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Statements (559)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:academic
gptkb:logic gptkb:mathematical_concept gptkb:philosophy branch of mathematical logic theoretical computer science concept Academic discipline Philosophical field field of logic |
| gptkbp:allows |
withdrawal of inferences
|
| gptkbp:alternativeName |
logic_family
Logic Mathematical_Logic Mathematical_logic Modal_Logic Non-monotonic_logic Philosophical_Logic Philosophy_of_mathematics Reasoning Temporal_logic constructive_mathematics formal_logic iterative_method logic_system logical_form logician mathematical_logic mathematical_method mathematical_model mathematical_theory modal_logic non-classical_logic numerical_method philosophical_logic philosophy_of_mathematics propositional_logic syllogism temporal_logic theoretical_framework theoretical_model theory type type_theory |
| gptkbp:appliesTo |
gptkb:logic
gptkb:mathematics computer science |
| gptkbp:contrastsWith |
monotonic logic
|
| gptkbp:debatedBy |
gptkb:Platonism
gptkb:mathematics gptkb:mathematical_nominalism gptkb:epistemology_of_mathematics gptkb:mathematical_structuralism constructivism logicism mathematical fictionalism existence of mathematical objects objectivity of mathematics infinity in mathematics nature of mathematical proof relationship between mathematics and reality role of logic in mathematics applicability of mathematics foundations of arithmetic mathematical empiricism mathematical intuitionism mathematical realism vs. anti-realism nature of mathematical objects paradoxes in set theory role of Gödel's incompleteness theorems role of abstraction in mathematics role of axioms in mathematics role of category theory in mathematics role of completeness in mathematics role of computation in mathematics role of computer-assisted proof role of consistency in mathematics role of creativity in mathematics role of decidability in mathematics role of diagrams in mathematics role of experimental mathematics role of explanation in mathematics role of intuition in mathematical discovery role of intuition in mathematics role of language in mathematics role of mathematical applicability role of mathematical beauty role of mathematical communication role of mathematical culture role of mathematical discovery role of mathematical education role of mathematical explanation role of mathematical generality role of mathematical invention role of mathematical notation role of mathematical practice role of mathematical proof assistants role of mathematical rigor role of mathematical simplicity role of mathematics in philosophy role of model theory role of models in mathematics role of philosophy in mathematics role of proof in mathematics role of proof theory role of recursion theory role of set theory in mathematics role of undecidability in mathematics role of visualization in mathematics status of mathematical statements |
| gptkbp:describes |
reasoning with incomplete information
|
| gptkbp:developedBy |
gptkb:Alonzo_Church
gptkb:Bertrand_Russell gptkb:Robin_Milner gptkb:Haskell_Curry gptkb:Jean-Yves_Girard gptkb:Per_Martin-Löf gptkb:Thoralf_Skolem gptkb:William_Howard gptkb:C.I._Lewis gptkb:Frank_P._Ramsey gptkb:John_C._Reynolds 19th century 20th century late 20th century |
| gptkbp:field |
gptkb:artificial_intelligence
gptkb:logic |
| gptkbp:fieldOfStudy |
gptkb:Mathematics
gptkb:philosophy |
| gptkbp:firstDescribed |
early 20th century
|
| gptkbp:formedBy |
gptkb:Kripke_Semantics
|
| gptkbp:hasApplication |
gptkb:Ethics
gptkb:Metaphysics gptkb:knowledge_representation gptkb:Dynamic_Logic gptkb:Epistemology gptkb:Fuzzy_Logic gptkb:Automated_Reasoning gptkb:Deontic_Reasoning gptkb:Description_Logics gptkb:Modal_Realism gptkb:Multi-agent_Systems gptkb:Security_Protocols gptkb:Counterfactual_Reasoning gptkb:Game_Theory Ontology Verification Linguistic Analysis Temporal Reasoning |
| gptkbp:hasAxiom |
gptkb:S5
B D T S4 S4.2 S4.3 |
| gptkbp:hasProperty |
conclusions can be invalidated by new information
|
| gptkbp:hasSubfield |
gptkb:logic
