From math.semantic.web at gmail.com Tue Feb 5 18:07:59 2013 From: math.semantic.web at gmail.com (Christoph LANGE) Date: Tue, 05 Feb 2013 17:07:59 +0000 Subject: [Hets-users] MathServeBroker and Vampire proof attempts hang beyond timeout Message-ID: <51113C6F.3050209@gmail.com> Hi all, is MathServeBroker running properly? My current proof attempts using MathServeBroker or Vampire (which, IIUC, runs on MathServeBroker as well) hang beyond the 10-second timeout, requiring me to kill Hets. Cheers, and thanks in advance for any help, Christoph -- Christoph Lange, School of Computer Science, University of Birmingham http://cs.bham.ac.uk/~langec/, Skype duke4701 ? Intelligent Computer Mathematics, 7?12 Jul, Bath, UK; Deadline 8 Mar http://cicm-conference.org/2013/ ? SePublica Workshop @ ESWC 2013. Montpellier, France, 26-30 May. http://sepublica.mywikipaper.org From math.semantic.web at gmail.com Tue Feb 5 18:53:33 2013 From: math.semantic.web at gmail.com (Christoph LANGE) Date: Tue, 05 Feb 2013 17:53:33 +0000 Subject: [Hets-users] Fixed: firewall issue [Re: MathServeBroker and Vampire proof attempts hang beyond timeout] In-Reply-To: <51113E06.6050500@dfki.de> References: <51113C6F.3050209@gmail.com> <51113E06.6050500@dfki.de> Message-ID: <5111471D.7090708@gmail.com> 2013-02-05 17:14 Christian Maeder: > They run for me. Thanks, Christian, it turned out to be a firewall issue. The firewall at the University of Birmingham blocks most non-standard ports (even port 8080!), but with a different network connection it worked for me. Cheers, Christoph -- Christoph Lange, School of Computer Science, University of Birmingham http://cs.bham.ac.uk/~langec/, Skype duke4701 ? Intelligent Computer Mathematics, 7?12 Jul, Bath, UK; Deadline 8 Mar http://cicm-conference.org/2013/ ? SePublica Workshop @ ESWC 2013. Montpellier, France, 26-30 May. http://sepublica.mywikipaper.org From math.semantic.web at gmail.com Wed Feb 6 01:12:01 2013 From: math.semantic.web at gmail.com (Christoph LANGE) Date: Wed, 06 Feb 2013 00:12:01 +0000 Subject: [Hets-users] How to model my own, totally ordered real numbers? Message-ID: <51119FD1.9080103@gmail.com> Hi all, for a formalization of auction theory (see http://www.cs.bham.ac.uk/research/projects/formare/code/auction-theory/ if interested) I would like to specify a custom sort of real numbers, which only satisfies those axioms that I really need, not all axioms of the actual real numbers (e.g. HasCASL/Real). Some of the things that my real numbers need include the operators <=, >=, > and <, and these should be transitive. Given spec MyReals = sort MyReal; preds __>=__: MyReal * MyReal; __<=__: MyReal * MyReal; ... end is there a way of reusing Basic/RelationsAndOrders#ExtTotalOrder in a definitional way? I would somehow like to define the spec MyReals as an extension of the spec ExtTotalOrder, where the sort Elem of ExtTotalOrder maps to MyReal, and the ExtTotalOrder operators <=, >=, > and < with all of their properties (e.g. transitivity) map to the corresponding operators defined on the sort MyReal. I understand that the views in Basic/RelationsAndOrders (e.g. TotalOrder_in_Nat) achieve something similar. However, they are not definitional links; instead, Nat has its own axiomatization of the comparison operators, and the view postulates that the total order axioms can be proved within the theory Nat. But I don't want to do axiomatize these operators myself, but simply reuse the axioms from Basic/RelationsAndOrders. Any hints are appreciated. Cheers, and thanks in advance, Christoph -- Christoph Lange, School of Computer Science, University of Birmingham http://cs.bham.ac.uk/~langec/, Skype duke4701 ? Intelligent Computer Mathematics, 7?12 Jul, Bath, UK; Deadline 8 Mar http://cicm-conference.org/2013/ ? SePublica Workshop @ ESWC 2013. Montpellier, France, 26-30 May. http://sepublica.mywikipaper.org From Till.Mossakowski at dfki.de Thu Feb 7 16:11:33 2013 From: Till.Mossakowski at dfki.de (Till Mossakowski) Date: Thu, 07 Feb 2013 16:11:33 +0100 Subject: [Hets-users] How to model my own, totally ordered real numbers? In-Reply-To: <51119FD1.9080103@gmail.com> References: <51119FD1.9080103@gmail.com> Message-ID: <5113C425.50108@dfki.de> Hi Christoph, we have specified a weak theory of real numbers in CASL: http://www.informatik.uni-bremen.de/agbkb/publikationen/bibsearch/detail_e.htm?pk_int=1328 I have fetched the CASL theory from some old backup folder, updated it, and checked it in: Basic/Reals.casl If you want to import the theory of total orders, just write ExtTotalOrder with Elem |-> Real then ... But you could also use ordered fields instead of just total orders. All the best, Till Am 06.02.2013 01:12, schrieb Christoph LANGE: > Hi all, > > for a formalization of auction theory (see > http://www.cs.bham.ac.uk/research/projects/formare/code/auction-theory/ > if interested) I would like to specify a custom sort of real numbers, > which only satisfies those axioms that I really need, not all axioms of > the actual real numbers (e.g. HasCASL/Real). > > Some of the things that my real numbers need include the operators <=, >> =, > and <, and these should be transitive. Given > > spec MyReals = > sort MyReal; > preds > __>=__: MyReal * MyReal; > __<=__: MyReal * MyReal; > ... > end > > is there a way of reusing Basic/RelationsAndOrders#ExtTotalOrder in a > definitional way? > > I would somehow like to define the spec MyReals as an extension of the > spec ExtTotalOrder, where the sort Elem of ExtTotalOrder maps to MyReal, > and the ExtTotalOrder operators <=, >=, > and < with all of their > properties (e.g. transitivity) map to the corresponding operators > defined on the sort MyReal. > > I understand that the views in Basic/RelationsAndOrders (e.g. > TotalOrder_in_Nat) achieve something similar. However, they are not > definitional links; instead, Nat has its own axiomatization of the > comparison operators, and the view postulates that the total order > axioms can be proved within the theory Nat. But I don't want to do > axiomatize these operators myself, but simply reuse the axioms from > Basic/RelationsAndOrders. > > Any hints are appreciated. > > Cheers, and thanks in advance, > > Christoph > -- Prof. Dr. Till Mossakowski Cartesium, room 2.51 Phone +49-421-218-64226 DFKI GmbH Bremen Fax +49-421-218-9864226 Cyber-Physical Systems Till.Mossakowski at dfki.de Enrique-Schmidt-Str. 5, D-28359 Bremen http://www.informatik.uni-bremen.de/~till/ Deutsches Forschungszentrum fuer Kuenstliche Intelligenz GmbH principal office, *not* the address for mail etc.!!!: Trippstadter Str. 122, D-67663 Kaiserslautern management board: Prof. Wolfgang Wahlster (chair), Dr. Walter Olthoff supervisory board: Prof. Hans A. Aukes (chair) Amtsgericht Kaiserslautern, HRB 2313 From math.semantic.web at gmail.com Thu Feb 7 16:49:43 2013 From: math.semantic.web at gmail.com (Christoph LANGE) Date: Thu, 07 Feb 2013 15:49:43 +0000 Subject: [Hets-users] What does 'Used Axioms: declarationN' mean when using SPASS? Message-ID: <5113CD17.3080604@gmail.com> Hi all, I proved some theorems with SPASS, and in the list of Used Axioms I see entries like declarationN, where N is a number. Where do I find these declarations? In the SPASS output they only occur in the final line "Formulae used in the proof". The dfg input file for SPASS has a list_of_declarations. So is declaration23 the 23rd entry of this list? Cheers, and thanks in advance, Christoph -- Christoph Lange, School of Computer Science, University of Birmingham http://cs.bham.ac.uk/~langec/, Skype duke4701 ? Intelligent Computer Mathematics, 7?12 Jul, Bath, UK; Deadline 8 Mar http://cicm-conference.org/2013/ ? SePublica Workshop @ ESWC 2013. Montpellier, France, 26-30 May. http://sepublica.mywikipaper.org From Till.Mossakowski at dfki.de Thu Feb 7 17:03:42 2013 From: Till.Mossakowski at dfki.de (Till Mossakowski) Date: Thu, 07 Feb 2013 17:03:42 +0100 Subject: [Hets-users] What does 'Used Axioms: declarationN' mean when using SPASS? In-Reply-To: <5113CD17.3080604@gmail.com> References: <5113CD17.3080604@gmail.com> Message-ID: <5113D05E.1040307@dfki.de> Dear Christoph, > I proved some theorems with SPASS, and in the list of Used Axioms I see > entries like declarationN, where N is a number. > > Where do I find these declarations? > > In the SPASS output they only occur in the final line "Formulae used in > the proof". > > The dfg input file for SPASS has a list_of_declarations. So is > declaration23 the 23rd entry of this list? Yes, I think so. Note that these declarations are generated by the logic translation from CASL to SoftFOL. This means that they can be used as axioms in the proof, but cannot be traced back to axioms (only to signature declarations) in the original specification. Best, Till -- Prof. Dr. Till Mossakowski Cartesium, room 2.51 Phone +49-421-218-64226 DFKI GmbH Bremen Fax +49-421-218-9864226 Cyber-Physical Systems Till.Mossakowski at dfki.de Enrique-Schmidt-Str. 5, D-28359 Bremen http://www.informatik.uni-bremen.de/~till/ Deutsches Forschungszentrum fuer Kuenstliche Intelligenz GmbH principal office, *not* the address for mail etc.!!!: Trippstadter Str. 122, D-67663 Kaiserslautern management board: Prof. Wolfgang Wahlster (chair), Dr. Walter Olthoff supervisory board: Prof. Hans A. Aukes (chair) Amtsgericht Kaiserslautern, HRB 2313 From math.semantic.web at gmail.com Thu Feb 7 17:10:44 2013 From: math.semantic.web at gmail.com (Christoph LANGE) Date: Thu, 07 Feb 2013 16:10:44 +0000 Subject: [Hets-users] How to reasonably minimize the list of axioms used by a proof Message-ID: <5113D204.3080705@gmail.com> Hi all, when using darwin or eprover I frequently experience that the proofs use more axioms than necessary, or at least they _report_ so, or Hets _interprets_ their output so. (This is different from, e.g., SPASS.) I'm interested in seeing what axioms these provers really need, but what is the best way of finding out? At the moment I'm manually unselecting some of the less plausible axioms in "Prove?Axioms to include" and then running the prover again. Maybe you think that this manual minimization doesn't make sense at all, but if it does: Wouldn't it help to be able to deselect some axioms for the next proof attempt right from the list of "Used Axioms"? (If you think the latter makes sense, I'll be happy to file it as a feature request.) Cheers, Christoph -- Christoph Lange, School of Computer Science, University of Birmingham http://cs.bham.ac.uk/~langec/, Skype duke4701 ? Intelligent Computer Mathematics, 7?12 Jul, Bath, UK; Deadline 8 Mar http://cicm-conference.org/2013/ ? SePublica Workshop @ ESWC 2013. Montpellier, France, 26-30 May. http://sepublica.mywikipaper.org From Till.Mossakowski at dfki.de Thu Feb 7 17:41:31 2013 From: Till.Mossakowski at dfki.de (Till Mossakowski) Date: Thu, 07 Feb 2013 17:41:31 +0100 Subject: [Hets-users] How to reasonably minimize the list of axioms used by a proof In-Reply-To: <5113D204.3080705@gmail.com> References: <5113D204.3080705@gmail.com> Message-ID: <5113D93B.8010901@dfki.de> Dear Christoph, good point. At the moment, let me hint of the possibility to script Hets with the option "hets -I". With this, you easily can