assumes that individuals have stable preferences, access to relevant information, and seek
Homo_economicus
Overuse of a shared resource
these classes and distinguish between psychological individual differences (stable personality traits) and situational factors (the environment). Situational
Tragedy_of_the_commons
Facilitating a peaceful outcome to a dispute
meeting the needs of others and have a general concern for maintaining stable, positive social relationships. When faced with conflict, individuals with
Conflict_resolution
Control logic tool developed by MathWorks
MATLAB/Simulink/Stateflow Standards A. Tiwari. "Formal Semantics and Analysis Methods for Simulink Stateflow Models" (PDF). SRI International Computer Science Laboratory
Stateflow
Logical paradox in decision-making theory
Studies: An Irish Quarterly Review, 86(344), 346–359. http://www.jstor.org/stable/30091841 Blumner, Robyn E. (August–September 2016). "Is My Intolerance of
Paradox_of_tolerance
Type of perfect Bayesian equilibrium
dominated strategies Markov perfect equilibrium Mertens-stable equilibrium Nash equilibrium Open-loop model Pareto efficiency Payoff dominance Perfect Bayesian
Separating_equilibrium
English saying meaning "equivalent retaliation"
theory Dynamic inconsistency Escalation of commitment Farsightedness Game semantics Hierarchy of beliefs Imperfect information Incomplete information Information
Tit_for_tat
Solution concept of a non-cooperative game
above there are both stable and unstable equilibria. The equilibria involving mixed strategies with 100% probabilities are stable. If either player changes
Nash_equilibrium
Standard example in game theory
that unfair ZD strategies are not evolutionarily stable. The key intuition is that an evolutionarily stable strategy must not only be able to invade another
Prisoner's_dilemma
Concept in game theory
predictors in a regression model. In this context, the "players" are the individual predictors or variables in the model, and the "gain" is the total
Shapley_value
Situation where total gains match total losses
considered when introducing a new model, which will lead to economic leakage and injection. Thus introducing new models requires caution. For example, if
Zero-sum_game
Solution concept for non-cooperative games
and Player Splitting. The stable sets of the product of two independent games are the products of their stable sets. Stable sets are not affected by splitting
Mertens-stable_equilibrium
Human behavior pattern in which the participant takes on increasing risk
when subjects view current issues as having unstable reasoning rather than stable reasoning, or when the individual is unwilling to admit mistakes. They then
Escalation_of_commitment
Decrease in severity of conflicts
As of 2016, there are 19 articles in literature that define or provide a model of de-escalation. Articles converge on a number of themes (i.e. de-escalation
De-escalation
Programming language
safety – There are no runtime exceptions. All exceptions have defined semantics and are always caught. Concurrency safety – The type system employs reference
Pony_(programming_language)
Israeli-American psychologist and economist (1934–2024)
results discussed at the time about economic behavior under risk in a simple model, whose predictions were systematically supported by psychological experiments
Daniel_Kahneman
Decision rule used for minimizing the possible loss for a worst-case scenario
worst possible result is then no payment. However, this solution is not stable, since if B believes A will choose A2 then B will choose B1 to gain 1; then
Minimax
Modelling evolution using differential equations
A mathematical model of evolution needs to be dynamical that is, it needs to represent change over time. Although evolutionary stable strategies are important
Evolutionary_dynamics
Organized collection of data in computing
database reorganization. But Codd was more interested in the difference in semantics: the use of explicit identifiers made it easier to define update operations
Database
Political model of international conflict resolution
Politics portal Two-level game theory is a political model, derived from game theory, that illustrates the domestic-international interactions between
