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Studying Algebraic Structures using Prover9 and Mace4 [article]

Rob Arthan, Paulo Oliva
2019 arXiv   pre-print
The specific tools in our case study are Prover9 and Mace4; the algebraic structures are generalisations of Heyting algebras known as hoops.  ...  a class of algebraic structures.  ...  At a more advanced level, we have discussed our own research using Prover9 and Mace4 to investigate algebraic structures.  ... 
arXiv:1908.06479v1 fatcat:rffhjsvmgbczrnsly5solzqgla

Internal axioms for domain semirings

Jules Desharnais, Georg Struth
2011 Science of Computer Programming  
New axioms for domain operations on semirings and Kleene algebras are proposed.  ...  They lead to a simple and natural algebraic approach to modal logics based on equational reasoning.  ...  Acknowledgements We are most grateful to Peter Jipsen for interesting discussions, to Viorica Sofronie-Stokkermans for important references, and to the referees for their comments.  ... 
doi:10.1016/j.scico.2010.05.007 fatcat:vjhanynf5jh6fbybs3ffq3oo5q

Mining counterexamples for wide-signature algebras with an Isabelle server [article]

Wesley Fussner, Boris Shminke
2021 arXiv   pre-print
We propose an approach for searching for counterexamples of statements about algebraic structures with a medium-sized signature using the Isabelle proof assistant in an efficient, parallel manner.  ...  We contribute a Python client Isabelle server and other scripts implementing our approach, and provide results of our computational experiments.  ...  In partnership with automated theorem proving, finite model builders have been applied highly effectively in studies of algebraic structures (e.g., for quasigroups and loops [9] ).  ... 
arXiv:2109.05264v1 fatcat:ewhovkrt3rbvlbvjlsiagfjk2y

On Automated Program Construction and Verification [chapter]

Rudolf Berghammer, Georg Struth
2010 Lecture Notes in Computer Science  
" domain-specific algebraic theories that have been designed and optimised for automation.  ...  Based on the standard methods of Dijkstra, Gries and Hoare, it supports a game of proof and refutation with automated theorem provers, model search tools and computer algebra systems combined with "hidden  ...  Besides Prover9 and Mace4 we also use the RelView system [5] .  ... 
doi:10.1007/978-3-642-13321-3_4 fatcat:xxip7nxymjcfnmslpok5eov27y

(Dual) Hoops Have Unique Halving [chapter]

Rob Arthan, Paulo Oliva
2013 Lecture Notes in Computer Science  
The semantics of these logics can be given using specialisations of algebraic structures known as hoops and coops.  ...  As part of an investigation into the metatheory of propositional continuous logic, we were indebted to Prover9 for finding proofs of important algebraic laws.  ...  for including our problem set in the TPTP Problem Library and for running the problems on a selection of provers; and to Bob Veroff for helping us understand Prover9 performance.  ... 
doi:10.1007/978-3-642-36675-8_9 fatcat:6mg6y3njmfcq5m62yhacg4avmq

Can Refinement be Automated?

Peter Höfner, Georg Struth
2008 Electronical Notes in Theoretical Computer Science  
We use McCune's Prover9 in combination with the counterexample search tool Mace4 [19] in a rather naïve approach, i.e, without much tuning.  ...  ., for deconstructing and reconstructing concurrency, for simulation and for loop refinement. • We use this toolkit for automatically verifying two complex laws for data refinement and atomicity refinement  ...  Prover9 and Mace4 We use McCune's Prover9 tool [19] for proving theorems in demonic refinement algebra. Prover9 is a saturation-based theorem prover for first-order equational logic.  ... 
doi:10.1016/j.entcs.2008.02.021 fatcat:tqtg3hmpmzgchbeyngwupaza7y

(Dual) Hoops Have Unique Halving [article]

Rob Arthan, Paulo Oliva
2013 arXiv   pre-print
This extension is designed to give a more satisfactory model theory for continuous structures. The semantics of these logics can be given using specialisations of algebraic structures known as hoops.  ...  As part of an investigation into the metatheory of propositional continuous logic, we were indebted to Prover9 for finding a proof of an important algebraic law.  ...  for including our problem set in the TPTP Problem Library and for running the problems on a selection of provers; and to Bob Veroff for helping us understand Prover9 performance.  ... 
arXiv:1203.0436v2 fatcat:u254uohbbndebo2dhgxo5ozr6q

Automated Verification Of Role-Based Access Control Policies Constraints Using Prover9

