Statements (214)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:Logic
gptkb:musical_group |
| gptkbp:character_traits |
D4 (dihedral group of order 8) x Z2
D4 (dihedral group of order 8) |
| gptkbp:contains |
identity permutation
|
| gptkbp:developed_by |
gptkb:C._I._Lewis
|
| gptkbp:difficulty |
gptkb:true
|
| gptkbp:element |
gptkb:24
permutations of 4 elements (1,2)(3,4) (1,2,3,4) (1,3)(2,4) (1,4)(2,3) (1,4,3,2) |
| gptkbp:has |
on 4 points
|
| gptkbp:has_applications_in |
in algebra
|
| gptkbp:has_character_table |
5 rows, 5 columns
|
| gptkbp:has_conjugacy_class_sizes |
1, 6, 8, 6, 3
1, 6, 8, 3, 6 |
| gptkbp:has_conjugacy_classes |
gptkb:5
|
| gptkbp:has_exhibition |
⟨a,b | a^2 = b^3 = (ab)^2 = 1⟩
|
| gptkbp:has_generators |
(1,2), (1,2,3,4)
|
| gptkbp:has_influence_on |
philosophical logic
computational logic modal logics |
| gptkbp:has_permutation_representation |
4! = 24
|
| gptkbp:has_produced |
3-cycles
transpositions two transpositions |
| gptkbp:has_property |
reflexivity
transitivity |
| gptkbp:has_representations |
in various fields of mathematics
|
| gptkbp:has_subgroup |
gptkb:W3_C
gptkb:S4 gptkb:A4 gptkb:S3 gptkb:D4 C4 S2 Z2 x Z2 V4 (Klein four-group) S4 itself |
| gptkbp:has_symmetric_group |
S_n for n=4
|
| gptkbp:has_variants |
S4.2
S4.3 |
| https://www.w3.org/2000/01/rdf-schema#label |
S4
|
| gptkbp:is |
false
|
| gptkbp:is_a |
gptkb:musical_group
axiomatic system transitive modal logic |
| gptkbp:is_a_center_for |
gptkb:musical_group
|
| gptkbp:is_agroup |
gptkb:true
|
| gptkbp:is_applied_in |
theory of knowledge
formal epistemology modal logic temporal logic deontic logic dynamic logic |
| gptkbp:is_characterized_by |
axioms
modal axioms rules of inference necessity and possibility operators |
| gptkbp:is_compared_to |
gptkb:K
S5 |
| gptkbp:is_cyclic |
false
|
| gptkbp:is_finite_group |
gptkb:true
|
| gptkbp:is_non_abelian |
gptkb:true
|
| gptkbp:is_related_to |
gptkb:crypt
gptkb:topology gptkb:Artificial_Intelligence gptkb:Quantum_Mechanics gptkb:strategy gptkb:machine_learning gptkb:sociology gptkb:statistical_mechanics gptkb:philosophy gptkb:psychology Galois theory geometry linear algebra mathematical physics algorithm design computation theory information theory linguistics mathematical modeling number theory operations research representation theory algebraic topology bioinformatics data science signal processing coding theory finite fields graph theory mathematical logic network theory complexity theory control theory chaos theory dynamical systems econometrics systems theory discrete mathematics computational biology Kripke semantics mathematical finance combinatorial designs permutation group S4.1 S4.4 S4.5 |
| gptkbp:is_represented_in |
gptkb:Cayley_graph
permutation matrices group of permutations permutations of 4 elements 4x4 permutation matrices |
| gptkbp:is_studied_in |
gptkb:Mathematics
theoretical computer science abstract algebra philosophy of language |
| gptkbp:is_the_symmetry_group_of |
gptkb:Polygon
|
| gptkbp:is_transitive |
gptkb:true
|
| gptkbp:is_used_in |
gptkb:crypt
gptkb:original_programming gptkb:Artificial_Intelligence gptkb:computer_science gptkb:Mathematics gptkb:quantum_computing gptkb:Physics gptkb:strategy gptkb:urban_planning gptkb:machine_learning gptkb:logistics gptkb:supply_chain_management gptkb:statistical_mechanics gptkb:musical_group gptkb:military_defense gptkb:philosophy formal verification geometry mathematical physics algorithm design cognitive science combinatorial optimization computation theory financial modeling information theory knowledge representation mathematical modeling natural language processing operations research representation theory resource allocation scheduling problems statistical modeling algebraic topology data science predictive modeling coding theory graph theory mathematical logic network theory optimization problems transportation planning network optimization climate modeling complex systems decision theory market design multi-agent systems social choice theory chaos theory combinatorics dynamical systems group actions automated reasoning healthcare analytics system dynamics program semantics theoretical linguistics design theory theoretical modeling environmental modeling knowledge-based systems ecological modeling economic modeling formal methods voting systems biological modeling computational modeling logic programming finite group theory simulation modeling medical modeling cognitive modeling psychological modeling behavioral modeling reasoning systems descriptive modeling empirical modeling exploratory modeling normative modeling organizational modeling political modeling prescriptive modeling sociological modeling |
| gptkbp:offers_degree |
gptkb:4
|
| gptkbp:order |
gptkb:24
|
| gptkbp:bfsParent |
gptkb:Dota_2
gptkb:Apple_Watch gptkb:Evil_Geniuses |
| gptkbp:bfsLayer |
4
|