Two-level_game_theory
Economic model
Cournot competition is an economic model describing a market where n ≥ 2 {\displaystyle n\geq 2} firms simultaneously compete by choosing the quantity
Cournot_competition
Economic model of competition
Bertrand competition is a model of competition used in economics, named after Joseph Louis François Bertrand (1822–1900). It describes interactions among
Bertrand_competition
Paper-and-pencil game for two players
dominated strategies Markov perfect equilibrium Mertens-stable equilibrium Nash equilibrium Open-loop model Pareto efficiency Payoff dominance Perfect Bayesian
Tic-tac-toe
Making of satisfactory, not optimal, decisions
rational entities, as in rational choice theory or Downs' political agency model. The concept of bounded rationality complements the idea of rationality
Bounded_rationality
Israeli psychologist (1937–1996)
theory representativeness heuristic Tversky index support theory contrast model feature matching account of similarity Kahneman said that Tversky "had simply
Amos_Tversky
Method in artificial intelligence
a_{i})\in R} ), all these semantics coincide—only one extension is grounded, stable, preferred, and complete. Some other semantics have been defined. One
Argumentation_framework
Subset of a game; used in game theory
dominated strategies Markov perfect equilibrium Mertens-stable equilibrium Nash equilibrium Open-loop model Pareto efficiency Payoff dominance Perfect Bayesian
Subgame
Implementation of the programming language Prolog
Comparison of Prolog implementations Prolog syntax and semantics "Ann: SWI-Prolog 10.0.0 (Stable)". 3 December 2025. Retrieved 5 December 2025. Tate, Bruce
SWI-Prolog
properties. Only symmetric equilibria can be evolutionarily stable states in single population models. Symmetric game Thijssen, J. J. J.; Huisman, K. J. M.;
Symmetric_equilibrium
Military strategy during the Cold War with regard to the use of nuclear weapons
of the attacker accomplishing the action × Benefits of the action) This model is frequently simplified in game-theoretic terms as: Costs × P(Costs) >
Deterrence_theory
Language model application development framework
news, movie information, and weather; Bash for summarization, syntax and semantics checking, and execution of shell scripts; multiple web scraping subsystems
LangChain
Term in game theory
dominated strategies Markov perfect equilibrium Mertens-stable equilibrium Nash equilibrium Open-loop model Pareto efficiency Payoff dominance Perfect Bayesian
Move_by_nature
Mathematical models of strategic interactions
Several logical theories have a basis in game semantics. In addition, computer scientists have used games to model interactive computations. Also, game theory
Game_theory
Model for mathematical theories
assumptions, saturated models (albeit of very large cardinality) exist for arbitrary theories. For λ-stable theories, saturated models of cardinality λ exist
Saturated_model
Loom has a formal semantics that maps declarations in Loom to statements in set theory and first-order logic. This formal semantics enables a type of
LOOM_(ontology)
Iterated game for peace and conflict studies
example. Herbert Gintis, Game Theory Evolving: A Problem-centered Introduction to Modeling Strategic Behavior, Princeton University Press, 2000, p. 133
Peace_war_game
Game whose outcome can be correctly predicted
dominated strategies Markov perfect equilibrium Mertens-stable equilibrium Nash equilibrium Open-loop model Pareto efficiency Payoff dominance Perfect Bayesian
Solved_game
Computer Language for System Modeling
is an object-oriented, declarative, multi-domain modeling language for component-oriented modeling of complex systems, e.g., systems containing mechanical
Modelica
Hand game for two players or more
Models of evolution demonstrate how intragenomic competition can lead to rock paper scissors dynamics from a relatively general evolutionary model. The
Rock_paper_scissors
Concept in game theory
how other players act. They model the level of "rational expectation" players have by their ability to form priors (models) about the behavior of other
Focal_point_(game_theory)
Probabilistic logic programming language
distribution semantics, a probability distribution is defined over the two-valued well-founded models of the atoms in the program. The probability of a model is