Khair Eddin Sabri
2015 International Journal of Security Privacy and Trust Management  
Then, we use a general purpose theorem prover tool called Prover9 for proving the satisfaction of constraints.  ...  Access control policies are used to restrict access to sensitive records for authorized users only.  ...  Rusnok and Adlassnig [10] use Prover9 for detecting inconsistency in health records. Furthermore, Prover9 is used to prove theorems related to algebraic structures [11, 12, 13] .  ... 
doi:10.5121/ijsptm.2015.4101 fatcat:uj5f6cuwfjd55nu3c47t62fj7q

Automated Verification of Relational While-Programs [chapter]

Rudolf Berghammer, Peter Höfner, Insa Stucke
2014 Lecture Notes in Computer Science  
We show how to automatically verify imperative programs for relation-based discrete structures by combining relation algebra and the well-known assertion-based verification method with automated theorem  ...  We also treat the automatic verification of the equivalence of common-logical and relation-algebraic specifications.  ...  NICTA is funded by the Australian Government through the Department of Communications and the Australian Research Council through the ICT Centre of Excellence Program.  ... 
doi:10.1007/978-3-319-06251-8_11 fatcat:hjdc3zloovhgnctwp62pha3ysi

Automated verification of refinement laws

Peter Höfner, Georg Struth, Geoff Sutcliffe
2009 Annals of Mathematics and Artificial Intelligence  
We used ATP to verify a toolkit of basic refinement laws.  ...  Demonic refinement algebras are variants of Kleene algebras.  ...  Acknowledgements We are very grateful to Tony Hoare for his comments and encouragement.  ... 
doi:10.1007/s10472-009-9151-8 fatcat:7z4ojbrc3nd57n3bgpdf4vk6he

Reasoning about taxonomies in first-order logic

David Thau, Bertram Ludäscher
2007 Ecological Informatics  
The formalization of taxonomies and the relationships between them via our FOL language Ltax allows us to clarify (a) what it means for a taxonomy to be consistent, (b) to be inconsistent, (c) whether  ...  We illustrate our logic-based formalization and the resulting opportunities for automated reasoning support for biological taxonomies using examples involving the classification of a genus of plants.  ...  We used two automatic reasoners: Prover9 and Mace4. 20 Prover9 is a resolution-based first-order logic theorem prover.  ... 
doi:10.1016/j.ecoinf.2007.07.005 fatcat:3a2ix6zu7faijdumfy3zvuudaa

Relational Lattice Axioms [article]

Marshall Spight, Vadim Tropashko
2008 arXiv   pre-print
Relational lattice is a formal mathematical model for Relational algebra. It reduces the set of six classic relational algebra operators to two: natural join and inner union.  ...  New results include additional axioms, equational definition for set difference (more generally anti-join), and case study demonstrating application of the relational lattice theory for query transformations  ...  The brackets are used strictly for algebraic purpose of grouping operations.  ... 
arXiv:0807.3795v1 fatcat:s6hmfbcdrbfhja2rpuc4vawgju

On Affine Logic and Łukasiewicz Logic [article]

Rob Arthan, Paulo Oliva
2014 arXiv   pre-print
The multi-valued logic of Łukasiewicz is a substructural logic that has been widely studied and has many interesting properties.  ...  We present these results using derived connectives to clarify and motivate the proofs and give several applications.  ...  with Prover9 and Mace4.  ... 
arXiv:1404.0570v2 fatcat:hx7j2fbx4ncczpctfylg3md63q

On hom-algebras with surjective twisting

Aron Gohr
2010 Journal of Algebra  
As an application, an earlier result (Fregier and Gohr [1]) on weakly unital hom-algebras is recovered with a different proof.  ...  A hom-associative structure is a set A together with a binary operation and a self-map α such that an α-twisted version of associativity is fulfilled. In this paper, we assume that α is surjective.  ...  In the research leading to this work, we were aided by the computer programs Prover9 and Mace4 written by William McCune [7] .  ... 
doi:10.1016/j.jalgebra.2010.05.003 fatcat:uv3vzxa6vzhyjhwmv5jlg6a7my

On hom-algebras with surjective twisting [article]

Aron Gohr
2009 arXiv   pre-print
As an application, an earlier result by Yael Fregier and the author on weakly unital hom-algebras is recovered with a different proof.  ...  A hom-associative structure is a set A together with a binary operation and a selfmap α such that an α-twisted version of associativity is fulfilled. In this paper, we assume that α is surjective.  ...  In the research leading to this work, we were aided by the computer programs Prover9 and Mace4 written by William McCune [6] .  ... 
arXiv:0906.3270v3 fatcat:jntgwvjzw5ekrjtlxrabcyyvxi
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