First-order_logic - Wikiparency

# First-order logic ## ALGORITHM — First-order logic (MicroSim) (three.js) *Interactive microsim added from the ALGORITHM hub · live: https://wikitube-3d-microsims.netlify.app/First-order_logic.html* ## Controls -> what each maps to (three.js) | Control | Maps to | Range / values | Meaning | |---|---|---|---| | IsRed(x) | Unary color predicate | Choice (1 of 6) | Highlights every domain object that is red | | IsBlue(x) | Unary color predicate | Choice (1 of 6) | Highlights every blue object | | IsGreen(x) | Unary color predicate | Choice (1 of 6) | Highlights every green object | | IsSphere(x) | Unary shape predicate | Choice (1 of 6) | Highlights every object that is a sphere | | IsCube(x) | Unary shape predicate | Choice (1 of 6) | Highlights every cube | | IsCone(x) | Unary shape predicate | Choice (1 of 6) | Highlights every cone | <div class="microsim-player">  <p class="wt-pending"><strong>Microsim staged, not yet on the CDN.</strong> <code>First-order_logic.html</code> is built and deploy-ready in <code>Microsims for Dissemination/</code>, but the Netlify project still serves the geometry+spintronics set only. The player is disabled until the deploy lands; the explanatory text below is unchanged.</p>   </div> ## About this microsim The sim draws a small domain of objects — colored geometric solids — and lets you evaluate one predicate against every object at once. IsRed(x), IsBlue(x), and IsGreen(x) filter the domain by color; IsSphere(x), IsCube(x), and IsCone(x) filter it by shape. As you switch among the six choices, the canvas highlights exactly the objects that make the chosen predicate true — that predicate's *extension* over the domain. This is show-before-tell: before meeting the formal definition of an interpretation, you can see that a predicate is just the set of domain objects for which it holds, and that this set is what quantifiers count over. ## Links (Wikipedia order)  `ACL2` · `Abelian_group` · `Absorption_(logic)` · `Abstract_algebra` · `Abstract_logic` · `Academic_Press` · `Ackermann_set_theory` · `Alan_Turing` · `Aleph_number` · `Alfred_Tarski` · `Algebra` · `Algebraic_logic` · [[Algorithm]] · `Alonzo_Church` · `Alphabet_(formal_languages)` · `American_Mathematical_Society` · `Amsterdam` · `Argument` · `Arithmetic` · `Arity` · `Association_for_Symbolic_Logic` · `Associative_property` · `Atomic_formula` · `Atomic_model_(mathematical_logic)` · `Atomic_sentence` · `Automata_theory` · `Automated_theorem_proving` · `Axiom` · `Axiom_of_choice` · `Axiom_of_extensionality` · `Axiom_schema` · `Axiomatic_system` · `Banach–Tarski_paradox` · `Ben_Goertzel` · `Berlin` · `Biconditional_elimination` · `Biconditional_introduction` · `Bijection` · `Binary_operation` · `Boolean-valued_function` · `Boolean_algebra` · `Boolean_algebras_canonically_defined` · `Boolean_function` · `Cantor's_diagonal_argument` · `Cantor's_paradox` · `Cantor's_theorem` · `Cardinal_number` · `Cardinality` · `Cartesian_product` · `Categorical_theory` · `Category_(mathematics)` · `Category_of_sets` · `Category_theory` · `Charles_Sanders_Peirce` · `Church_encoding` · `Church–Turing_thesis` · `Class_(set_theory)` · `Classical_logic` · `Codomain` · `Commutative_property` · `Compactness_theorem` · `Complement_(set_theory)` · `Complete_theory` · `Completeness_(logic)` · `Computability_theory` · `Computable_function` · `Computable_set` · `Computably_enumerable_set` · `Computational_complexity` · `Computational_complexity_theory` · `Computational_linguistics` · [[Computer_science]] · `Concrete_category` · `Conditional_proof` · `Congruence_relation` · `Conjunction_elimination` · `Conjunction_introduction` · `Conservative_extension` · `Consistency` · `Constructible_universe` · `Construction_of_the_real_numbers` · `Constructive_dilemma` · `Constructive_set_theory` · `Context-free_grammar` · `Continuum_hypothesis` · `Converse_(logic)` · `Converse_nonimplication` · `Countable_set` · `Cylindric_algebra` · `Data_type` · `David_Hilbert` · `De_Morgan's_laws` · `Decidability_(logic)` · `Decision_problem` · `Destructive_dilemma` · `Diagram_(mathematical_logic)` · `Directed_graph` · `Disjunction_elimination` · `Disjunction_introduction` · `Disjunctive_syllogism` · `Distributive_property` · `Domain_of_a_function` · `Domain_of_discourse` · `Double_negation` · `Dover_Publications` · `Edward_N._Zalta` · `Elementary_class` · `Elementary_equivalence` · `Elementary_function_arithmetic` · `Elliott_Mendelson` · `Elsevier` · `Empty_set` · `Encyclopedia_of_Mathematics` · `Entscheidungsproblem` · `Enumeration` · `Equality_(mathematics)` · `Equiconsistency` · `Equivalence_relation` · `Euclid's_Elements` · `Euclidean_geometry` · `Exclusive_or` · `Existential_generalization` · `Existential_instantiation` · `Existential_quantification` · `Exportation_(logic)` · `Expression_(mathematics)` · `Extension_by_new_constant_and_function_names` · `Extensionality` · `FO(.)` · `False_(logic)` · `Finitary_relation` · `Finite-valued_logic` · `Finite_model_theory` · `Finite_set` · `Fixed-point_logic` · `Forcing_(mathematics)` · `Formal_grammar` · `Formal_language` · `Formal_methods` · `Formal_proof` · `Formal_specification` · [[Formal_system]] · `Formal_verification` · `Formation_rule` · `Foundations_of_geometry` · `Foundations_of_mathematics` · `Free_logic` · `Free_variables_and_bound_variables` · `Function_(mathematics)` · `Functional_completeness` · `Fuzzy_set` · `Game_semantics` · `Garden_City,_New_York` · `General_set_theory` · `George_Boolos` · `Gottlob_Frege` · `Graph_(discrete_mathematics)` · `Grothendieck_universe` · `Ground_expression` · `Group_(mathematics)` · `Gunther_Schmidt` · `Gödel's_completeness_theorem` · `Gödel's_incompleteness_theorems` · `Gödel_numbering` · `Halting_problem` · `Harvard_University_Press` · `Harvey_Friedman_(mathematician)` · `Heidelberg` · `Heinz-Dieter_Ebbinghaus` · `Herbert_Enderton` · `Hereditary_set` · `Higher-order_logic` · `Hilbert's_axioms` · `Hilbert_system` · `History_of_logic` · `Hypothetical_syllogism` · `Identity_of_indiscernibles` · `Image_(mathematics)` · `Inaccessible_cardinal` · `Independence_(mathematical_logic)` · `Inference` · `Infinitary_logic` · `Infinite-valued_logic` · `Infinite_set` · [[Information_theory]] · `Inhabited_set` · `Injective_function` · `Integer` · `Interpretation_(logic)` · `Interpretation_(model_theory)` · `Intersection_(set_theory)` · `Intuitionistic_logic` · `Isomorphism` · `Jeremy_Avigad` · `John_Etchemendy` · `Jon_Barwise` · `Józef_Maria_Bocheński` · `Kolmogorov_complexity` · `Kripke–Platek_set_theory` · `Kurt_Gödel` · `Lambda_calculus` · `Large_cardinal` · `Latin_script` · `Lattice_(order)` · `Lemma_(mathematics)` · `Lindström's_theorem` · `Linguistics` · `List_of_axioms` · `List_of_first-order_theories` · `List_of_formal_systems` · `List_of_logic_symbols` · `List_of_mathematical_theories` · `List_of_rules_of_inference` · `List_of_set_identities_and_relations` · `List_of_statements_independent_of_ZFC` · [[Logic]] · [[Logic_gate]] · `Logic_of_graphs` · `Logic_translation` · `Logical_NOR` · `Logical_biconditional` · `Logical_conjunction` · `Logical_connective` · `Logical_consequence` · `Logical_constant` · `Logical_disjunction` · `Logical_equality` · `Logical_equivalence` · `Logical_truth` · `Logicism` · `Lojban` · `London` · `Löwenheim–Skolem_theorem` · `Many-valued_logic` · `Map_(mathematics)` · `Material_conditional` · `Material_implication_(rule_of_inference)` · `Material_nonimplication` · `Mathematical_Reviews` · `Mathematical_Tripos` · `Mathematical_linguistics` · `Mathematical_logic` · `Mathematical_notation` · `Mathematical_object` · `Mathematics` · `Melvin_Fitting` · `Menlo_Park,_California` · `Metalanguage` · `Metalogic` · `Metamath` · `Method_of_analytic_tableaux` · `Mineola,_New_York` · `Minimal_axioms_for_Boolean_algebra` · `Mizar_system` · `Modal_logic` · `Model_checking` · `Model_complete_theory` · `Model_theory` · `Modus_non_excipiens` · `Modus_ponendo_tollens` · `Modus_ponens` · `Modus_tollens` · `Monadic_predicate_calculus` · `Monadic_second-order_logic` · `Morse–Kelley_set_theory` · `NIMPLY_gate` · `NP_(complexity)` · `Naive_set_theory` · `Natural_deduction` · `Natural_language_processing` · `Natural_number` · `Negation` · `Negation_introduction` · `New_Foundations` · `New_York_City` · `Non-Euclidean_geometry` · `Non-classical_logic` · `Non-logical_symbol` · `Non-standard_model` · `Non-standard_model_of_arithmetic` · `Number_theory` · `Open_formula` · `Operation_(mathematics)` · `Order_of_operations` · `Ordered_field` · `Ordered_pair` · `Ordinal_analysis` · `Ordinal_number` · `P_(complexity)` · `P_versus_NP_problem` · `Pairing_function` · `Paradoxes_of_set_theory` · `Parse_tree` · `Partition_of_a_set` · `Paul_Halmos` · `Peano_axioms` · `Peter_B._Andrews` · `Philadelphia` · `Philosophy` · `Philosophy_of_logic` · `Philosophy_of_mathematics` · `Plato` · `Plural_quantification` · `Power_set` · `Predicate_variable` · `Prime_model` · `Prime_number_theorem` · `Primitive_recursive_arithmetic` · `Primitive_recursive_function` · `Principia_Mathematica` · `Prior_Analytics` · `Production_(computer_science)` · `Programming_language` · `Programming_language_theory` · `Prolog` · `Proof_assistant` · `Proof_of_impossibility` · `Proof_theory` · [[Proposition]] · `Propositional_formula` · `Propositional_logic` · `Propositional_variable` · `Providence,_Rhode_Island` · `Quantifier_(logic)` · `Quantifier_rank` · `Raymond_Smullyan` · `Recursion` · `Regular_expression` · `Relation_(mathematics)` · `Relation_(philosophy)` · `Relation_algebra` · `Relational_algebra` · `Relational_model` · `Republic_(Plato)` · `Resolution_(logic)` · `Reverse_mathematics` · `Robinson_arithmetic` · `Routledge` · `Rule_of_inference` · `Rule_of_replacement` · `Russell's_paradox` · `SRI_International` · `Saint_Joseph's_University` · `Satisfiability` · `Saturated_model` · `Schröder–Bernstein_theorem` · `Scope_(logic)` · `Search_algorithm` · `Second-order_arithmetic` · `Second-order_logic` · `Self-verifying_theories` · `Semantic_theory_of_truth` · `Semantics` · `Sentence_(mathematical_logic)` · `Sequent_calculus` · `Set_(mathematics)` · [[Set_theory]] · `Sheffer_stroke` · `Signature_(logic)` · `Singleton_(mathematics)` · `Skolem's_paradox` · `Skolem_arithmetic` · `Socrates` · `Soundness` · `Spectrum_of_a_sentence` · `Spectrum_of_a_theory` · `Springer` · `Springer_Science+Business_Media` · `Square_of_opposition` · `Stanford_Encyclopedia_of_Philosophy` · `Stewart_Shapiro` · `Strength_(mathematical_logic)` · `Structure_(mathematical_logic)` · `Substitution_(logic)` · `Substructure_(mathematics)` · `Supertask` · `Surjective_function` · `Syllogism` · `Symbol_(formal)` · `Syntax` · `Syntax_(logic)` · `T-norm_fuzzy_logics` · `T-schema` · `Tarski's_axiomatization_of_the_reals` · `Tarski's_axioms` · `Tarski's_undefinability_theorem` · `Tarski–Grothendieck_set_theory` · `Tautology_(logic)` · `Tautology_(rule_of_inference)` · `Term_(logic)` · `Term_logic` · `Theorem` · `Theories_of_truth` · `Theory_(mathematical_logic)` · `Three-valued_logic` · `Timeline_of_mathematical_logic` · `Topology` · `Transfer_principle` · `Transitive_set` · `True_arithmetic` · `Truth_function` · `Truth_predicate` · `Truth_table` · `Truth_value` · `Tuple` · `Turing_machine` · `Two-element_Boolean_algebra` · `Type_(model_theory)` · `Type_theory` · `Ultraproduct` · `Uncountable_set` · `Undecidable_problem` · `Undergraduate_Texts_in_Mathematics` · `Union_(set_theory)` · `Uniqueness_quantification` · `Universal_generalization` · `Universal_instantiation` · `Universal_quantification` · `Universal_set` · `Universe_(mathematics)` · `Urelement` · `Validity_(logic)` · `Variable_(mathematics)` · `Venn_diagram` · `Von_Neumann_universe` · `Von_Neumann–Bernays–Gödel_set_theory` · `Well-formed_formula` · `Wiley_(publisher)` · `Wilfrid_Hodges` · `Wilhelm_Ackermann` · `Willard_Van_Orman_Quine` · `Wolfgang_Rautenberg` · `XNOR_gate` · `Zermelo–Fraenkel_set_theory` > Canonical promoted article — per-hub sections below.  *Built to the [[WT!Three_js_Microsim_Master_Class|three.js Master Class]].*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/First-order_logic) : [Wikitube](https://en.wikitube.io/wiki/First-order_logic) ## Previous hub tags Tree parent: [[Game_theory]]. Legacy hubs: none. --- *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*