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.
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.
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.
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.
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 amazon.com :
"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.
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
Many thanks to Geraint Wiggins for this improved pdf of the book.
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.
Early papers on theorem-proving, logic programming and knowledge representation:
Kowalski, R. and Kuehner, D.,
Resolution with Selection Function
In Artificial Intelligence, Vol. 2, 1971, pp. 227-60.
Reprinted in Anthology of Automated Theorem-Proving Papers, Vol. 2, Springer-Verlag, 1983, pp. 542-577.
Procedure Using Connection Graphs
In JACM Vol. 22, No. 4, 1975, pp. 572-595.
van Emden, M. and Kowalski, R. The Semantics of Predicate Logic as a Programming Language In JACM , Vol. 23, No. 4, 1976, pp. 733-742.
Deliyanni, A. and Kowalski, R.
Logic and Semantic Networks
In CACM, Vol. 22, No. 3, 1979, pp. 184-192.
Algorithm = Logic + Control
In CACM, Vol. 22, No. 7, 1979, pp. 424-436. Reprinted in Programming Languages: A Grand Tour, Third Edition, (ed. E. Horwitz), Computer Science Press, Maryland, 1986, pp. 480-492.
Kowalski, R. The Relationship between Logic Programming and Logic Specification In Phil. Trans. R. Soc. Lond. A, Vol 312, 1984, pp. 345-361.
Kowalski, R. The Limitations of Logic In Proceedings of ACM Computer Science Conference, 1986, pp 7-13. Revised version in Proceedings of SEAS, Heidelberg, 1986, pp. 1-13. Also in Knowledge Base Management Systems, (eds. C. Thanos and J. W. Schmidt), Springer-Verlag, pp. 477-489.
Kowalski, R., Sadri, F. and Soper, P. Integrity Checking in Deductive Databases In Proceedings of VLDB, Morgan Kaufmann, Los Altos, Ca., 1987, pp. 61-69.
Kowalski, R. The Early Years of Logic Programming In CACM, 1988, Vol. 31, No. 1, pp. 38-43.
Legal reasoning and argumentation
Sergot, M., Sadri, F., Kowalski,
R., Kriwaczek, F., Hammond, P., and Cory,T.
The British Nationality Act as a Logic Program
In CACM, Vol. 29, No. 5, 1986, pp. 370-386.
Treatment of Negation in Logic Programs for Representing Legislation
In Proceedings of Second International Conference on AI and Law, (ed. E. Rissland) Vancouver, Canada, ACM Press, 1989, pp. 11-15.
R. Kowalski, Legislation as Logic Programs
In: Logic Programming in Action (eds. G. Comyn , N. E. Fuchs, M. J. Ratcliffe), Springer Verlag, pages 203-230 (1992)
Kowalski, F. Toni,
and Reconciliation ,
In: International Symposium on Fifth Generation Computer Systems '94, Workshop on Legal Reasoning, Tokyo, pages 9-16 (1994)
Kowalski, F. Toni, Abstract
In: Artificial Intelligence and Law Journal 4(3-4), Special Issue on Logical Models of Argumentation, H. Prakken and G. Sartor, eds., Kluwer Academic Publishers, pages 275-296 (1996)
Kowalski, R. and Kim, J. S.
Metalogic Programming Approach to Multi-Agent Knowledge and Belief
In Artificial Intelligence and Mathematical Theory of Computation (ed. V. Lifschitz), Academic Press, 1991, pp. 231-246.
without Model Theory ,
In: What is a logical system?, D. Gabbay ed., Oxford University Press (1995)
Kowalski, R. and Sergot, M.
Logic-based Calculus of Events
In New Generation Computing, Vol. 4, No.1, February 1986, pp. 67-95. Also in Knowledge Base Management-Systems, (eds. C. Thanos and J. W. Schmidt), Springer-Verlag, pp. 23-51. Also in The Language of Time: A Reader (eds. Inderjeet Mani, J. Pustejovsky, and R. Gaizauskas) Oxford University Press. 2005.
Updates in the Event Calculus
In Journal of Logic Programming, 1992, Vol. 12, No. 162, pp. 121-146.