gptkb:set_theory gptkb:Curry–Howard_correspondence gptkb:Game_theory gptkb:Martin-Löf_type_theory gptkb:dependent_type_theory gptkb:homotopy_type_theory gptkb:linear_type_theory gptkb:polymorphic_type_theory gptkb:Automata_theory gptkb:Abductive_logic gptkb:Affine_logic gptkb:Branching_time_logic gptkb:Defeasible_logic gptkb:Dialectical_logic gptkb:Dynamic_epistemic_logic gptkb:Dynamic_logic gptkb:Free_logic gptkb:Higher-order_logic gptkb:Hybrid_logic gptkb:Inductive_logic gptkb:Interval_temporal_logic gptkb:Justification_logic gptkb:Lambek_calculus gptkb:Linear_temporal_logic gptkb:Lukasiewicz_logic gptkb:Modal_μ-calculus gptkb:Probabilistic_logic gptkb:Quantum_logic gptkb:Syllogistic_logic gptkb:T-norm_fuzzy_logic gptkb:Term_logic gptkb:Transcendental_logic gptkb:Gödel_logic gptkb:Set_theory Constructivism analytic philosophy computability theory model theory philosophy of identity philosophy of language philosophy of mind philosophy of science proof theory recursion theory philosophy of logic fuzzy logic intuitionistic logic Model theory Proof theory dynamic logic philosophy of action philosophy of probability Category theory intersection type theory recursive type theory simple type theory substructural type theory many-valued logic paraconsistent logic philosophy of reference deontic logic philosophy of artificial intelligence philosophy of computation quantum logic Algebraic logic Classical logic Computational logic Conditional logic Counterfactual logic Default logic Deontic logic Description logic Description logic with inverse roles Description logic with nominals Description logic with number restrictions Description logic with role antisymmetry Description logic with role asymmetry Description logic with role chains Description logic with role complement Description logic with role composition Description logic with role difference Description logic with role disjointness Description logic with role equivalence Description logic with role exclusion Description logic with role functionality Description logic with role hierarchies Description logic with role implication Description logic with role inclusion Description logic with role inclusion axioms Description logic with role intersection Description logic with role irreflexivity Description logic with role negation Description logic with role reflexivity Description logic with role symmetry Description logic with role transitivity Description logic with role union Description logic with role value assignments Description logic with role value chains Description logic with role value complements Description logic with role value compositions Description logic with role value constraints Description logic with role value dependencies Description logic with role value exclusions Description logic with role value hierarchies Description logic with role value implications Description logic with role value inclusion axioms Description logic with role value intersections Description logic with role value maps Description logic with role value negations Description logic with role value restrictions Description logic with role value unions Description logic with transitive roles Epistemic logic Informal logic Intuitionistic logic Linear logic Many-valued logic Modal description logic Modal logic Non-classical logic Paraconsistent logic Philosophical logic Predicate logic Propositional logic Recursion theory Relevant logic Residuated logic Subjunctive logic Substructural logic Symbolic logic Type theory epistemic logic non-monotonic logic relevance logic substructural logic dialetheism philosophy of truth philosophy of reasoning philosophy of information free logic philosophy of category theory philosophy of set theory philosophy of meaning philosophy of necessity alethic logic defeasible logic erotetic logic philosophy of Platonism philosophy of abduction philosophy of anti-realism philosophy of argumentation philosophy of conditionals philosophy of constructivism philosophy of counterfactuals philosophy of deduction philosophy of entailment philosophy of explanation philosophy of finitism philosophy of formal systems philosophy of formalism philosophy of induction philosophy of inference philosophy of intuitionism philosophy of logic programming philosophy of logicism philosophy of modality philosophy of model theory philosophy of nominalism philosophy of paradoxes philosophy of possibility philosophy of predicativism philosophy of proof theory philosophy of quantification philosophy of realism philosophy of structuralism philosophy of vagueness |
| https://www.w3.org/2000/01/rdf-schema#label |
logic
|
| gptkbp:includes |
gptkb:Necessity