automate such attempts using a shell script. But of course, please also file a feature request. Best, Till Am 07.02.2013 17:10, schrieb Christoph LANGE: > Hi all, > > when using darwin or eprover I frequently experience that the proofs use > more axioms than necessary, or at least they _report_ so, or Hets > _interprets_ their output so. (This is different from, e.g., SPASS.) > > I'm interested in seeing what axioms these provers really need, but what > is the best way of finding out? At the moment I'm manually unselecting > some of the less plausible axioms in "Prove?Axioms to include" and then > running the prover again. > > Maybe you think that this manual minimization doesn't make sense at all, > but if it does: Wouldn't it help to be able to deselect some axioms for > the next proof attempt right from the list of "Used Axioms"? (If you > think the latter makes sense, I'll be happy to file it as a feature > request.) > > Cheers, > > Christoph > -- Prof. Dr. Till Mossakowski Cartesium, room 2.51 Phone +49-421-218-64226 DFKI GmbH Bremen Fax +49-421-218-9864226 Cyber-Physical Systems Till.Mossakowski at dfki.de Enrique-Schmidt-Str. 5, D-28359 Bremen http://www.informatik.uni-bremen.de/~till/ Deutsches Forschungszentrum fuer Kuenstliche Intelligenz GmbH principal office, *not* the address for mail etc.!!!: Trippstadter Str. 122, D-67663 Kaiserslautern management board: Prof. Wolfgang Wahlster (chair), Dr. Walter Olthoff supervisory board: Prof. Hans A. Aukes (chair) Amtsgericht Kaiserslautern, HRB 2313 From math.semantic.web at gmail.com Thu Feb 7 20:13:31 2013 From: math.semantic.web at gmail.com (Christoph LANGE) Date: Thu, 07 Feb 2013 19:13:31 +0000 Subject: [Hets-users] How to model my own, totally ordered real numbers? In-Reply-To: <5113C425.50108@dfki.de> References: <51119FD1.9080103@gmail.com> <5113C425.50108@dfki.de> Message-ID: <5113FCDB.7080604@gmail.com> Hi Till, 2013-02-07 15:11 Till Mossakowski: > we have specified a weak theory of real numbers in CASL: > http://www.informatik.uni-bremen.de/agbkb/publikationen/bibsearch/detail_e.htm?pk_int=1328 Thanks! Indeed Markus Roggenbach had pointed this out to me off-list. Initially I was reluctant to use it, as it seemed to provide a lot of stuff I don't need, but then again, if it works, why not. At the point that I have reached now I do need a totally ordered commutative field, with some of the additional convenience operators provided by the Ext* specs in Basic/Reals. > I have fetched the CASL theory from some old backup folder, updated it, > and checked it in: Basic/Reals.casl So, thanks, this is very helpful. > If you want to import the theory of total orders, just write > > ExtTotalOrder with Elem |-> Real > then > ... It's actually ExtTotalOrder[TotalOrder], isn't it? (I don't exactly understand why, though. For any of these Ext* specs, including those in Basic/RelationsAndOrders, wouldn't it suffice to say "spec ExtFoo = Foo then end"?) > But you could also use ordered fields instead of just total orders. Using ExtOrderedField alone does not yet give me >=, which I need, and which ExtTotalOrder provides. However it seems that as soon as I form the union of ExtOrderedField and ExtTotalOrder, I get some "hiding links" in the development graph, and then those proofs that used to work before time out. When I define, e.g., spec Real = ExtArchimedianField[ArchimedianField] with Elem |-> Real or when I use BasicReal, which is essentially the same with more functionality, I see that two purple edges (are these the "hiding links"?) point into the node Real. Before understanding this my alternatives seem to be: * basing my reals on ExtTotalOrder and specifying my own axioms for some of the field operators (I need * and - so far), or * basing them on ExtOrderedField and specifying my own axioms for some additional comparison operators (e.g. >=), or * doing my formalization the hard way without convenience operators (but this is certainly not what our target audience would appreciate, as they need something that is as close as possible to textbook mathematics) I hope there is a way to avoid any of these "alternatives". If you would like to have a look, I have committed my sources to the usual place. Cheers, Christoph -- Christoph Lange, School of Computer Science, University of Birmingham http://cs.bham.ac.uk/~langec/, Skype duke4701 ? Intelligent Computer Mathematics, 7?12 Jul, Bath, UK; Deadline 8 Mar http://cicm-conference.org/2013/ ? SePublica Workshop @ ESWC 2013. Montpellier, France, 26-30 May. http://sepublica.mywikipaper.org From Till.Mossakowski at dfki.de Thu Feb 7 21:07:36 2013 From: Till.Mossakowski at dfki.de (Till Mossakowski) Date: Thu, 07 Feb 2013 21:07:36 +0100 Subject: [Hets-users] How to model my own, totally ordered real numbers? In-Reply-To: <5113FCDB.7080604@gmail.com> References: <51119FD1.9080103@gmail.com> <5113C425.50108@dfki.de> <5113FCDB.7080604@gmail.com> Message-ID: <51140988.3010306@dfki.de> Hi Christoph, > It's actually ExtTotalOrder[TotalOrder], isn't it? (I don't exactly > understand why, though. For any of these Ext* specs, including those in > Basic/RelationsAndOrders, wouldn't it suffice to say "spec ExtFoo = Foo > then end"?) Indeed, ExtTotalOrder is parameterised by TotalOrder. The reason is that any total order, say Nat, whose total order property is expressed as a view: view v : TotalOrder to Nat = ... end can then be used to enrich the total order with the new symbols: ExtTotalOrder[view v] And if you just want to enrich abstract total orders with the new symbols, you write ExtTotalOrder[TotalOrder]. You could also