Sequent Schema for Derived Rules
This paper presents a general sequent schema language that can be used for specifying sequent-style rules for a logical theory. We show how by adding the sequent schema language to a theory we gain an ability to prove new inference rules within the theory itself. We show that the extension of any su...
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| creator | Nogin, Aleksey Hickey, Jason |
| description | This paper presents a general sequent schema language that can be used for specifying sequent-style rules for a logical theory. We show how by adding the sequent schema language to a theory we gain an ability to prove new inference rules within the theory itself. We show that the extension of any such theory with our sequent schema language and with any new rules found using this mechanism is conservative.
By using the sequent schema language in a theorem prover, one gets an ability to allow users to derive new rules and then use such derived rules as if they were primitive axioms. The conservativity result guarantees the validity of this approach. This property makes it a convenient tool for implementing a derived rules mechanism in theorem provers, especially considering that the application of the rules expressed in the sequent schema language can be efficiently implemented using MetaPRL’s fast rewriting engine. |
| doi_str_mv | 10.1007/3-540-45685-6_19 |
| format | Book Chapter |
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By using the sequent schema language in a theorem prover, one gets an ability to allow users to derive new rules and then use such derived rules as if they were primitive axioms. The conservativity result guarantees the validity of this approach. This property makes it a convenient tool for implementing a derived rules mechanism in theorem provers, especially considering that the application of the rules expressed in the sequent schema language can be efficiently implemented using MetaPRL’s fast rewriting engine.</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 9783540440390</identifier><identifier>ISBN: 3540440399</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 9783540456858</identifier><identifier>EISBN: 3540456856</identifier><identifier>DOI: 10.1007/3-540-45685-6_19</identifier><identifier>OCLC: 958522756</identifier><identifier>LCCallNum: QA76.9.S88</identifier><language>eng</language><publisher>Germany: Springer Berlin / Heidelberg</publisher><subject>Applied sciences ; Computer science; control theory; systems ; Context Variable ; Exact sciences and technology ; Inference Rule ; Logical Theory ; Order Variable ; Programming theory ; Theorem Prover ; Theoretical computing</subject><ispartof>Lecture notes in computer science, 2002, Vol.2410, p.281-297</ispartof><rights>Springer-Verlag Berlin Heidelberg 2002</rights><rights>2003 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><relation>Lecture Notes in Computer Science</relation></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttps://ebookcentral.proquest.com/covers/3071645-l.jpg</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/3-540-45685-6_19$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/3-540-45685-6_19$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>309,310,779,780,784,789,790,793,4050,4051,27925,38255,41442,42511</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=14636051$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><contributor>Carreno, Victor A</contributor><contributor>Tahar, Sofiene</contributor><contributor>Munoz, Cesar A</contributor><contributor>Carreño, Victor A.</contributor><contributor>Tahar, Sofiène</contributor><contributor>Muñoz, César A.</contributor><creatorcontrib>Nogin, Aleksey</creatorcontrib><creatorcontrib>Hickey, Jason</creatorcontrib><title>Sequent Schema for Derived Rules</title><title>Lecture notes in computer science</title><description>This paper presents a general sequent schema language that can be used for specifying sequent-style rules for a logical theory. We show how by adding the sequent schema language to a theory we gain an ability to prove new inference rules within the theory itself. We show that the extension of any such theory with our sequent schema language and with any new rules found using this mechanism is conservative.
