{"id":"https://openalex.org/W7166463527","doi":"https://doi.org/10.4204/eptcs.447.27","title":"On Modal Logics of Connectedness in Metric Spaces","display_name":"On Modal Logics of Connectedness in Metric Spaces","publication_year":2026,"publication_date":"2026-06-28","ids":{"openalex":"https://openalex.org/W7166463527","doi":"https://doi.org/10.4204/eptcs.447.27"},"language":"en","primary_location":{"id":"doi:10.4204/eptcs.447.27","is_oa":true,"landing_page_url":"https://doi.org/10.4204/eptcs.447.27","pdf_url":"https://eptcs.web.cse.unsw.edu.au/paper.cgi?AiML2026.27.pdf","source":{"id":"https://openalex.org/S4210216316","display_name":"Electronic Proceedings in Theoretical Computer Science","issn_l":"2075-2180","issn":["2075-2180"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310318029","host_organization_name":"Open Publishing Association","host_organization_lineage":["https://openalex.org/P4310318029"],"host_organization_lineage_names":["Open Publishing Association"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Proceedings in Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://eptcs.web.cse.unsw.edu.au/paper.cgi?AiML2026.27.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139541411","display_name":"John Harding","orcid":null},"institutions":[{"id":"https://openalex.org/I10052268","display_name":"New Mexico State University","ror":"https://ror.org/00hpz7z43","country_code":"US","type":"education","lineage":["https://openalex.org/I10052268"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Harding","raw_affiliation_strings":["New Mexico State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"New Mexico State University","institution_ids":["https://openalex.org/I10052268"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5139533838","display_name":"Ilya Shapirovsky","orcid":null},"institutions":[{"id":"https://openalex.org/I10052268","display_name":"New Mexico State University","ror":"https://ror.org/00hpz7z43","country_code":"US","type":"education","lineage":["https://openalex.org/I10052268"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ilya Shapirovsky","raw_affiliation_strings":["New Mexico State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"New Mexico State University","institution_ids":["https://openalex.org/I10052268"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I10052268"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.82179809,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"447","issue":null,"first_page":"484","last_page":"499"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.40310001373291016,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.40310001373291016,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.2092999964952469,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.09889999777078629,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.7017999887466431},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.5472000241279602},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.5034999847412109},{"id":"https://openalex.org/keywords/social-connectedness","display_name":"Social connectedness","score":0.4652999937534332},{"id":"https://openalex.org/keywords/t-norm","display_name":"T-norm","score":0.43459999561309814},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.43149998784065247},{"id":"https://openalex.org/keywords/accessibility-relation","display_name":"Accessibility relation","score":0.40049999952316284},{"id":"https://openalex.org/keywords/injective-metric-space","display_name":"Injective metric space","score":0.39899998903274536},{"id":"https://openalex.org/keywords/convex-metric-space","display_name":"Convex metric space","score":0.39329999685287476},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.39239999651908875}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7985000014305115},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.7017999887466431},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.5472000241279602},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5281999707221985},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.5034999847412109},{"id":"https://openalex.org/C201943243","wikidata":"https://www.wikidata.org/wiki/Q7551008","display_name":"Social connectedness","level":2,"score":0.4652999937534332},{"id":"https://openalex.org/C2721081","wikidata":"https://www.wikidata.org/wiki/Q2383161","display_name":"T-norm","level":5,"score":0.43459999561309814},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.43149998784065247},{"id":"https://openalex.org/C11191006","wikidata":"https://www.wikidata.org/wiki/Q2663311","display_name":"Accessibility relation","level":4,"score":0.40049999952316284},{"id":"https://openalex.org/C177547787","wikidata":"https://www.wikidata.org/wiki/Q6034319","display_name":"Injective metric space","level":3,"score":0.39899998903274536},{"id":"https://openalex.org/C196613150","wikidata":"https://www.wikidata.org/wiki/Q3966092","display_name":"Convex metric space","level":3,"score":0.39329999685287476},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.39239999651908875},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3817000091075897},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.3709999918937683},{"id":"https://openalex.org/C191226916","wikidata":"https://www.wikidata.org/wiki/Q5384710","display_name":"Equivalence of