{"id":"https://openalex.org/W7127316405","doi":"https://doi.org/10.48550/arxiv.2602.01856","title":"Preservation Theorems for Unravelling-Invariant Classes: A Uniform Approach for Modal Logics and Graph Neural Networks","display_name":"Preservation Theorems for Unravelling-Invariant Classes: A Uniform Approach for Modal Logics and Graph Neural Networks","publication_year":2026,"publication_date":"2026-02-02","ids":{"openalex":"https://openalex.org/W7127316405","doi":"https://doi.org/10.48550/arxiv.2602.01856"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.01856","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.01856","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.01856","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5124898949","display_name":"Przemys\u0142aw Andrzej Wa\u0142\u0119ga","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Wa\u0142\u0119ga, Przemys\u0142aw Andrzej","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5124926918","display_name":"Bernardo Cuenca Grau","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Grau, Bernardo Cuenca","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5124898949"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.6935999989509583,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.6935999989509583,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.10639999806880951,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.04969999939203262,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.7080000042915344},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6080999970436096},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.5706999897956848},{"id":"https://openalex.org/keywords/modal-\u03bc-calculus","display_name":"Modal \u03bc-calculus","score":0.5594000220298767},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.5584999918937683},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.4564000070095062},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.4528000056743622},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.43799999356269836}],"concepts":[{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.7080000042915344},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6811000108718872},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6080999970436096},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.5706999897956848},{"id":"https://openalex.org/C173125200","wikidata":"https://www.wikidata.org/wiki/Q5275729","display_name":"Modal \u03bc-calculus","level":5,"score":0.5594000220298767},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.5584999918937683},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47279998660087585},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.4564000070095062},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.4528000056743622},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4505000114440918},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.43799999356269836},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.4368000030517578},{"id":"https://openalex.org/C78344899","wikidata":"https://www.wikidata.org/wiki/Q638442","display_name":"Modal operator","level":4,"score":0.4050000011920929},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.3919999897480011},{"id":"https://openalex.org/C160131679","wikidata":"https://www.wikidata.org/wiki/Q2462350","display_name":"Kripke semantics","level":4,"score":0.3862000107765198},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3580999970436096},{"id":"https://openalex.org/C2779808786","wikidata":"https://www.wikidata.org/wiki/Q6664603","display_name":"Locality","level":2,"score":0.33889999985694885},{"id":"https://openalex.org/C11191006","wikidata":"https://www.wikidata.org/wiki/Q2663311","display_name":"Accessibility relation","level":4,"score":0.33090001344680786},{"id":"https://openalex.org/C86602344","wikidata":"https://www.wikidata.org/wiki/Q7667918","display_name":"T-norm fuzzy logics","level":5,"score":0.31610000133514404},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.3059999942779541},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2840000092983246}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.01856","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.01856","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.01856","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.01856","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,22,50,96],"study":[1],"preservation":[2,53,64,77,154],"theorems":[3],"for":[4,146,156],"modal":[5,42,62,74,85,138,175,187],"logics":[6,43],"over":[7],"finite":[8,125,134],"structures":[9],"with":[10,57,68,80,180],"respect":[11],"to":[12,129,185],"three":[13],"fundamental":[14],"semantic":[15],"relations:":[16],"embeddings,":[17],"injective":[18,66,157],"homomorphisms,":[19,158],"and":[20,44,76,114],"homomorphisms.":[21],"focus":[23],"on":[24,102],"classes":[25,103],"of":[26,104,107,136,150,165],"pointed":[27],"Kripke":[28],"models":[29,106],"that":[30,52,98,115,169],"are":[31],"invariant":[32],"under":[33,54,65,78],"bounded":[34,109],"unravellings,":[35],"a":[36,92,112,124,161],"natural":[37],"locality":[38],"condition":[39],"satisfied":[40],"by":[41,45],"graph":[46],"neural":[47],"networks":[48],"(GNNs).":[49],"show":[51],"embeddings":[55],"coincides":[56],"definability":[58,69,81],"in":[59,70,82],"existential":[60,71,83],"graded":[61,73,174],"logic;":[63,75],"homomorphisms":[67,79],"positive":[72,84],"logic.":[86,188],"A":[87],"key":[88],"technical":[89],"contribution":[90],"is":[91,119],"structural":[93],"well-quasi-ordering":[94,122],"result.":[95],"prove":[97],"the":[99,116,147],"embedding":[100],"relation":[101],"tree-shaped":[105],"uniformly":[108],"height":[110],"forms":[111],"well-quasi-order,":[113],"bounded-height":[117],"assumption":[118],"essential.":[120],"This":[121],"yields":[123],"minimal-tree":[126],"argument":[127],"leading":[128],"explicit":[130],"syntactic":[131],"characterisations":[132],"via":[133],"disjunctions":[135],"(graded)":[137],"formulae.":[139],"As":[140],"an":[141],"application,":[142],"we":[143,159],"derive":[144],"consequences":[145],"expressive":[148],"power":[149],"GNNs.":[151],"Using":[152],"our":[153],"theorem":[155],"obtain":[160],"new":[162],"logical":[163],"characterisation":[164],"monotonic":[166,178],"GNNs,":[167],"showing":[168],"they":[170],"capture":[171],"exactly":[172],"existential-positive":[173,186],"logic,":[176],"while":[177],"GNNs":[179],"MAX":[181],"aggregation":[182],"correspond":[183],"precisely":[184]},"counts_by_year":[],"updated_date":"2026-02-04T23:14:21.375766","created_date":"2026-02-04T00:00:00"}
