# Automated Reasoning

The Automated Reasoning activity is part of the Trustworthy Systems.

### Aim

The aim of this activitiy is to provide and further develop general automated and interactive reasoning tools for sofware verification. As opposed to specific automation activities in the Trustworthy Systems project, such as File System Verification, Binary Verification, or Automated C Code Abstraction, this activity has a more general scope, looking at fundamental automated reasoning techniques such as automated first-order theorem proving, first-order model checking, and development on the interactive theorem prover HOL4.

### Approach

In order to support a wide spectrum of verification tasks and application areas, our research covers a variety of methods:

• Interactive theorem proving for design-time verification of complex systems
• Dynamic systems verification at design-time and at runtime based on temporal logic
• Automated theorem proving as back-end reasoners embedded in verification tools

A neighboring project develops the Goanna bug-finding tool.

## Technical Research Challenges

• Interactive Theorem Proving
We are developing the HOL4 interactive theorem prover. Contact: Michael Norrish, michael.norrish<at>data61.csiro.au

• Dynamic systems verification
In contrast to most mainstream approaches, which are grounded in propositional or quantifier-free logic, we emphasize the role of first-order logic for supporting more faithful system modelling.
• Development of automated theorem proving methods for fragments of CTL* over first-order logic modulo background theories, the Fitzroy system.
• Developing runtime verification methods over first-order logic
• Applications: business rules and process verification, Android security, analysing models from the Security Architecture project
• Automated theorem proving
We focus on methods and tools for automated theorem proving in first-order logic modulo background theories (such as integer arithmetic).
• Providing better alternatives to SMT solvers to reason with quantified formulas
• Calculi and implemented systems, in particular based on Model Evolution and Superposition calculi (the Beagle theorem prover); see here for implemented systems.
• Embedding automated theorem provers as back-end reasoners for interactive theorem proving and for dynamic systems verification