By using the sequent schema language in a theorem prover, one gets an ability to allow users to derive new rules and then use such derived rules as if they were primitive axioms. The conservativity result guarantees the validity of this approach. This property makes it a convenient tool for implementing a derived rules mechanism in theorem provers, especially considering that the application of the rules expressed in the sequent schema language can be efficiently implemented using MetaPRL’s fast rewriting engine.</description><subject>Applied sciences</subject><subject>Computer science; control theory; systems</subject><subject>Context Variable</subject><subject>Exact sciences and technology</subject><subject>Inference Rule</subject><subject>Logical Theory</subject><subject>Order Variable</subject><subject>Programming theory</subject><subject>Theorem Prover</subject><subject>Theoretical computing</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>9783540440390</isbn><isbn>3540440399</isbn><isbn>9783540456858</isbn><isbn>3540456856</isbn><fulltext>true</fulltext><rsrctype>book_chapter</rsrctype><creationdate>2002</creationdate><recordtype>book_chapter</recordtype><recordid>eNpFkMtLAzEQxuMTl9q7x7143DrJ5HmU-oSCYPUc0jSx1W23Jq3gf2_6AIeBgZn5vmF-hFxRGFAAdYON4NBwIbVopKXmiPSN0liau54-JhWVlDaI3Jz8zziggVNSAQJrjOJ4TiojtGBMCXlB-jl_QglkikpRkXocvjdhua7HfhYWro5dqu9Cmv-Eaf26aUO-JGfRtTn0D7VH3h_u34ZPzejl8Xl4O2pWVKNpDFchBKTOS9QgWdTAwAQzNVOITEVTzlOIUXgeEQwCSI1FgB4mAFRhj1zvfVcue9fG5JZ-nu0qzRcu_VrKJUoQtOwN9nu5jJYfIdlJ131lS8FusVm0hYLdIbJbbEWAB-PUlVfz2oatwpenk2v9zK3WIWWLUIBwYVlJA_gHpfpmkQ</recordid><startdate>2002</startdate><enddate>2002</enddate><creator>Nogin, Aleksey</creator><creator>Hickey, Jason</creator><general>Springer Berlin / Heidelberg</general><general>Springer Berlin Heidelberg</general><general>Springer</general><scope>FFUUA</scope><scope>IQODW</scope></search><sort><creationdate>2002</creationdate><title>Sequent Schema for Derived Rules</title><author>Nogin, Aleksey ; Hickey, Jason</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p1839-947eee31ac638062f80209e9d9d0f27f927510ff5c4f309300683ee33c0b00173</frbrgroupid><rsrctype>book_chapters</rsrctype><prefilter>book_chapters</prefilter><language>eng</language><creationdate>2002</creationdate><topic>Applied sciences</topic><topic>Computer science; control theory; systems</topic><topic>Context Variable</topic><topic>Exact sciences and technology</topic><topic>Inference Rule</topic><topic>Logical Theory</topic><topic>Order Variable</topic><topic>Programming theory</topic><topic>Theorem Prover</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nogin, Aleksey</creatorcontrib><creatorcontrib>Hickey, Jason</creatorcontrib><collection>ProQuest Ebook Central - Book Chapters - Demo use only</collection><collection>Pascal-Francis</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nogin, Aleksey</au><au>Hickey, Jason</au><au>Carreno, Victor A</au><au>Tahar, Sofiene</au><au>Munoz, Cesar A</au><au>Carreño, Victor A.</au><au>Tahar, Sofiène</au><au>Muñoz, César A.</au><format>book</format><genre>bookitem</genre><ristype>CHAP</ristype><atitle>Sequent Schema for Derived Rules</atitle><btitle>Lecture notes in computer science</btitle><seriestitle>Lecture Notes in Computer Science</seriestitle><date>2002</date><risdate>2002</risdate><volume>2410</volume><spage>281</spage><epage>297</epage><pages>281-297</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>9783540440390</isbn><isbn>3540440399</isbn><eisbn>9783540456858</eisbn><eisbn>3540456856</eisbn><abstract>This paper presents a general sequent schema language that can be used for specifying sequent-style rules for a logical theory. We show how by adding the sequent schema language to a theory we gain an ability to prove new inference rules within the theory itself. We show that the extension of any such theory with our sequent schema language and with any new rules found using this mechanism is conservative.
By using the sequent schema language in a theorem prover, one gets an ability to allow users to derive new rules and then use such derived rules as if they were primitive axioms. The conservativity result guarantees the validity of this approach. This property makes it a convenient tool for implementing a derived rules mechanism in theorem provers, especially considering that the application of the rules expressed in the sequent schema language can be efficiently implemented using MetaPRL’s fast rewriting engine.</abstract><cop>Germany</cop><pub>Springer Berlin / Heidelberg</pub><doi>10.1007/3-540-45685-6_19</doi><oclcid>958522756</oclcid><tpages>17</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0302-9743 |
| ispartof | Lecture notes in computer science, 2002, Vol.2410, p.281-297 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_14636051 |
| source | Springer Books |
| subjects | Applied sciences Computer science control theory systems Context Variable Exact sciences and technology Inference Rule Logical Theory Order Variable Programming theory Theorem Prover Theoretical computing |
| title | Sequent Schema for Derived Rules |
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