Dr Odinaldo Rodrigues

Welcome to my web page

I am a member of the Software Modelling and Applied Logic group in the Department of Informatics at King's College London

My research concentrates mainly in the area of Artificial Intelligence, more specifically in the formalisation of the common-sense reasoning, non-monotonic reasoning, and numerical aspects of argumentation.

For further information about my academic activities at King's, some references to my research work and how to get in touch with me, please use the links on the menu.

Thank you for your visit!

Research interests

My research interests currently revolve around aspects related to Artificial Intelligence, especially in the formalisation of common-sense reasoning. These include belief revision, abduction, argumentation theory and non-monotonic reasoning in general.

I work both with the theoretical aspects AI, e.g., foundations of AI, translations between logical systems, belief revision in non-classical logics, merging of argumentation systems, as well as with the application of AI in computer science, including optmisation techniques for requirements engineering, implementation of non-monotonic reasoning systems, BDI systems, concept classification and the like.

The main areas of research interest are summarised below:

Artificial Intelligence

  • Agents systems
  • BDI reasoning
  • Optimisation, searching, etc

Formalisation of the common-sense reasoning

  • Non-monotonic reasoning
  • Belief revision
  • Database updates
  • Argumentation theory
  • Voting problems and preference aggregation
  • Abduction

PC membership

  • IJCAI, 2015 - Senior Programme Committee member
  • AAAI, 2015 - Programme Committee member
  • TAFA, 2015 - Programme Committee member

Other activities


I have taught several modules at BSc and MSc level including:

  • Data Structures and their Implementation in C++ (1999 and 2000)
  • Computational Logic (2001)
  • Database Systems (1999 to 2002)
  • Artificial Intelligence (2002 and 2007)
  • Conceptual Analysis (2003 and 2004)
  • Internet Systems (2005 and 2006)
  • Distributed Systems (2006 and 2007)
  • Computer Science Logic (2008)