R. Kowalski, F. Sadri, The situation calculus and event calculus compared , In: Proc. International Logic Programming Symposium, ILPS'94 (1994)
F. Sadri, R. Kowalski, Variants of the event calculus , In: Proc. International Conference on Logic Programming, L. Sterling, ed., MIT Press (1995)
R. Kowalski, F. Sadri, Reconciling the Situation Calculus and Event Calculus , In: Journal of Logic Programming Vol. 31, pages 39-58, Special Issue on Reasoning about Action and Change (1997)
Abductive Logic Programming
K. Eshghi and R. Kowalski, Abduction Compared with Negation as Failure, Sixth International Conference on Logic Programming (1989)
Kakas, R. Kowalski, F. Toni, Abductive logic programming ,
In: Journal of Logic and Computation 2(6) pages 719-770 (1992)
R. Kowalski, F. Toni, G. Wetzel,
Towards a declarative and efficient glass-box CLP language ,
In: Proc. of Logic Programming Workshop WLP'94, N. Fuchs and G. Gottlob, eds.,
F. Toni, R. Kowalski, Reduction of abductive logic programs to normal logic programs , In: Proc. International Conference on Logic Programming, L. Sterling, ed., MIT Press, pages 367-381 (1995)
Wetzel, R. Kowalski, F. Toni,
Theorem-Proving Approach to CLP, In: Proc. of Logic Programming Workshop WLP'95, A. Krall
and U. Geske, eds.,
R. Kowalski, G. Wetzel, F. Toni, A Unifying Framework for ALP, CLP and SQO , Technical Report, Department of Computing, Imperial College, London (1996)
Fung, T.H. and Kowalski, R. The IFF Proof Procedure for Abductive Logic Programming. Journal of Logic Programming, 1997.
A. C. Kakas, R. Kowalski, F. Toni, The Role of Abduction in Logic Programming , In: Handbook of Logic in Artificial Intelligence and Logic Programming 5, pages 235-324, D.M. Gabbay, C.J. Hogger and J.A. Robinson eds., Oxford University Press (1998)
R.A. Kowalski, F. Toni, G. Wetzel, Executing Suspended Logic Programs , In: Fundamenta Informatica 34 (3) (1998)
From Abduction to Argumentation
A. Bondarenko, F. Toni, R. Kowalski, An Assumption-based Framework for Non-monotonic Reasoning , In: Proc. 2nd International Workshop on Logic Programming and Non-monotonic Reasoning, L.M. Pereira and A. Nerode, eds., pages 171-189 (1993)
F. Toni, R. Kowalski, An argumentation-theoretic approach to logic program transformation , In: Proc. LOPSTR'95, International Workshop on Logic Program Synthesis and Transformation, M. Proietti ed., LNCS 1048, Springer Verlag, pages 61-75 (1995)
P.M. Dung, R. Kowalski, F. Toni, Synthesis of proof procedures for default reasoning , In: Proc. LOPSTR'96, International Workshop on Logic Program Synthesis and Transformation, J. Gallagher ed., LNCS 1207, Springer Verlag, pages 313-324 (1996)
A. Bondarenko, P.M. Dung, R. Kowalski, F. Toni, An abstract, argumentation-theoretic approach to default reasoning, In: Artificial Intelligence 93(1-2) pages 63-101 (1997)
Dung, P. M., Kowalski, R., and Toni, F. Dialectic proof procedures for assumption-based, admissible argumentation , Journal of Artificial Intelligence 170(2), February 2006, pp. 114-159
Kowalski, R., Logic-based Open Systems, Department of Computing, Imperial College, 1985. In Representation and Reasoning. Jakob ph. Hoepelman (Hg.) Max Niemeyer Verlag, Tübingen 1988, pp. 125-134.
R. Kowalski, Using metalogic to reconcile reactive with rational agents , In: Meta-Logics and Logic Programming (K. Apt and F. Turini, eds.), MIT Press (1995)
R. Kowalski, F. Sadri, Towards a unified agent architecture that combines rationality with reactivity, In: Proc. International Workshop on Logic in Databases, San Miniato, Italy, Springer- Verlag, LNCS 1154 (1996)
R. Kowalski, F. Sadri, An Agent Architecture that Unifies Rationality with Reactivity , Department of Computing, Imperial College (1997)
R. Kowalski, F. Sadri, From Logic Programming towards Multi-agent Systems , In: Annals of Mathematics and Artificial Intelligence Volume 25, pages 391-419 (1999)
R. Kowalski, Artificial intelligence and the Natural World , Cognitive Processing, Volume 2 (2001)
R. Kowalski, Logic Programming MIT Encyclopaedia of Cognitive Science (eds. R A Wilson and F C Keil) MIT Press (1999)
R. Kowalski, Logic Programming and the Real World Logic Programming Newsletter. January 2001
R. Kowalski, Directions for Logic Programming Computational Logic: Logic Programming and Beyond (eds. A C Kakas and F Sadri) Springer, 2002, 26-32.
R. Kowalski, A logic-based model for conflict resolution April 2003.
R. Kowalski, Logic and Modularity April 2005.
R. Kowalski, Computational Logic as a Dual Process Model of Thought February 2006.
R. Kowalski, Time to think like a Computer , New Scientist 3 December 2011
Updated 10 February 2015