abbreviate this, like spec RichTotalOrder = ExtTotalOrder[TotalOrder] end and then use RichTotalOrder. >> But you could also use ordered fields instead of just total orders. > > Using ExtOrderedField alone does not yet give me >=, which I need, and > which ExtTotalOrder provides. However it seems that as soon as I form > the union of ExtOrderedField and ExtTotalOrder, I get some "hiding > links" in the development graph, and then those proofs that used to work > before time out. oh, I just forgot to add ExtTotalOrder to ExtOrderedField. Have fixed this now. > When I define, e.g., > > spec Real = ExtArchimedianField[ArchimedianField] with Elem |-> Real > > or when I use BasicReal, which is essentially the same with more > functionality, I see that two purple edges (are these the "hiding > links"?) point into the node Real. No. The purple links are there because they indicate that some nodes are hidden in order to reduce the complexity of the graph. You can show these nodes with Edit->Hide/Show names/nodes/edges->Hide/Show unnamed nodes without open proofs. > Before understanding this my alternatives seem to be: > * basing my reals on ExtTotalOrder and specifying my own axioms for some > of the field operators (I need * and - so far), or > * basing them on ExtOrderedField and specifying my own axioms for some > additional comparison operators (e.g. >=), or > * doing my formalization the hard way without convenience operators (but > this is certainly not what our target audience would appreciate, as they > need something that is as close as possible to textbook mathematics) > > I hope there is a way to avoid any of these "alternatives". Hope that my fix above solves your problem. Best, Till -- Prof. Dr. Till Mossakowski Cartesium, room 2.51 Phone +49-421-218-64226 DFKI GmbH Bremen Fax +49-421-218-9864226 Cyber-Physical Systems Till.Mossakowski at dfki.de Enrique-Schmidt-Str. 5, D-28359 Bremen http://www.informatik.uni-bremen.de/~till/ Deutsches Forschungszentrum fuer Kuenstliche Intelligenz GmbH principal office, *not* the address for mail etc.!!!: Trippstadter Str. 122, D-67663 Kaiserslautern management board: Prof. Wolfgang Wahlster (chair), Dr. Walter Olthoff supervisory board: Prof. Hans A. Aukes (chair) Amtsgericht Kaiserslautern, HRB 2313 From Till.Mossakowski at dfki.de Thu Feb 7 22:04:04 2013 From: Till.Mossakowski at dfki.de (Till Mossakowski) Date: Thu, 07 Feb 2013 22:04:04 +0100 Subject: [Hets-users] How to model my own, totally ordered real numbers? In-Reply-To: <51140988.3010306@dfki.de> References: <51119FD1.9080103@gmail.com> <5113C425.50108@dfki.de> <5113FCDB.7080604@gmail.com> <51140988.3010306@dfki.de> Message-ID: <511416C4.3080909@dfki.de> P.S. please find attached some methodological guidelines explaining the ExtXXX specification style (see section 4.1.5). Best, Till Am 07.02.2013 21:07, schrieb Till Mossakowski: > Hi Christoph, > > > It's actually ExtTotalOrder[TotalOrder], isn't it? (I don't exactly >> understand why, though. For any of these Ext* specs, including those in >> Basic/RelationsAndOrders, wouldn't it suffice to say "spec ExtFoo = Foo >> then end"?) > > Indeed, ExtTotalOrder is parameterised by TotalOrder. The reason is that > any total order, say Nat, whose total order property is expressed as a > view: > view v : TotalOrder to Nat = ... end > can then be used to enrich the total order with the new symbols: > ExtTotalOrder[view v] > And if you just want to enrich abstract total orders with the new > symbols, you write ExtTotalOrder[TotalOrder]. > You could also abbreviate this, like > spec RichTotalOrder = ExtTotalOrder[TotalOrder] end > and then use RichTotalOrder. > >>> But you could also use ordered fields instead of just total orders. >> >> Using ExtOrderedField alone does not yet give me >=, which I need, and >> which ExtTotalOrder provides. However it seems that as soon as I form >> the union of ExtOrderedField and ExtTotalOrder, I get some "hiding >> links" in the development graph, and then those proofs that used to work >> before time out. > > oh, I just forgot to add ExtTotalOrder to ExtOrderedField. Have fixed > this now. > >> When I define, e.g., >> >> spec Real = ExtArchimedianField[ArchimedianField] with Elem |-> Real >> >> or when I use BasicReal, which is essentially the same with more >> functionality, I see that two purple edges (are these the "hiding >> links"?) point into the node Real. > > No. The purple links are there because they indicate that some nodes are > hidden in order to reduce the complexity of the graph. You can show > these nodes with Edit->Hide/Show names/nodes/edges->Hide/Show unnamed > nodes without open proofs. > > >> Before understanding this my alternatives seem to be: >> * basing my reals on ExtTotalOrder and specifying my own axioms for some >> of the field operators (I need * and - so far), or >> * basing them on ExtOrderedField and specifying my own axioms for some >> additional comparison operators (e.g. >=), or >> * doing my formalization the hard way without convenience operators (but >> this is certainly not what our target audience would appreciate, as they >> need something that is as close as possible to textbook mathematics) >> >> I hope there is a way to avoid any of these "alternatives". > > Hope that my fix above solves your problem. > > Best, Till > -- Prof. Dr. Till Mossakowski Cartesium, room 2.51 Phone +49-421-218-64226 DFKI GmbH Bremen Fax +49-421-218-9864226 Cyber-Physical Systems Till.Mossakowski at dfki.de Enrique-Schmidt-Str. 5, D-28359 Bremen http://www.informatik.uni-bremen.de/~till/ Deutsches Forschungszentrum