metrics","level":4,"score":0.3684000074863434},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.35499998927116394},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.35100001096725464},{"id":"https://openalex.org/C129301229","wikidata":"https://www.wikidata.org/wiki/Q741865","display_name":"Uniform continuity","level":3,"score":0.34439998865127563},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.33880001306533813},{"id":"https://openalex.org/C162329640","wikidata":"https://www.wikidata.org/wiki/Q332648","display_name":"Covering space","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C47776270","wikidata":"https://www.wikidata.org/wiki/Q1455249","display_name":"Topological vector space","level":3,"score":0.3253999948501587},{"id":"https://openalex.org/C145084290","wikidata":"https://www.wikidata.org/wiki/Q2713824","display_name":"Metric map","level":4,"score":0.30390000343322754},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.3034999966621399},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2928999960422516},{"id":"https://openalex.org/C140936041","wikidata":"https://www.wikidata.org/wiki/Q1801244","display_name":"Zero-dimensional space","level":4,"score":0.290800005197525},{"id":"https://openalex.org/C153782549","wikidata":"https://www.wikidata.org/wiki/Q175116","display_name":"Discrete space","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C106558176","wikidata":"https://www.wikidata.org/wiki/Q284347","display_name":"T1 space","level":5,"score":0.28040000796318054},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2786000072956085},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.2782000005245209},{"id":"https://openalex.org/C109023228","wikidata":"https://www.wikidata.org/wiki/Q257272","display_name":"Separated sets","level":5,"score":0.26969999074935913},{"id":"https://openalex.org/C154497576","wikidata":"https://www.wikidata.org/wiki/Q7247777","display_name":"Product metric","level":3,"score":0.2694999873638153},{"id":"https://openalex.org/C174265945","wikidata":"https://www.wikidata.org/wiki/Q1142889","display_name":"Isolated point","level":4,"score":0.26100000739097595},{"id":"https://openalex.org/C41261874","wikidata":"https://www.wikidata.org/wiki/Q3855712","display_name":"Intrinsic metric","level":4,"score":0.26019999384880066}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.4204/eptcs.447.27","is_oa":true,"landing_page_url":"https://doi.org/10.4204/eptcs.447.27","pdf_url":"https://eptcs.web.cse.unsw.edu.au/paper.cgi?AiML2026.27.pdf","source":{"id":"https://openalex.org/S4210216316","display_name":"Electronic Proceedings in Theoretical Computer Science","issn_l":"2075-2180","issn":["2075-2180"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310318029","host_organization_name":"Open Publishing Association","host_organization_lineage":["https://openalex.org/P4310318029"],"host_organization_lineage_names":["Open Publishing Association"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Proceedings in Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2606.31880","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.31880","pdf_url":"https://arxiv.org/pdf/2606.31880","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.4204/eptcs.447.27","is_oa":true,"landing_page_url":"https://doi.org/10.4204/eptcs.447.27","pdf_url":"https://eptcs.web.cse.unsw.edu.au/paper.cgi?AiML2026.27.pdf","source":{"id":"https://openalex.org/S4210216316","display_name":"Electronic Proceedings in Theoretical Computer Science","issn_l":"2075-2180","issn":["2075-2180"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310318029","host_organization_name":"Open Publishing Association","host_organization_lineage":["https://openalex.org/P4310318029"],"host_organization_lineage_names":["Open Publishing Association"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Proceedings in Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4266027607","display_name":"RTG: Research Training Group in Logic and its Application","funder_award_id":"2231414","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7166463527.pdf","grobid_xml":"https://content.openalex.org/works/W7166463527.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"For":[0],"a":[1,12,23,37,45,47,57,68,79,104],"positive":[2],"number":[3],"a,":[4],"each":[5],"metric":[6,62,92],"space":[7,25],"carries":[8],"the":[9,33,65,74,83,88,95,98,114],"relation":[10],"D":[11,36,46],"consisting":[13],"of":[14,19,52,60,70,82,85],"those":[15],"pairs":[16],"that":[17,110],"are":[18],"distance":[20,71,106],"less":[21],"than":[22],"apart.A":[24],"X":[26],"is":[27,39,44],"said":[28],"to":[29],"be":[30],"a-connected,":[31],"if":[32],"graph":[34],"(X,":[35],")":[38],"connected":[40,86],"(that":[41],"is,":[42],"there":[43],"-path":[48],"between":[49],"every":[50],"pair":[51],"points":[53],"in":[54,64,94],"X).We":[55],"give":[56,78],"complete":[58,80],"axiomatization":[59,81],"a-connected":[61],"spaces":[63,93],"language":[66,96],"with":[67,97],"family":[69],"modalities":[72],"and":[73,103],"universal":[75,101],"modality.Then":[76],"we":[77],"logic":[84],"(in":[87],"classical":[89],"topological":[90,99],"sense)":[91],"modality,":[100,102],"single":[105],"modality.We":[107],"also":[108],"show":[109],"these":[111],"logics":[112],"have":[113],"finite":[115],"model":[116],"property.":[117]},"counts_by_year":[],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2026-06-29T00:00:00"}