gptkb:Platonism gptkb:autoepistemic_logic constructivism formal semantics logicism intuitionism structuralism default logic Possibility circumscription |
| gptkbp:influenced |
gptkb:artificial_intelligence
gptkb:logic computer science linguistics theoretical computer science |
| gptkbp:notableAchievement |
gptkb:Church–Turing_thesis
gptkb:Gödel's_incompleteness_theorems gptkb:Russell's_paradox gptkb:Zermelo–Fraenkel_set_theory gptkb:Cantor's_theorem gptkb:Turing's_halting_problem gptkb:Löwenheim–Skolem_theorem gptkb:Compactness_theorem gptkb:Completeness_theorem gptkb:Axiom_of_choice gptkb:Cohen's_forcing |
| gptkbp:notableContributor |
gptkb:Alfred_North_Whitehead
gptkb:Bertrand_Russell gptkb:David_Hilbert gptkb:Georg_Cantor gptkb:Imre_Lakatos gptkb:Kurt_Gödel gptkb:Ludwig_Wittgenstein gptkb:Michael_Dummett gptkb:Richard_Dedekind gptkb:Paul_Benacerraf gptkb:Hartry_Field gptkb:L.E.J._Brouwer gptkb:Frege |
| gptkbp:notableFigure |
gptkb:Alan_Turing
gptkb:Alfred_Tarski gptkb:Alonzo_Church gptkb:Bertrand_Russell gptkb:David_Hilbert gptkb:David_Lewis gptkb:Emil_Post gptkb:Georg_Cantor gptkb:John_von_Neumann gptkb:Kurt_Gödel gptkb:Michael_Dummett gptkb:Paul_Cohen gptkb:Ruth_Barcan_Marcus gptkb:Saul_Kripke gptkb:Stephen_Kleene gptkb:W.V.O._Quine gptkb:Thoralf_Skolem gptkb:Kit_Fine gptkb:Peter_Geach gptkb:Timothy_Williamson gptkb:Arthur_Prior gptkb:Graham_Priest gptkb:Susan_Haack gptkb:Jaakko_Hintikka John N. Crossley |
| gptkbp:notableFor |
gptkb:Java
gptkb:logic gptkb:ATS gptkb:Agda gptkb:Coq gptkb:Dafny gptkb:Elm gptkb:Epigram gptkb:F# gptkb:HOL_theorem_prover gptkb:Haskell gptkb:Lean gptkb:NuPRL gptkb:OCaml gptkb:PureScript gptkb:Purescript gptkb:ReasonML gptkb:Swift gptkb:TypeScript gptkb:proof-carrying_code gptkb:Idris gptkb:C# gptkb:Kotlin gptkb:Rust gptkb:Scala gptkb:category_theory formal methods formal semantics proof theory ML automated theorem proving homotopy theory compiler design constructive logic dependently typed programming functional programming languages logic programming mathematical foundations mathematical proof assistants proof assistants static analysis type checking type inference |
| gptkbp:operator |
Necessarily
Possibly |
| gptkbp:parentField |
gptkb:logic
gptkb:mathematics gptkb:philosophy |
| gptkbp:publishedIn |
gptkb:Journal_of_Symbolic_Logic
gptkb:Annals_of_Pure_and_Applied_Logic gptkb:Archive_for_Mathematical_Logic gptkb:Mathematical_Logic_Quarterly gptkb:Notre_Dame_Journal_of_Formal_Logic |
| gptkbp:relatedTo |
gptkb:artificial_intelligence
gptkb:lambda_calculus gptkb:logic gptkb:mathematics gptkb:philosophy gptkb:set_theory gptkb:Classical_Logic gptkb:category_theory gptkb:Non-classical_Logic computer science constructivism metaphysics philosophy of language theoretical computer science intuitionistic logic belief revision defeasible reasoning |
| gptkbp:studies |
gptkb:identity
gptkb:logic gptkb:mathematics gptkb:set_theory gptkb:Proof gptkb:Possible_Worlds Truth completeness computability theory formal systems foundations of mathematics independence model theory paradoxes proof theory recursion theory reference inference truth consistency formal languages mathematical objects quantification meaning type systems types Argumentation decidability vagueness axiomatic systems mathematical reasoning soundness Inference Logical consequence Logical form Principles of valid reasoning logical consequence logical truth expressiveness mathematical structures mathematical knowledge mathematical truth nature of mathematics Modality |
| gptkbp:subspecies |
gptkb:Deontic_Logic
gptkb:Alethic_Logic gptkb:Doxastic_Logic gptkb:Epistemic_Logic gptkb:Temporal_Logic |
| gptkbp:symbol |
□
◇ |
| gptkbp:usedIn |
gptkb:Linguistics
gptkb:artificial_intelligence gptkb:programming_language gptkb:knowledge_representation Computer Science automated reasoning formal verification proof assistants |
| gptkbp:uses |
gptkb:lambda_calculus
gptkb:logic gptkb:set_theory gptkb:first-order_logic gptkb:second-order_logic formal systems model theory predicate logic proof theory symbolic logic formal languages logical connectives quantifiers axioms proofs axiomatic systems rules of inference symbolic notation |
| gptkbp:bfsParent |
gptkb:Alan_Turing
gptkb:Bertrand_Russell gptkb:David_Hilbert gptkb:Gottfried_Wilhelm_Leibniz gptkb:John_Myhill gptkb:John_von_Neumann gptkb:Josiah_Royce gptkb:Walter_Pitts gptkb:Yehoshua_Bar-Hillel gptkb:milk gptkb:philosophy gptkb:print |
| gptkbp:bfsLayer |
3
|