fuer Kuenstliche Intelligenz GmbH principal office, *not* the address for mail etc.!!!: Trippstadter Str. 122, D-67663 Kaiserslautern management board: Prof. Wolfgang Wahlster (chair), Dr. Walter Olthoff supervisory board: Prof. Hans A. Aukes (chair) Amtsgericht Kaiserslautern, HRB 2313 -------------- next part -------------- A non-text attachment was scrubbed... Name: M-6.pdf Type: application/pdf Size: 298496 bytes Desc: not available URL: From math.semantic.web at gmail.com Fri Feb 8 01:01:34 2013 From: math.semantic.web at gmail.com (Christoph LANGE) Date: Fri, 08 Feb 2013 00:01:34 +0000 Subject: [Hets-users] How to model my own, totally ordered real numbers? In-Reply-To: <51140988.3010306@dfki.de> References: <51119FD1.9080103@gmail.com> <5113C425.50108@dfki.de> <5113FCDB.7080604@gmail.com> <51140988.3010306@dfki.de> Message-ID: <5114405E.3000803@gmail.com> Hi Till, thanks for your explanations and fixes. 2013-02-07 20:07 Till Mossakowski: >> Using ExtOrderedField alone does not yet give me >=, which I need, and >> which ExtTotalOrder provides. However it seems that as soon as I form >> the union of ExtOrderedField and ExtTotalOrder, I get some "hiding >> links" in the development graph, and then those proofs that used to work >> before time out. > > oh, I just forgot to add ExtTotalOrder to ExtOrderedField. Have fixed > this now. I see that the "hiding link" complaint traces back to Algebra_I/Field. I am not exactly familiar with hiding yet, but it seems that this is intended for Field. BTW the full text is: This node has incoming hiding links! The theory shown may be too weak for proving. A consistency check may wrongly succeed. If possible use the normal form of this node. Anyway the problem is that my proofs really no longer work. You can see this in my file Vickrey.casl by switching between the two alternatives I prepared for "spec Real": 1. reusing ExtOrderedField 2. declaring all sorts, predicates and operators I need without providing axioms In case (2) the first three theorems in SecondPriceAuction, the theory on which I am currently working, can be proved (using SPASS). In case (1) I get the warning mentioned above, and all proof attempts time out. What is the problem? Cheers, Christoph -- Christoph Lange, School of Computer Science, University of Birmingham http://cs.bham.ac.uk/~langec/, Skype duke4701 ? Intelligent Computer Mathematics, 7?12 Jul, Bath, UK; Deadline 8 Mar http://cicm-conference.org/2013/ ? SePublica Workshop @ ESWC 2013. Montpellier, France, 26-30 May. http://sepublica.mywikipaper.org From Till.Mossakowski at dfki.de Fri Feb 8 11:21:24 2013 From: Till.Mossakowski at dfki.de (Till Mossakowski) Date: Fri, 08 Feb 2013 11:21:24 +0100 Subject: [Hets-users] How to model my own, totally ordered real numbers? In-Reply-To: <5114405E.3000803@gmail.com> References: <51119FD1.9080103@gmail.com> <5113C425.50108@dfki.de> <5113FCDB.7080604@gmail.com> <51140988.3010306@dfki.de> <5114405E.3000803@gmail.com> Message-ID: <5114D1A4.6050807@dfki.de> Dear Christoph, indeed, Hets still lacks proof support for %implied goals in presence of hiding, see http://trac.informatik.uni-bremen.de:8080/hets/ticket/1103 I see two workarounds: 1. you use "then %implies" (see the above ticket for details) 2. you use a variant of ExtOrderedField that is based on ConstructField instead of Field (then there is no hiding) Best, Till Am 08.02.2013 01:01, schrieb Christoph LANGE: > Hi Till, > > thanks for your explanations and fixes. > > 2013-02-07 20:07 Till Mossakowski: >>> Using ExtOrderedField alone does not yet give me >=, which I need, and >>> which ExtTotalOrder provides. However it seems that as soon as I form >>> the union of ExtOrderedField and ExtTotalOrder, I get some "hiding >>> links" in the development graph, and then those proofs that used to work >>> before time out. >> >> oh, I just forgot to add ExtTotalOrder to ExtOrderedField. Have fixed >> this now. > > I see that the "hiding link" complaint traces back to Algebra_I/Field. > I am not exactly familiar with hiding yet, but it seems that this is > intended for Field. > > BTW the full text is: This node has incoming hiding links! The theory > shown may be too weak for proving. A consistency check may wrongly > succeed. If possible use the normal form of this node. > > Anyway the problem is that my proofs really no longer work. You can see > this in my file Vickrey.casl by switching between the two alternatives I > prepared for "spec Real": > > 1. reusing ExtOrderedField > 2. declaring all sorts, predicates and operators I need without > providing axioms > > In case (2) the first three theorems in SecondPriceAuction, the theory > on which I am currently working, can be proved (using SPASS). In case > (1) I get the warning mentioned above, and all proof attempts time out. > > What is the problem? > > Cheers, > > Christoph > -- Prof. Dr. Till Mossakowski Cartesium, room 2.51 Phone +49-421-218-64226 DFKI GmbH Bremen Fax +49-421-218-9864226 Cyber-Physical Systems Till.Mossakowski at dfki.de Enrique-Schmidt-Str. 5, D-28359 Bremen http://www.informatik.uni-bremen.de/~till/ Deutsches Forschungszentrum fuer Kuenstliche Intelligenz GmbH principal office, *not* the address for mail etc.!!!: Trippstadter Str. 122, D-67663 Kaiserslautern management board: Prof. Wolfgang Wahlster (chair), Dr. Walter Olthoff supervisory board: Prof. Hans A. Aukes (chair) Amtsgericht Kaiserslautern, HRB 2313 From math.semantic.web at gmail.com Fri Feb 8 16:57:16 2013 From: math.semantic.web at gmail.com (Christoph LANGE) Date: Fri, 08 Feb 2013 15:57:16 +0000 Subject: [Hets-users] How