## People

### Past

• Andreas Bauer
• Jan-Christoph Kuester
• Joshua Bax
• Peter Baumgartner

## Publications

 Peter Baumgartner SMTtoTPTP — a converter for theorem proving formats International Conference on Automated Deduction, pp. 285–294, Berlin, Germany, August, 2015 Peter Baumgartner, Joshua Bax and Uwe Waldmann Beagle — a hierarchic superposition theorem prover International Conference on Automated Deduction, pp. 367–377, Berlin, Germany, August, 2015 Peter Baumgartner, Joshua Bax and Uwe Waldmann Finite quantification in hierarchic theorem proving International Joint Conference on Automated Reasoning, pp. 152–167, Vienna, Austria, July, 2014 Aditi Barthwal and Michael Norrish A mechanisation of some context-free language theory in HOL4 Journal of Computer and System Sciences, Volume 80, Number 2, pp. 346–362, March, 2014 Peter Baumgartner Model evolution based theorem proving IEEE Intelligent Systems Magazine (IEEE ISM), Volume 29, Number 1, pp. 4–10, February, 2014 Peter Baumgartner and Uwe Waldmann Hierarchic superposition with weak abstraction and the beagle theorem prover Deduction and Arithmetic (Dagstuhl Seminar 13411), pp. 7, Dagstuhl, Germany,, February, 2014 Ramana Kumar, Magnus Myreen, Michael Norrish and Scott Owens CakeML: A verified implementation of ML ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 179–191, San Diego, January, 2014 Peter Baumgartner Automatische inferenz Handbuch der Kuenstlichen Intelligenz, pp. 129–167, Oldenbourg Verlag, 2013 Peter Baumgartner and Joshua Bax Proving infinite satisfiability International Conference on Logic for Programming, Artificial Intelligence and Reasoning, pp. 86–95, Stellenbosch, South Africa, December, 2013 Joseph Chan and Michael Norrish A string of pearls: Proofs of fermat's little theorem Journal of Formal Reasoning, Volume 6, Number 1, pp. 63–87, December, 2013 Peter Baumgartner and Uwe Waldmann Hierarchic superposition: Completeness without compactness Fifth International Conference on Mathematical Aspects of Computer and Information Sciences (MACIS 2013), pp. 8–12, Nanning, China, November, 2013 Andreas Bauer, Peter Baumgartner, Diller Martin and Michael Norrish Tableaux for verification of data-centric processes Automated Reasoning with Analytic Tableaux and Related Methods, pp. 28–43, Nancy, France, September, 2013 Andreas Bauer, Jan-Christoph Kuester and Gil Vegliach From propositional to first-order monitoring 4th International Conference on Runtime Verification (RV), Rennes, France, September, 2013 Michael Norrish and Brian Huffman Ordinals in HOL: Transfinite arithmetic up to (and beyond) $\omega_1$ International Conference on Interactive Theorem Proving, pp. 133–146, Rennes, France, July, 2013 Peter Baumgartner and Uwe Waldmann Hierarchic superposition with weak abstraction International Conference on Automated Deduction, pp. 39–57, Lake Placid, New York, USA, June, 2013 Hing-Lun Chan and Michael Norrish A string of pearls: Proofs of fermat’s little theorem International Conference on Certified Programs and Proofs, pp. 188–207, Kyoto, Japan, October, 2012 Peter Baumgartner, Bjoern Pelzer and Cesare Tinelli Model evolution with equality — revised and implemented Journal of Symbolic Computation, Volume 47, Number 9, pp. 1011–1045, September, 2012 Andreas Bauer and Ylies Falcone Decentralised LTL monitoring International Symposium on Formal Methods (FM), pp. 88-100, Paris/France, August, 2012Best Paper Award! Andreas Bauer, Jan-Christoph Kuester and Gil Vegliach Runtime verification meets android security 4th NASA Formal Methods Symposium (NFM), pp. 174–180, Norfolk, Virginia, USA, April, 2012 Geoff Sutcliffe, Stephan Schulz, Koen Claessen and Peter Baumgartner The TPTP typed first-order form and arithmetic Proceedings of the 18th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, pp. 406–419, Merida, Venezuela, March, 2012 Peter Baumgartner and Uwe Waldmann A combined superposition and model evolution calculus Journal of Automated Reasoning, Volume 47, Number 2, pp. 191–227, August, 2011 Michael Norrish Mechanised computability theory International Conference on Interactive Theorem Proving, pp. 297—311, Nijmegen, The Netherlands, August, 2011 Andreas Bauer and Martin Leucker The theory and practice of SALT NASA Formal Methods Symposium, pp. 28, Pasadena, CA, USA, April, 2011 Andreas Bauer, Martin Leucker and Christian Schallhart Runtime verification for LTL and TLTL ACM Transactions on Software Engineering and Methodology, Volume 20, Number 4, pp. 75, April, 2011 Peter Baumgartner and Cesare Tinelli Model evolution with equality modulo built-in theories International Conference on Automated Deduction, pp. 