Dirk Pattinson: Software
Software
Here are some software packages that have been developed that
actually bring theoretical ideas onto the machine. Mainly, these are
concerned with exact real arithmetic and (modal) theorem proving.
Within the COOL project, we did succeed
to gain EPSRC funding to
implement a larger-scale automated reasoning platform based on the
coalgebraic paradigm that will extend the prototype below.
Graded and Probabablistic Modal Logic Solver
The code below implements the tableau calculus for both graded and
probabilistic modal logic based on mixed integer programming. We are
implementing a standard (unlabelled) tableau calculus, the rules of
which are implemented with the help of mixed integer programming.
Propositional connectives are represented using binary decision
diagrams. The main novelty lies in the rules that have a similar
format for both graded and probabilistic modal logic.
Download
Please note the DISCLAIMER.
Documentation
The implementation is based on and described in the following
papers:
L. Schröder and D. Pattinson.
PSPACE bounds for rank-1 modal logics.
ACM Transactions on Computational Logics, 10(2), 2009.
[ bib |
.pdf ]
-
W. Snell, D. Pattinson, and F. Widmann.
Solving graded/probabilistic modal logic via linear inequalities,
2011.
[ bib |
.pdf ]
Developers
- William Snell, Imperial College London
- Dirk Pattinson, Imperial College London
- Florian Widmann, Imperial College London
IC-ODE-Solvers
IC-ODE-solvers is a C package, which solves initial value problems,
using interval arithmetic and rational arithmetic packages. The
package contains programs based on domian-theoretic versions of
Picard's and Euler's methods to solve initial value problems.
The installation method and a few examples are provided in this
package in order to help the user. All feedbacks and comments should
be sent to the email provided in the package.
Download
Please note the DISCLAIMER.
Documentation
The implementation is based on the papers
- A. Edalat and D. Pattinson.
A domain-theoretic account of Picard's theorem.
LMS Journal of Computation and Mathematics, 10:83-118,
2007.
[ bib |
.pdf ]
- A. Edalat and D. Pattinson.
A domain theoretic account of Euler's method for solving initial
value problems.
In J. Dongarra, K. Madsen, and J. Wasniewski,
editors, Proc.
PARA 2004, volume 3732 of Lecture Notes in Comp.
Sci., pages 112-121,
2006.
[ bib |
.pdf ]
Developers
- Abbas Edalat, Imperial College London
- Ali Khanban, Imperial College London
- Dirk Pattinson, Imperial College London
COLOSS: The Coalgebraic Logic Satisfiability Solver
COLOSS, the Coalgebraic Logic Satisfiability Solver, decides
satisfiability of modal formulas in a generic and compositional way.
It
implements a uniform polynomial space algorithm to decide
satisfiability
for modal logics that are amenable to coalgebraic semantics. This
includes e.g. the logics K, KD, Pauly's coalition logic, graded
modal logic, and probabilistic modal logic. Logics are easily
integrated into COLOSS by providing a complete axiomatisation of
their
coalgebraic semantics in a specific format. Moreover, COLOSS is
compositional: it synthesises decision procedures for modular
combinations of logics that include the fusion of two modal logics
as a special case.
One thus automatically obtains reasoning support
e.g.
for logics interpreted over probabilistic automata that combine
non-determinism and probabilities in different ways.
Download
Please note the DISCLAIMER.
Documentation
The following system description gives an overview of the CoLoSS
system.
- G. Calin, R. Myers, D. Pattinson, and
L. Schröder.
ColoSS: The coalgebraic logic satisfiability solver.
Electr. Notes Theor. Comput. Sci., 231:41-54, 2009.
Proc. Methods for Modalities 5 (2007).
[ bib |
.pdf ]
Developers
- Georgel Calin, Jacobs University Bremen, Germany
- Rob Myers, Imperial College London
- Dirk Pattinson, Imperial College London
- Lutz Schröder, DFKI Lab Bremen and Universität Bremen, Germany