to model my own, totally ordered real numbers? In-Reply-To: <5114D1A4.6050807@dfki.de> References: <51119FD1.9080103@gmail.com> <5113C425.50108@dfki.de> <5113FCDB.7080604@gmail.com> <51140988.3010306@dfki.de> <5114405E.3000803@gmail.com> <5114D1A4.6050807@dfki.de> Message-ID: <5115205C.1010109@gmail.com> Hi Till, 2013-02-08 10:21 Till Mossakowski: > 1. you use "then %implies" (see the above ticket for details) OK, I still don't fully understand the, well, _implications_ of this, so I'll ask further questions in that ticket. > 2. you use a variant of ExtOrderedField that is based on ConstructField > instead of Field (then there is no hiding) This doesn't seem so trivial to do, as I also need the additional functionality of ExtField, which somehow depends on Field. Anyway, what's working for me now is that I define the real numbers as I need them from scratch, and hard-code exactly those axioms that I need: spec Real = sort Real; preds __>=__, __>__, __<__, __<=__: Real * Real; ops 0, 1: Real; __*__, __-__: Real * Real -> Real; forall x,y,z:Real . x < y <=> x <= y /\ not x = y %(lt_def)% . x > y <=> not x <= y %(gt_def)% . x <= y /\ y <= z => x <= z %(lt_trans)% . x * 1 = x %(1_mult)% . x * 0 = 0 %(0_mult)% . x - 0 = x %(minus_0)% end I am not sure, however, for how long this will be maintainable, so I'm still interested in better alternatives. Cheers, Christoph -- Christoph Lange, School of Computer Science, University of Birmingham http://cs.bham.ac.uk/~langec/, Skype duke4701 ? Intelligent Computer Mathematics, 7?12 Jul, Bath, UK; Deadline 8 Mar http://cicm-conference.org/2013/ ? SePublica Workshop @ ESWC 2013. Montpellier, France, 26-30 May. http://sepublica.mywikipaper.org From Till.Mossakowski at dfki.de Fri Feb 8 18:58:48 2013 From: Till.Mossakowski at dfki.de (Till Mossakowski) Date: Fri, 08 Feb 2013 18:58:48 +0100 Subject: [Hets-users] How to model my own, totally ordered real numbers? In-Reply-To: <5115205C.1010109@gmail.com> References: <51119FD1.9080103@gmail.com> <5113C425.50108@dfki.de> <5113FCDB.7080604@gmail.com> <51140988.3010306@dfki.de> <5114405E.3000803@gmail.com> <5114D1A4.6050807@dfki.de> <5115205C.1010109@gmail.com> Message-ID: <51153CD8.3080807@dfki.de> Hi Christoph, >> 2. you use a variant of ExtOrderedField that is based on ConstructField >> instead of Field (then there is no hiding) > > This doesn't seem so trivial to do, as I also need the additional > functionality of ExtField, which somehow depends on Field. I meant: just define MyExtField in the same way as ExtField (but based on ConstructField), etc. It is just some copy and paste... Best, Till -- Prof. Dr. Till Mossakowski Cartesium, room 2.51 Phone +49-421-218-64226 DFKI GmbH Bremen Fax +49-421-218-9864226 Cyber-Physical Systems Till.Mossakowski at dfki.de Enrique-Schmidt-Str. 5, D-28359 Bremen http://www.informatik.uni-bremen.de/~till/ Deutsches Forschungszentrum fuer Kuenstliche Intelligenz GmbH principal office, *not* the address for mail etc.!!!: Trippstadter Str. 122, D-67663 Kaiserslautern management board: Prof. Wolfgang Wahlster (chair), Dr. Walter Olthoff supervisory board: Prof. Hans A. Aukes (chair) Amtsgericht Kaiserslautern, HRB 2313 From math.semantic.web at gmail.com Fri Feb 8 23:23:10 2013 From: math.semantic.web at gmail.com (Christoph LANGE) Date: Fri, 08 Feb 2013 22:23:10 +0000 Subject: [Hets-users] Strategy for proving when complete proof times out but all of its steps work? Message-ID: <51157ACE.20206@gmail.com> Hi all, in my further progress with http://www.cs.bham.ac.uk/research/projects/formare/code/auction-theory/Vickrey.casl I encountered a new type of problem: The provers time out when I try a certain proof at once, but after I have proven several smaller goals (and included these theorems into the knowledge base) it does work. (BTW I even need different provers to get the small steps done, but this is probably not inherent to the problem but rather an issue of timeouts given different aspects the different provers are optimized for.) The structure of the problem is the following: . E => B = C %(sub1)% %implied %% works with SPASS . S => E %(sub2)% %implied %% works with SPASS . S => A = B %(sub3)% %implied %% works with eprover . S => A = C %(thm1)% %implied %% works with eprover Concretely I am speaking of the following in the spec SecondPriceAuction: sub1 = test_payoff3_all sub2 = test1_spa_win_val_exists sub3 = test2_spa_winner_payoff_0.5step thm1 = second_price_auction_winner_payoff The letters above each abbreviate terms, where S is the most complex one, a 5-argument conjunction. With a significantly higher timeout (e.g. 100 seconds) I can't prove thm1 at once either, but this is probably due to the high (exponential?) complexity of the problem. Is there any way I can "script" the proof attempts in that I guide Hets or the individual provers to pursue a certain strategy? Any guidance on how to manage this is appreciated. I could imagine that part of the answer is to use smaller theories, but from my human perspective this "theorem" is quite trivial already. It follows by simple calculational reasoning from the definitions of the predicates/functions involved. Its Isabelle proof (which I had formalized separately) roughly looks like: have "A = B" using unfolding by simp also have "... = B'" using unfolding by simp also have "... = C" using unfolding by simp finally show "A = C" by simp Cheers, Christoph -- Christoph Lange, School of Computer Science, University of Birmingham http://cs.bham.ac.uk/~langec/, Skype duke4701 ? Intelligent Computer Mathematics, 7?12 Jul, Bath, UK; Deadline 8 Mar