Robert Kowalski

Professor Emeritus and Distinguished Research Fellow

Department of Computing
Imperial College London

180 Queen's Gate, London SW7 2BZ, UK.

Email: rak at

Please note that I am no longer accepting research students.

Curriculum Vitae

A Short Story of My Life and Work

Old paper: Logic as a Computer Language for Children, In Proceedings of European Conference on Artificial Intelligence, Orsay, France, July 1982. Reprinted in New Horizons in Educational Computing, (ed. M. Yazdani), Ellis Horwood Ltd., Chichester, 1984, pp. 121-144. Reprinted in Progress in Artificial Intelligence, (eds. L. Steel and J. A. Campbell), Ellis Horwood Ltd., Chichester.

This paper describes a project that, beginning in 1980, was aimed at teaching logic and computing to children, starting at the age of 10. The project used a declarative version of Prolog, with a sugared-up syntax.

New paper: Reactive Computing as Model Generation with Fariba Sadri, New Generation Computing, 2015, Volume 33, Issue 1, pp 33-67

In this paper we propose a logic-based, framework inspired by artificial intelligence, but scaled down for practical database and programming applications. Computation in the framework is viewed as the task of generating a sequence of state transitions, with the purpose of making an agent's goals all true. States are represented by sets of atomic sentences (or facts), representing the values of program variables, tuples in a coordination language, facts in relational databases, or Herbrand models.

In the model-theoretic semantics, the entire sequence of states and events are combined into a single model-theoretic structure, by associating timestamps with facts and events. But in the operational semantics, facts are updated destructively, without timestamps. We show that the model generated by destructive updates is identical to the model generated by reasoning with facts containing timestamps. We also extend the model with intentional predicates and composite event predicates defined by logic programs containing conditions in first-order logic, which query the current state.

New paper: A Logical Characterization of a Reactive System Language with Fariba Sadri. In the Proceedings of RuleML 2014.

Typical reactive system languages are programmed by means of rules of the form if antecedent then consequent. However, despite their seemingly logical character, hardly any reactive system languages give such rules a logical interpretation. In this paper, we investigate a simplified reactive system language KELPS, in which rules are universally quantified material implications, and computation attempts to generate a model that makes the rules true.

The operational semantics of KELPS is similar to that of other reactive system languages, and is similarly incomplete. It cannot make a rule true by making its antecedent false, or by making its consequent true whether or not its antecedent becomes true. In this paper, we characterize the reactive models, for which the operational semantics is complete. Informally speaking, a model is reactive if every action in the model is an instance of an action in the consequent of a rule whose earlier conditions are true.

New paper. History of Logic Programming

Volume 9, Computational Logic (Joerg Siekmann, editor).
In the History of Logic series, edited by Dov Gabbay and John Woods, Elsevier, 2014, pp 523-569.

This history covers some of the highlights of the development of logic programming from the late 1960s into the 21st century. It focuses on a number of issues that continue to be important today:

the difference between solving a goal by theorem-proving and solving it by model generation,
the difference between solving a goal top-down and solving it bottom-up, and
the relationship between declarative and procedural representations.

Computational Logic and Human Thinking:
How to be Artificially Intelligent

This earlier draft of a book of the same title, published in July 2011 by Cambridge University Press, presents the principles of Computational Logic, so that they can be applied in everyday life.  I have written the main part of the book informally, both to reach a wider audience and to argue more convincingly that Computational Logic is useful for human thinking. However, I have also included a number of additional, more formal chapters for the more advanced reader.

Here are some extracts from the reviews:

By Thomas A. Blackson, Arizona State University, on the back cover:
"Computational Logic and Human Thinking is a superb introduction both to AI from within a computational logic framework and to its application to human rationality and reasoning. Nothing else comes close. Kowalski writes with philosophical insight and just the right level of technical expertise. He puts the excitement back in AI. This sets Computational Logic and Human Thinking apart from the technically overwhelming, and all too often largely unintuitive and uninspiring, encyclopedic introductions that currently dominate the field.