85–100, Wroclaw, Poland, April, 2011 Aditi Barthwal and Michael Norrish A formalisation of the normal forms of context-free grammars in HOL4 19th EACSL Annual Conferences on Computer Science Logic, pp. 95–109, Brno, Czech Republic, August, 2010 Andreas Bauer and Patrik Haslum LTL goal specifications revisited European Conference on Arificial Intelligence, Lisbon, Portugal, August, 2010 Ramana Kumar and Michael Norrish (nominal) unification by recursive descent with triangular substitutions International Conference on Interactive Theorem Proving, pp. 51–66, Edinburgh, United Kingdom, July, 2010 Andreas Bauer, Martin Leucker and Christian Schallhart Comparing LTL semantics for runtime verification Journal of Logic and Computation, Volume 20, Number 3, pp. 651–674, June, 2010 Peter Baumgartner and Evgenij Thorstensen Instance based methods — an overview Künstliche Intelligenz, Volume 24, Number 1, pp. 35–42, April, 2010 Andreas Bauer, Martin Leucker, Christian Schallhart and Michael Tautschnig Don't care in SMT — building flexible yet efficient abstraction/refinement solvers International Journal on Software Tools for Technology Transfer (STTT, Springer), Volume 12, Number 1, pp. 23–37, February, 2010 Peter Baumgartner, Ulrich Furbach and Bjoern Pelzer The hyper tableaux calculus with equality and an application to finite model computation Journal of Logic and Computation, Volume 20, Number 1, pp. 77–101, February, 2010 Franz Baader, Andreas Bauer and Alwen Tiu Matching trace patterns with regular policies 3rd International Conference on Language and Automata Theory and Applications (LATA), pp. 105–116, Spain, November, 2009 Franz Baader, Andreas Bauer, Peter Baumgartner, Anne Cregan, Alfredo Gabaldon, Krystian Ji, Kevin Lee, David Rajaratnam and Rolf Schwitter A novel architecture for situation awareness systems TABLEAUX 2009 — The 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, pp. 77–92, Oslo, Norway, July, 2009 Peter Baumgartner and John Slaney Constraint modelling: A challenge for first order automated reasoning International Workshop on First-Order Theorem Proving (FTP'09), pp. 4–18, Oslo, Norway, July, 2009 Peter Baumgartner and Uwe Waldmann Superposition and model evolution combined Proceedings of the 22nd International Conference on Automated Deduction, pp. 17–34, Montreal, Canada, July, 2009 Peter Baumgartner, Alexander Fuchs, Hans de Nivelle and Cesare Tinelli Computing finite models by reduction to function-free clause logic Journal of Applied Logic, Volume 7, Number 1, pp. 58–74, January, 2009 Peter Baumgartner, Alexander Fuchs and Cesare Tinelli ME(LIA) — model evolution with linear integer arithmetic constraints Proceedings of the 15thInternational Conference on Logic for Programming, Artificial Intelligence and Reasoning, pp. 258–273, Doha, Qatar, November, 2008 Peter Baumgartner, Alessandro Armando and Gilles Dowek Automated reasoning — 4th international conference, IJCAR 2008 Volume 5195 in Lecture Notes in Artificial Intelligence, Springer, 2008 Konrad Slind and Michael Norrish A brief overview of HOL4 International Conference on Theorem Proving in Higher Order Logics, pp. 28–32, Montréal, Canada, August, 2008 Tom Ridge, Michael Norrish and Peter Sewell A rigorous approach to networking: TCP, from implementation to protocol to service International Symposium on Formal Methods (FM), pp. 294—309, Turku, Finland, May, 2008 Peter Baumgartner and Cesare Tinelli The model evolution calculus as a first-order DPLL method Artificial Intelligence, Volume 172, Number 4–5, pp. 591–632, January, 2008 Peter Baumgartner Logical engineering with instance-based methodsProceedings of the 21st International Conference on Automated Deduction, pp. 404–409, July, 2007 Peter Baumgartner, Ulrich Furbach and Bjoern Pelzer Hyper tableaux with equality Proceedings of the 21st International Conference on Automated Deduction, pp. 492–507, Bremen, Germany, July, 2007 Steve Bishop, Matthew Fairbairn, Michael Norrish, Peter Sewell, Michael Smith and Keith Wansbrough Engineering with logic: HOL specification and symbolic-evaluation testing for TCP implementations ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 55—66, Charleston, South Carolina, USA, January, 2006 Steve Bishop, Matthew Fairbairn, Michael Norrish, Peter Sewell, Michael Smith and Keith Wansbrough Rigorous specification and conformance testing techniques for network protocols, as applied to TCP, UDP, and sockets ACM Conference on Communications, pp. 265–276, Philadelphia, August, 2005 Michael Norrish Complete integer decision procedures as derived rules in HOL International Conference on Theorem Proving in Higher Order Logics, pp. 71–86, Rome, September, 2003