Current modules

Selected publications

[1] D. M. Gabbay and O. Rodrigues. Equilibrium states in numerical argumentation networks. Logica Universalis, pages 1--63, 2015. [ bib | DOI | http ]
[2] F. Meneguzzi, O. Rodrigues, N. Oren, W. W. Vasconcelos, and M. Luck. {BDI} reasoning with normative considerations. Engineering Applications of Artificial Intelligence, 43(0):127 -- 146, 2015. [ bib | DOI | http ]
[3] D. M. Gabbay and O. Rodrigues. Probabilistic argumentation: An equational approach. Logica Universalis, pages 1--38, 2015. [ bib | DOI | http ]
[4] D. Gabbay and O. Rodrigues. Degrees of undecidedness in loops in argumentation networks: a numerical approach, 2015. Draft. [ bib ]
[5] S. A. Hosseini, S. Modgil, and O. Rodrigues. Enthymeme construction in dialogues using shared knowledge. In S. Parsons, N. Oren, C. Reed, and F. Cerutti, editors, Proceedings of COMMA V, Frontiers in Artificial Intelligence and Applications, pages 325--332. IOS Press, 2014. DOI10.3233/978-1-61499-436-7-325. [ bib ]
[6] D. M. Gabbay and O. Rodrigues. A self-correcting iteration schema for argumentation networks. In S. Parsons, N. Oren, C. Reed, and F. Cerutti, editors, Proceedings of COMMA V, Frontiers in Artificial Intelligence and Applications, pages 377 -- 384. IOS Press, 2014. DOI: 10.3233/978-1-61499-436-7-377. [ bib ]
[7] D. M. Gabbay and O. Rodrigues. An equational approach to the merging of argumentation networks. Journal of Logic and Computation, 24:1253--1277, 2014. [ bib ]
[8] D. M. Gabbay and O. Rodrigues. A numerical approach to the merging of argumentation networks. In M. Fisher, L. van der Torre, M. Dastani, and G. Governatori, editors, Proceedings of CLIMA XIII, pages 195--212. Springer-Verlag, 2012. [ bib ]
[9] D Gabbay, O Rodrigues, and A Russo. Revision, Acceptability and Context: Theoretic and Algorithmic Aspects. Springer Verlag, 2010. [ bib | DOI | http ]
[10] D. M. Gabbay, G. Pigozzi, and O. Rodrigues. Belief revision, belief merging and voting. In G. Bonanno, W. van der Hoek, and M. Wooldridge, editors, Proceedings of the Seventh Conference on Logic and the Foundations of Games and Decision Theory (LOFT06), pages 71--78. University of Liverpool, 2006. [ bib ]
[11] C. Elsenbroich, D. M. Gabbay, and O. Rodrigues. Getting possibilities from the impossible. In Proceedings of NMR-06, pages 505--513. Institut fur Informatik, 2006. ISSN 1860-8477. [ bib ]
[12] O. Rodrigues. Iterated Revision and Automatic Similarity Generation, volume 2, pages 591--613. College Publications, 2005. [ bib ]
[13] D. M. Gabbay, O. Rodrigues, and J. Woods. Deletion in resource unbounded logics - Belief contraction, anti-formulae and resource overdraft: Part II. In S. Rahman, J. Symons, D. M. Gabbay, and J. P. van Bendegem, editors, Logic, Epistemology and the Unity of Science, volume 1, chapter 16, pages 291--326. Kluwer Academic Publishers, 2004. [ bib ]
[14] O. Rodrigues, A. d'Avila Garcez, and A. Russo. Reasoning about requirements evolution using clustered belief revision. In G. Spanoudakis A. S. d'Avila Garcez and A. Zisman, editors, Proceedings of ACM ESEC/FSE International Workshop on Intelligent Technologies for Software Engineering WITSE03, 2003. [ bib ]
[15] O. Rodrigues. Structured clusters: A framework to reason with contradictory interests. Journal of Logic and Computation, 13(1):69--97, 2003. [ bib ]
[16] D. M. Gabbay, O. Rodrigues, and J. Woods. Belief contraction, anti-formulae and resource overdraft: Part I - Deletion in resource bounded logics. Logic Journal of the IGPL, 10(6):601--652, November 2002. [ bib ]
[17] D. M. Gabbay, O. Rodrigues, and A. Russo. Information, Uncertainty, Fusion, chapter Revision by Translation, pages 3--31. Kluwer Academic Publishers, 1999. ISBN: 0-7923-8590-X. [ bib ]
[18] O. Rodrigues. A methodology for iterated information change. PhD thesis, Department of Computing, Imperial College, 1998. [ bib | .pdf ]
[19] D. M. Gabbay and O. Rodrigues. Structured belief bases: a practical approach to prioritised base revision. In D. M. Gabbay, Rudolf Kruse, Andreas Nonnengart, and Hans Jürgen Ohlbach, editors, Proceedings of First Internation Joint Conference on Qualitative and Quantitative Practical Reasoning, pages 267--281. Springer-Verlag, June 1997. [ bib ]
[20] D. M. Gabbay and O. Rodrigues. Structured databases: a framework to reason about belief change. In Guy McCusker and Sofia Jourdan, editors, Proceedings of the Theory and Formal Methods 1996 workshop. Imperial College - Department of Computing, Imperial College Press, March 1996. [ bib ]
[21] O. Rodrigues, M. Ryan, and P.-Y. Schobbens. Counterfactuals and updates as inverse modalities. In Yoav Shoham, editor, 6th Conference on Theoretical Aspects of Rationality and Knowledge, pages 163--174, 1996. [ bib ]
[22] D. M. Gabbay and O. Rodrigues. A methodology for iterated theory change. In D. M. Gabbay and Hans Jürgen Ohlbach, editors, Practical Reasoning - First International Conference on Formal and Applied Practical Reasoning, FAPR'96, Lecture Notes in Artificial Intelligence. Springer Verlag, 1996. [ bib ]
[23] Odinaldo Rodrigues and Mario Benevides. Promal — programming in modal action logic. In Manuel Hermenegildo and Jaan Penjam, editors, Programming Language Implementation and Logic Programming, volume 844 of Lecture Notes in Computer Science, pages 457--458. Springer Berlin Heidelberg, 1994. [ bib | DOI | http ]
[24] O. Rodrigues and M. R. F. Benevides. Belief revision in pseudo-definite sets. In Proceedings of the 11th Brazilian Symposium on Artificial Intelligence (SBIA '94), 1994. [ bib ]
[25] O. Rodrigues and M. R. F. Benevides. Revisão de crenças em conjuntos de cláusulas. Technical report, COPPE/UFRJ, Rio de Janeiro-RJ, BRAZIL, July 1993. Publicações Técnicas, ES-281/93. [ bib ]
[26] O. Rodrigues. Prolog modal de ação e revisão de crenças em conjuntos definidos. Master's thesis, COPPE - Universidade Federal do Rio de Janeiro - Brazil, 1993. Published in the Federal University of Rio de Janeiro, Brazil. [ bib ]
[27] O. Rodrigues and M. R. F. Benevides. Prolog modal de ação. In Anais do IX SBIA, pages 339--357, 1992. [ bib ]



Computation of Argumentation Semantics

The Gabbay-Rodrigues Iterative Solver (GRIS) is a lightweight solver written in C++ that can be used to compute the solutions of problems in the grounded and preferred semantics.