ProbLog
Special locking mechanism used in Linux
parallel operating system routines. The semantics stabilized as of version 2.5.59, and they are present in the 2.6.x stable kernel series. The seqlocks were
Seqlock
dominated strategies Markov perfect equilibrium Mertens-stable equilibrium Nash equilibrium Open-loop model Pareto efficiency Payoff dominance Perfect Bayesian
Transferable_utility
dominated strategies Markov perfect equilibrium Mertens-stable equilibrium Nash equilibrium Open-loop model Pareto efficiency Payoff dominance Perfect Bayesian
Coalition-proof Nash equilibrium
Coalition-proof_Nash_equilibrium
Condition in economics and game theory
theory Dynamic inconsistency Escalation of commitment Farsightedness Game semantics Hierarchy of beliefs Imperfect information Incomplete information Information
Perfect_information
Game where groups of players may enforce cooperative behaviour
unique vector. The core is contained in any stable set, and if the core is stable it is the unique stable set; see (Driessen 1988) for a proof. For simple
Cooperative_game_theory
Game theory model of aggression
occasioned by the passage of time. The model was originally formulated by John Maynard Smith; a mixed evolutionarily stable strategy (ESS) was determined by
War_of_attrition_(game)
Problem about bus travel
dominated strategies Markov perfect equilibrium Mertens-stable equilibrium Nash equilibrium Open-loop model Pareto efficiency Payoff dominance Perfect Bayesian
Wait/walk_dilemma
Belgian game theorist (1946–2012)
games, cooperative games, noncooperative games, repeated games, epistemic models of strategic behavior, and refinements of Nash equilibrium (see solution
Jean-François_Mertens
Set in game theory
coalition having at least (n+1)/2 members has an empty core. That is, no stable coalition exists. Consider a group of n miners, who have discovered large
Core_(game_theory)
Type of memory referring to general world knowledge
conceptual knowledge, perhaps in some categorically-organized fashion." Memory semantics Sparse distributed memory Semantic similarity McRae, Ken; Jones, Michael
Semantic_memory
STABLE MODEL-SEMANTICS
STABLE MODEL-SEMANTICS
Female
English
Feminine variant spelling of English unisex Stacey, STACEE means "resurrection."
Female
English
Variant spelling of English Mabel, MABLE means "lovable."Â
Girl/Female
Hindu, Indian, Traditional
Model; Idea
Boy/Male
Muslim
Model, Example
Boy/Male
Arabic, Muslim
Model; Example
Female
English
Elaborated form of English Star, STARLA means "star."
Surname or Lastname
English
English : topographic name for someone who lived by a stable, or an occupational name for someone employed in one, from Middle English stable, plural stables (via Old French from Latin stabulum, a derivative of stare ‘to stand’). In Middle English the term was used of the quarters occupied by cattle as well as those reserved for horses.
Surname or Lastname
English
English : occupational name for someone who looked after horses or cattle, from an agent derivative of Middle English stable ‘stable’.German (Stäbler) : occupational name for an official who carried a staff as a symbol of office, Middle High German stebelære.
Boy/Male
Shakespearean American English
Henry VI, Part 2' Sir John Stanley. 'King Henry the Sixth, Part III' Sir William Stanley. 'King...
Surname or Lastname
English
English : variant of Staple.
Male
French
French name derived from Latin amabilis, AMABLE means "lovable."
Boy/Male
Egyptian
To model.
Female
Yiddish
(×”Ö¸×דֶעל) Pet form of Yiddish Hode, HODEL means "myrtle tree."
Male
Yiddish
Pet form of Yiddish Mordche, MOTEL means "devotee of Marduk."Â
Surname or Lastname
English
English : from Middle English stapel ‘post’, hence a topographic name for someone who lived near a boundary post, or a habitational name from some place named with this word (Old English stapel), as for example Staple in Kent or Staple Fitzpaine in Somerset.Americanized spelling of German Stapel.
Surname or Lastname
English, Dutch, North German, and Danish
English, Dutch, North German, and Danish : variant of Stubbe.
Female
English
Feminine variant spelling of English unisex Stacey, STACIE means "resurrection."
