INFORMATION SCIENCES

E L S E V I E R Information Sciences 116 (1999) 1-2

Guest editorial

Logical methods for computational intelligence

Grigoris Antoniou a,l, Neil V. Murray b,, a School of Computing & Information Technology, Griffith University, QLD 4111, Australia b Department of Computer Science, University of Albany - SUNY, Albany, NY 12222, USA

Over the past years two main approaches to computational intelligence have emerged: the symbolic and the non-symbolic approach. Perhaps the most prominent methods of the symbolic approach are based on logic. Logical methods exhibit a series of desirable properties: transparent representation of information, precise understanding of the meaning of statements (semantics), sound reasoning methods, and explanation capabilities.

Two of the four papers in this issue are taken from the special session on logical methods for computational intelligence, held at the 3rd Joint Confer- ence on Information Sciences.

One topic was the presentation of machine-generated proofs in a way that appeals to humans. The idea is to summarize chunks of the proofs into "macro-steps" on a more abstract level that better resemble steps humans would take. The paper by Fehrer and Horacek is concerned with the presen- tation of inequalities in mathematical proofs; a short version was presented in the special session. Earlier investigations developed the idea that equalities can be quite naturally represented as a chain structure. Fehrer and Horacek show that the crucial property of equality that enables this natural representation is transitivity, a property shared by inequality. Thus they are able to generalize these ideas to chains of inequalities.

Intelligent systems are often faced with the problem of reasoning with in- complete information. Default reasoning, and in particular default logic, was a

* Corresponding author. E-maih nvm@es.albany.edu l E-mail: ga@cit.gu.edu.au

0020-0255/99/$19.00 © 1999 Elsevier Science Inc. All rights reserved. PII:S0020-0255(98)1 0091-9

G. Antoniou, N. I~ Murray / Information Sciences 116 (1999) 1-2

particular focus of the special session. It extends classical logic by default rules. A simple example is the closed world assumption known in the database area for a long time: If an assertion is not found in the database then it is assumed false by default.

Related to abduction and induction is the question: Where do default rules come from? This topic was treated at the special session and is the subject of the paper of Lamma et al. They describe a method for learning rules with exceptions, which are a kind of default rules.

One drawback of default logic is the lack of a reasonably efficient imple- mentation. The same can be said for autoepistemic logic and circumscription, two other widely studied approaches to non-monotonic reasoning. In the paper by Billington, a more recent approach involving defeasible logic is studied and extended. Defeasible logic does have an efficient implementation, but the proof theory only allows derivation of ground literals. Billington extends the theory to obtain proofs of universally and existentially quantified literals also.

The paper by Dormer and MacNish addresses learning algorithms, specif- ically speedup learning. Such algorithms involve the use of teacher-provided examples to guide the improvement of various processes, for examples plan- ning or search algorithms. The output of a state space search algorithm can be viewed as as plan. Given a super-polynomial planning algorithm ~ for domain @, we wish to know if a speedup learning algorithm La exists that will syn- thesize a new planning algorithm ~ ' from ~. The new algorithm should be efficient and make few errors. Dorner and MacNish characterize classes of domains for which such speedup learning is and is not solvable.