GRIS can be used to compute extensions as well as to provide answers to acceptability of arguments in one or all of the extensions under one of these two semantics.

GRIS can be downloaded from here.

Research projects

  • EPSRC grant number EP/E034446/1, Connections between belief revision, belief merging and voting, 2006
  • EPSRC grant number GR/R44706/01, Belief Contraction and Anti-Formulae. Logical Modelling of Deletion, 2002-2005

BSc projects

I prefer to supervise students in emerging topics or in an area related to my research interests.

I am only willing to supervise projects that attempt to improve your overall design, reasoning and programming skills. My project topic suggestions may appear demanding, but they are tailored to maximise your professional development and I will assist you throughout the development.

I may also be willing to supervise your own project in another area of computer science provided that

  • the topic of the project is interesting and involves more than basic programming, use of web technologies, and/or the implementaion of a mobile application;
  • the proposal suggests an innovative approach to a particular computer science problem; and
  • you are willing to work hard on it.

Topics suggestions for 2014/2015

WARNING: this list may contain more topics than I am able to supervise.

  1. [OR-1] An automatic natural deduction proof checker for propositional logic.

    Given a set of natural deduction rules, a set of premises, a conclusion and a proof in a pre-defined format, your tool should be able to tell whether the proof is correct or not.

    Your tool should be easy to use and accept proofs from a web interface or input file, convert the proof to an internal language and check whether the proof is correct indicating any wrong steps in the proof.


    Your tool will help logic students to learn natural deduction.

    Skills required

    • A good understanding of logic and propositional logic
    • Basic computing skills: data structures, web interfaces, etc
    • JAVA
  2. [OR-2] An extension to JASON

    JASON is an interpreter for an extended version of AgentSpeak. It can be extended in a number of different ways to perform different kinds of reasoning with agents.

    We will need to discuss one possible extension, that you will implement and discuss and illustrate its use in practice.

  3. [OR-3] Computing argumentation semantics

    Argumentation theory provides a means of deciding which arguments win based on the attack relationship of these arguments. An extension is the set of winning arguments under a particular semantics. An Abstract Argumentation Framework is a tuple , where A is a set of arguments and R is an attack relation on A x A.

    Deciding whether a subset of A is an extension of an argumentation framework is a complex problem.

    The objective of this project is to explore this problem as much as possible and come up with an efficient implementation to check whether a given set is an extension of an argumentation framework and/or calculate all extensions of such a framework.

    We are not concerned with the visualisation of the graphs which will be performed by an external application

    Skills required

    • basic computer science concepts: graphs, graph traversal, algorithms
    • interface and integration of system components
    • JAVA or C++
  4. [OR-4] A mobile application for Android or iOS (Android preferred)

    You need to write to me with the suggestion of a sophisticated application for android or iOS, which I will review, amend if necessary and only accept it if appropriate.

    Any topic suggestion must consist of a sophisticated application.

  5. [OR-5] Your own proposal

    A project topic of your choice, to be discussed and agreed.

    If you are considering submitting your own project proposal, be ambitious and prepared to submit an outline of your idea via e-mail to me before seeing me.

MSc projects

I prefer to supervise students in emerging topics or in an area related to my research interests.

I am only willing to supervise projects that attempt to improve your overall design, reasoning and programming skills. My project topic suggestions may appear demanding, but they are tailored to maximise your professional development and I will assist you throughout the development.

Topics suggestions for 2015

  1. To appear


Things I like to do

  • Write a bit of code: JAVA, C++, PHP, HTML, etc.
  • Play with my camera
  • Read books and stuff
  • Drink a lot of coffee
  • Fix the world
  • Learn about technology
  • Ride my bike
  • Travel the world
  • Maths and computing

Office hours (Summer 2015)

Please e-mail me for an appointment.

Contact details

Dr. Odinaldo Rodrigues
King's College London,
Department of Informatics
London, WC2R 2LS, UK
e-mail: odinaldo.rodrigues@kcl.ac.uk
Tel.: +44 20 7848 2087
Fax: +44 20 7848 2851
Office: S1.19, Strand Building, Strand Campus