Surname or Lastname
English (Devon and Cornwall)
English (Devon and Cornwall) : habitational name from Scoble in Devon.
Surname or Lastname
English
English : from an Old German personal name, Godilo, Godila.German (Gödel) : from a pet form of a compound personal name beginning with the element gÅd ‘good’ or god, got ‘god’.Variant of Godl or Gödl, South German variants of Gote, from Middle High German got(t)e, gö(t)te ‘godfather’.Jewish (Ashkenazic) : from the Yiddish male personal name Godl, a pet form of God, a variant of biblical Gad.
Female
English
English name derived from the vocabulary word, SABLE means "black," as a heraldic color. It is sometimes confused with the mammal of the same name but which has brown fur, not black, and which has a different origin.
STABLE MODEL-SEMANTICS
STABLE MODEL-SEMANTICS
Male
Egyptian
, Horus as the good spirit.
Boy/Male
Australian, Celtic, Gaelic
Free Man
Boy/Male
Arabic, Indian, Muslim
Cream; Character
Girl/Female
Australian, Greek, Latin
Farmer; Similar to Georgia
Female
English
English name derived from the name of the Calla Lily, from Greek kallaia, CALLA means "wattle of a cock," from kallos meaning "beauty."Â
Boy/Male
Hebrew
He will rejoice.
Girl/Female
American, Biblical, Christian, Gaelic, Hebrew, Indian, Irish, Punjabi, Sikh
Elevated Place; Hill; A Hair; A Wretch; One Banished
Surname or Lastname
English
English : variant spelling of Earl.
Girl/Female
Tamil
Action, A work of art
Boy/Male
Gujarati, Hindu, Indian, Malayalam, Marathi, Sanskrit
Bearer of Diamonds; Like Angel; Wealthy; Diamonds
STABLE MODEL-SEMANTICS
STABLE MODEL-SEMANTICS
STABLE MODEL-SEMANTICS
STABLE MODEL-SEMANTICS
STABLE MODEL-SEMANTICS
imp. & p. p.
of Stable
n.
The scale as affected by the various positions in it of the minor intervals; as, the Dorian mode, the Ionic mode, etc., of ancient Greek music.
n.
Something intended to serve, or that may serve, as a pattern of something to be made; a material representation or embodiment of an ideal; sometimes, a drawing; a plan; as, the clay model of a sculpture; the inventor's model of a machine.
a.
Suitable to be taken as a model or pattern; as, a model house; a model husband.
v. i.
Durable; not subject to overthrow or change; firm; as, a stable foundation; a stable position.
a.
Liable to, or subjected by law to, taxation; as, ratable estate.
v. i.
Firmly established; not easily moved, shaken, or overthrown; fixed; as, a stable government.
v. i.
To dwell or lodge in a stable; to dwell in an inclosed place; to kennel.
n.
The fiber of wool, cotton, flax, or the like; as, a coarse staple; a fine staple; a long or short staple.
v. t.
To sort according to its staple; as, to staple cotton.
adv.
In a stable manner; firmly; fixedly; steadily; as, a government stably settled.
n.
Anything which serves, or may serve, as an example for imitation; as, a government formed on the model of the American constitution; a model of eloquence, virtue, or behavior.
v. t.
To plan or form after a pattern; to form in model; to form a model or pattern for; to shape; to mold; to fashion; as, to model a house or a government; to model an edifice according to the plan delineated.
v. i.
A house, shed, or building, for beasts to lodge and feed in; esp., a building or apartment with stalls, for horses; as, a horse stable; a cow stable.
n.
A stable keeper.
a.
Not stable; not standing fast or firm; unstable; prone to change or recede from a purpose; mutable; inconstant.
a.
Being of reasonable or suitable size; as, sizable timber; sizable bulk.
v. i.
To make a copy or a pattern; to design or imitate forms; as, to model in wax.
v. t.
To put or keep in a stable.