http://cicm-conference.org/2013/ ? SePublica Workshop @ ESWC 2013. Montpellier, France, 26-30 May. http://sepublica.mywikipaper.org From Till.Mossakowski at dfki.de Sat Feb 9 18:26:18 2013 From: Till.Mossakowski at dfki.de (Till Mossakowski) Date: Sat, 09 Feb 2013 18:26:18 +0100 Subject: [Hets-users] Strategy for proving when complete proof times out but all of its steps work? In-Reply-To: <51157ACE.20206@gmail.com> References: <51157ACE.20206@gmail.com> Message-ID: <511686BA.8000300@dfki.de> Dear Christoph, you can script Hets with "hets -I". Pressing tab shows you the options. Best, Till Am 08.02.2013 23:23, schrieb Christoph LANGE: > Hi all, > > in my further progress with > http://www.cs.bham.ac.uk/research/projects/formare/code/auction-theory/Vickrey.casl > I encountered a new type of problem: The provers time out when I try a > certain proof at once, but after I have proven several smaller goals > (and included these theorems into the knowledge base) it does work. > (BTW I even need different provers to get the small steps done, but this > is probably not inherent to the problem but rather an issue of timeouts > given different aspects the different provers are optimized for.) > > The structure of the problem is the following: > > . E => B = C %(sub1)% %implied %% works with SPASS > . S => E %(sub2)% %implied %% works with SPASS > . S => A = B %(sub3)% %implied %% works with eprover > . S => A = C %(thm1)% %implied %% works with eprover > > Concretely I am speaking of the following in the spec SecondPriceAuction: > > sub1 = test_payoff3_all > sub2 = test1_spa_win_val_exists > sub3 = test2_spa_winner_payoff_0.5step > thm1 = second_price_auction_winner_payoff > > The letters above each abbreviate terms, where S is the most complex > one, a 5-argument conjunction. > > With a significantly higher timeout (e.g. 100 seconds) I can't prove > thm1 at once either, but this is probably due to the high (exponential?) > complexity of the problem. > > Is there any way I can "script" the proof attempts in that I guide Hets > or the individual provers to pursue a certain strategy? > > Any guidance on how to manage this is appreciated. I could imagine that > part of the answer is to use smaller theories, but from my human > perspective this "theorem" is quite trivial already. It follows by > simple calculational reasoning from the definitions of the > predicates/functions involved. Its Isabelle proof (which I had > formalized separately) roughly looks like: > > have "A = B" using unfolding > by simp > also have "... = B'" using unfolding definition(s)> by simp > also have "... = C" using unfolding definition(s)> by simp > finally show "A = C" by simp > > Cheers, > > Christoph > -- Prof. Dr. Till Mossakowski Cartesium, room 2.51 Phone +49-421-218-64226 DFKI GmbH Bremen Fax +49-421-218-9864226 Cyber-Physical Systems Till.Mossakowski at dfki.de Enrique-Schmidt-Str. 5, D-28359 Bremen http://www.informatik.uni-bremen.de/~till/ Deutsches Forschungszentrum fuer Kuenstliche Intelligenz GmbH principal office, *not* the address for mail etc.!!!: Trippstadter Str. 122, D-67663 Kaiserslautern management board: Prof. Wolfgang Wahlster (chair), Dr. Walter Olthoff supervisory board: Prof. Hans A. Aukes (chair) Amtsgericht Kaiserslautern, HRB 2313 From math.semantic.web at gmail.com Sat Feb 9 20:53:27 2013 From: math.semantic.web at gmail.com (Christoph LANGE) Date: Sat, 09 Feb 2013 19:53:27 +0000 Subject: [Hets-users] Strategy for proving when complete proof times out but all of its steps work? In-Reply-To: <511686BA.8000300@dfki.de> References: <51157ACE.20206@gmail.com> <511686BA.8000300@dfki.de> Message-ID: <5116A937.5000703@gmail.com> Hi Till, 2013-02-09 17:26 Till Mossakowski: > you can script Hets with "hets -I". thanks a lot, that's very helpful. (Actually I see that you had pointed this out to me before, but I had failed to make the connection to my current problem.) hets -I helped me to get my job done. (And additionally I found that I had to add a few auxiliary predicates such as foo(a, b, c, d) <=> bar(a, b) /\ baz(b, c) /\ blarg(c, d) to make some of the involved unifications easier for automated FOL provers. But in any case hets -I considerably speeded up my editing/testing workflow.) However I found some problems, which I have reported as tickets, mainly related to: * the user interaction on the command line not being completely self-explaining * the limited usability of "hets -I" in fully automated settings such as shell scripts or makefiles. See http://trac.informatik.uni-bremen.de:8080/hets/ticket/1106 http://trac.informatik.uni-bremen.de:8080/hets/ticket/1107 http://trac.informatik.uni-bremen.de:8080/hets/ticket/1108 http://trac.informatik.uni-bremen.de:8080/hets/ticket/1109 Cheers, Christoph -- Christoph Lange, School of Computer Science, University of Birmingham http://cs.bham.ac.uk/~langec/, Skype duke4701 ? SePublica Workshop @ ESWC 2013. Montpellier, France, 26-30 May. Deadline 4 Mar; http://sepublica.mywikipaper.org ? Intelligent Computer Mathematics, 7?12 Jul, Bath, UK; Deadline 8 Mar http://cicm-conference.org/2013/ ? Enabling Domain Experts to use Formalised Reasoning @ AISB 2013 3?5 April 2013, Exeter, UK. 3 Hands-on Tutorials on Economics http://cs.bham.ac.uk/research/projects/formare/events/aisb2013/ From math.semantic.web at gmail.com Tue Feb 19 21:26:41 2013 From: math.semantic.web at gmail.com (Christoph LANGE) Date: Tue, 19 Feb 2013 20:26:41 +0000 Subject: [Hets-users] Participate: Enabling Domain Experts to use Formalised Reasoning (AISB 2013, Exeter, UK, 3-5 Apr 2013). Tutorials on