By Donald Gillies, University College London, on the back cover:
"Artificial Intelligence (or AI) tries to program computers so that they can think intelligently like humans. In this book, one of the pioneers of AI suggests something new and original, namely to use the results of AI to improve human thinking ... Anyone who wants to reason better and more effectively in everyday life should study Robert Kowalski's book."

By Alan Bundy, Artificial Intelligence , June-July 2013:
"Computational Logic and Human Thinking might make an excellent basis for a course on AI for non-science students. It covers a wide range of AI techniques in an accessible form and within a uniform framework, with more technical details available as optional extensions. Moreover, Kowalski's enthusiasm for and dedication to his subject shines through on every page."

By George Luger, Computing in Science and Engineering , July/August 2012:
"In this serious and enjoyable book, Kowalski proposes a specific, utilitarian, and sufficient model, in the scientific sense, of human subject/world communications. And, as Aristotle suggested long ago, the sufficiency of this logic-based representational effort could offer insights that can lead to more coherent reasoning, writing, discussions, and arguments by human agents."

By Corrado Mencar, Computing Reviews , October, 2012:
"In sum, this book could be of greatest value to computer science students and professionals who want to improve their computational thinking and have come to see topical discipline to be applied to everyday problems and situations."

By Luis Moniz Pereira, Association of Logic Programming Newsletter , January 2012:
"The book is within clear grasp of a general higher-educated audience, because of the adept and informal naturalness with which it addresses, explains and exemplifies nevertheless non-trivial issues in knowledge representation and reasoning. It is also a treasure trove for teachers and researchers alike, as it admirably integrates the author's longstanding groundbreaking and fertile research efforts, and expounds with clarity and simplicity the unifying epistemological virtues of the Computational Logic paradigm - one that is supported by a vast community of researchers."

From :
"A job well done." "An interesting book." "An excellent book and deserves a wide readership!"

If you are teaching a course, and would like copies of slides, please email me at rak at doc dot ic dot ac dot uk. Jacinto Davila has also used a draft of this book for a course at
Universidad de Los Andes, Venezuela. Here is a link to his Spanish translation of an earlier draft.

Logic for Problem Solving

The preface describes the goals of the book in the following terms:

This book investigates the application of logic to problem-solving and computer programming. It assumes no previous knowledge of these fields, and may be appropriate therefore as an introduction to

Although the book was originally published in 1979 and based on lecture notes written in 1974, I like to think that much its content may still be relevant today.

Many thanks to Geraint Wiggins for this improved pdf of the book.

New book: Logic for Problem Solving, Revisited

As it says, "In this extended edition, Robert Kowalski revisits his classic text in the light of subsequent developments in a substantial commentary of fifty pages."


I have been working with WHO and UNICEF since 2009, helping to develop, implement and deploy a set of logical rules to assist in estimating global, country by country, infant immunization coverage . The problem is to reconcile inconsistencies when different sources of data conflict - for example when government reported data is inconsistent with survey data. The purpose of the logical rules is to make the reconciliation and estimation process more transparent and more consistent.

The rules have been implemented in XSB Prolog as a purely declarative logic program, and have been used to assist in making the estimates in 2010, 2011, 2012 and 2013 for each of the preceding years. In addition to helping to ensure transparency and consistency, the Prolog implementation has also proved useful in providing detailed documentation of the rationale for each of the estimates.

There are two articles describing our work. The first , published in the online journal PLOS-ONE, describes our work for a general audience with little or no computing background. The second , presented at JURISIN 2011, describes the work for a more academic audience and compares it with previous work on the logical formalisation of the British Nationality Act.

Selected bibliography:

Early papers on theorem-proving, logic programming and knowledge representation:

Legal reasoning and argumentation

Metalogic programming

Event Calculus

Abductive Logic Programming 

From Abduction to Argumentation

Intelligent Agents

   Miscellaneous papers

Updated 10 February 2015