{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71196"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71196","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Orthomodular Lattices and Cut Elimination","abstract":"The thesis is a start toward a positive solution of the word problem for freely generated orthomodular lattices. It was a proof theoretical 'partial' cut elimination procedure.","abstract_html":"The thesis is a start toward a positive solution of the word problem for freely generated orthomodular lattices. It was a proof theoretical 'partial' cut elimination procedure.","abstract_has_math":false,"creators":["Marble, Robert Patrick"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T06:18:00Z","date_published":"2014-12-16T06:18:00Z","updated_at":"2026-07-22T22:26:04Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8203523"],"render_values":[{"text":"(UMI)AAI8203523","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71196","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Marble, Robert Patrick"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T06:18:00Z","10000-01-01","1981"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/71196","(UMI)AAI8203523"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The thesis is a start toward a positive solution of the word problem for freely generated orthomodular lattices. It was a proof theoretical 'partial' cut elimination procedure.","A Gentzen type sequent calculus (OMO) is defined which can be seen to characterize a free orthomodular lattice L in the sense that two words u and v (on the generating set of L) are equal in L if and only if u (--->) v and v (--->) u are sequents which are derivable in the calculus OMO. Several types of applications of the cut rules of OMO are singled out and called benign cuts. They have the property that their application does not lead to the complete elimination of the atomic components of their cut formulas from their proof branches. Their use, then, does not hinder the recovery from an endsequent of information about all formulas used in a proof of that sequent, during an algorithmic process of deciding about the derivability of that sequent.","The inference rule which is used to manifest the orthomodularity of models of OMO is the rule OM:","(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)","It is shown that an OMO proof of the form","where P and Q are cut-free and contain no applications of rule OM, can be reconstructed to prove the same endsequent without the use of any cuts which are not benign.","Made available in DSpace on 2014-12-16T06:18:00Z (GMT). No. of bitstreams: 1 8203523.pdf: 1824368 bytes, checksum: a964b058f71f6c318734195980483ce9 (MD5) Previous issue date: 1981","Embargo set by: Seth Robbins for item 71362 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","89 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1981."]},{"key":"dc:title","label":"Title","values":["Orthomodular Lattices and Cut Elimination"]}]}],"canonical_facts":{"dc:creator":["Marble, Robert Patrick"],"dc:date":["2014-12-16T06:18:00Z","10000-01-01","1981"],"dc:description":["The thesis is a start toward a positive solution of the word problem for freely generated orthomodular lattices. It was a proof theoretical 'partial' cut elimination procedure.","A Gentzen type sequent calculus (OMO) is defined which can be seen to characterize a free orthomodular lattice L in the sense that two words u and v (on the generating set of L) are equal in L if and only if u (--->) v and v (--->) u are sequents which are derivable in the calculus OMO. Several types of applications of the cut rules of OMO are singled out and called benign cuts. They have the property that their application does not lead to the complete elimination of the atomic components of their cut formulas from their proof branches. Their use, then, does not hinder the recovery from an endsequent of information about all formulas used in a proof of that sequent, during an algorithmic process of deciding about the derivability of that sequent.","The inference rule which is used to manifest the orthomodularity of models of OMO is the rule OM:","(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)","It is shown that an OMO proof of the form","where P and Q are cut-free and contain no applications of rule OM, can be reconstructed to prove the same endsequent without the use of any cuts which are not benign.","Made available in DSpace on 2014-12-16T06:18:00Z (GMT). No. of bitstreams: 1 8203523.pdf: 1824368 bytes, checksum: a964b058f71f6c318734195980483ce9 (MD5) Previous issue date: 1981","Embargo set by: Seth Robbins for item 71362 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","89 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1981."],"dc:identifier":["http://hdl.handle.net/2142/71196","(UMI)AAI8203523"],"dc:subject":["Mathematics"],"dc:title":["Orthomodular Lattices and Cut Elimination"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:04Z"}