Matching, Auctions, Finance. Message-ID: <5123E001.4060700@gmail.com> Do-Form: Enabling Domain Experts to use Formalised Reasoning http://cs.bham.ac.uk/research/projects/formare/events/aisb2013 CALL FOR PARTICIPATION Symposium at the annual convention of the AISB (Society for the Study of Artificial Intelligence and Simulation of Behaviour; http://www.aisb.org.uk) University of Exeter, UK 3-5 April 2013 http://emps.exeter.ac.uk/computer-science/research/aisb/ (early registration deadline 5 March) HANDS-ON TUTORIAL SESSIONS (details below) with * M. Utku ?nver (matching markets) * Peter Cramton (auctions) * Neels Vosloo (finance markets regulation) (http://www.cs.bham.ac.uk/research/projects/formare/events/aisb2013/invited.php) PAPER and DEMO PRESENTATIONS on * environmental models * controlled natural languages * ontologies * auction theory * software verification * formal specification * autonomous systems * self-explaining systems (http://www.cs.bham.ac.uk/research/projects/formare/events/aisb2013/proceedings.php) This symposium is motivated by the long-term VISION of making information systems dependable. In the past even mis-represented units of measurements caused fatal ENGINEERING disasters. In ECONOMICS, the subtlety of issues involved in good auction design may have led to low revenues in auctions of public goods such as the 3G radio spectra. Similarly, banks' value-at-risk (VaR) models ? the leading method of financial risk measurement ? are too large and change too quickly to be thoroughly vetted by hand, the current state of the art; in the London Whale incident of 2012, JP Morgan claimed that its exposures were $67mn under one of its VaR models, and $129 under another one. Verifying a model's properties requires formally specifying them; for VaR models, any work would have to start with this most basic step, as regulators' current desiderata are subjective and ambiguous. We believe that these problems can be addressed by representing the knowledge underlying such models and mechanisms in a formal, explicit, machine-verifiable way. Contemporary computer science offers a wide choice of knowledge representation languages well supported by verification tools. Such tools have been successfully applied, e.g., for verifying software that controls commuter rail or payment systems. Still, DOMAIN EXPERTS without a strong computer science background find it challenging to choose the right tools and to use them. This symposium aims at investigating ways to support them. Some problems can be addressed now, others will bring new challenges to computer science. THE SYMPOSIUM is designed to bring domain experts and formalisers into close and fruitful contact with each other: domain experts will be able to present their fields and problems to formalisers; formalisers will be exposed to new and challenging problem areas. We will combine talks and hands-on sessions to ensure close interaction among participants from both sides. World-class economists will offer HANDS-ON TUTORIAL SESSIONS on the following topics: * MATCHING MARKETS (M. Utku ?nver, Boston College): These include matching students to schools, interns to hospitals, and kidney donors to recipients. See the documentation for the 2012 Nobel Memorial Prize in Economic Sciences for more background information. * AUCTIONS (Peter Cramton, University of Maryland): Peter has been working on auctions for Ofcom UK (4G spectrum auction), the UK Department of the Environment and Climate Change, and others ? and most recently on the ?applicant auctions? for the new top-level Internet domains issued by the ICANN. * FINANCE MARKETS REGULATION (Neels Vosloo, Financial Services Authority, UK): It is currently impossible for regulators to properly inspect risk management models. Test portfolios are a promising tool for identifying problems with risk management models. To what extent can techniques from mechanised reasoning automate some of the inspection process? COMMENTS/QUESTIONS/ENQUIRIES to be sent to DoForm2013 at easychair.org -- Christoph Lange, School of Computer Science, University of Birmingham http://cs.bham.ac.uk/~langec/, Skype duke4701 ? SePublica Workshop @ ESWC 2013. Montpellier, France, 26-30 May. Deadline 4 Mar; http://sepublica.mywikipaper.org ? Intelligent Computer Mathematics, 7?12 Jul, Bath, UK; Deadline 8 Mar http://cicm-conference.org/2013/ ? Enabling Domain Experts to use Formalised Reasoning @ AISB 2013 3?5 April 2013, Exeter, UK. 3 Hands-on Tutorials on Economics http://cs.bham.ac.uk/research/projects/formare/events/aisb2013/ -- Christoph Lange, Universit?t Bremen (now: University of Birmingham) http://kwarc.info/clange, Skype duke4701 ? SePublica Workshop @ ESWC 2013. Montpellier, France, 26-30 May. Deadline 4 Mar; http://sepublica.mywikipaper.org ? Intelligent Computer Mathematics, 7?12 Jul, Bath, UK; Deadline 8 Mar http://cicm-conference.org/2013/ ? Enabling Domain Experts to use Formalised Reasoning @ AISB 2013 3?5 April 2013, Exeter, UK. 3 Hands-on Tutorials on Economics http://cs.bham.ac.uk/research/projects/formare/events/aisb2013/ -- Christoph Lange, School of Computer Science, University of Birmingham http://cs.bham.ac.uk/~langec/, Skype duke4701 ? SePublica Workshop @ ESWC 2013. Montpellier, France, 26-30 May. Deadline 4 Mar; http://sepublica.mywikipaper.org ? Intelligent Computer Mathematics, 7?12 Jul, Bath, UK; Deadline 8 Mar http://cicm-conference.org/2013/ ? Enabling Domain Experts to use Formalised Reasoning @ AISB 2013 3?5 April 2013, Exeter, UK. 3 Hands-on Tutorials on Economics http://cs.bham.ac.uk/research/projects/formare/events/aisb2013/