Logic & Formal Reasoning
What Is the Well-Dressed AI Educator Wearing Now?
A funny thing happened to me at IJCAI-81. I went to a panel on "Education in AI" and stepped back into an argument that I had thought settled several years ago. The debate was between the "scruffies," led by Roger Schank and Ed Feignbaum, and the "neats," led by Nils Nilsson. The neats argued that no education in AI was complete without a strong theoretical component, containing, for instance, courses on predicate logic and automata theory. The scruffies maintained that such a theoretical component was not only unnecessary, but harmful.
Logic for Natural Language Analysis
Pereira, Fernando Carlos Neves
This work investigates the use of formal logic as a practical tool for describing the syntax and semantics of a subset of English, and building a computer program to answer data base queries expressed in that subset. To achieve an intimate connection between logical descriptions and computer programs, all the descriptions given are in the definite clause subset of the predicate calculus, which is the basis of the programming language Prolog. The logical descriptions run directly as efficient Prolog programs. Three aspects of the use of logic in natural language analysis are covered: formal representation of syntactic rules by means of a grammar formalism based on logic, extraposition grammars;. formal semantics for the chosen English subset, appropriate for data base queries; informal semantic and pragmatic rules to translate analysed sentences into their formal semantics. On these three aspects, the work improves and extends earlier work by Colmerauer and others, where the use of computational logic in language analysis was first introduced. The University of Edinburgh
LOGLISP: an alternative to PROLOG
Our own early attempts (as devoted users of LISP) to use PROLOG convinced us that it would be worth the effort to create within LISP a faithful implementation of Kowalski's logic programming idea. We felt it would be very convenient to be able to set up a knowledge base of assertions inside a LISP workspace, and to compute the answers to queries simply by executing appropriate function calls.In Hayes, J. E., Michie, D., and Pao, Y.-H. (Eds.), Machine Intelligence 10. Ellis Horwood.
Higher-order extensions to PROLOG: are they needed?
PROLOG is a simple and powerful progamming language based on first-order logic. This paper examines two possible extensions to the language which would generally be considered "higher-order".t The first extension introduces lambda expressions and predicate variables so that functions and relations can be treated as 'first class' data objects. We argue that this extension does not add anything to the real power of the language. The other extension concerns the introduction of set expressions to denote the set of all (provable) solutions to some goal. We argue that this extension does indeed fill a real gap in the language, but must be defined with care.In Hayes, J. E., Michie, D., and Pao, Y.-H. (Eds.), Machine Intelligence 10. Ellis Horwood.
The Knowledge Level: Presidential Address
This is the first presidential address of AAAI, the American Association for Artificial Intelligence. In the grand scheme of history of artificial intelligence (AI), this is surely a minor event. The field this scientific society represents has been thriving for quite some time. No doubt the society itself will make solid contributions to the health of our field. But it is too much to expect a presidential address to have a major impact. So what is the role of the presidential address and what is the significance of the first one? I believe its role is to set a tone, to provide an emphasis. I think the role of the first address is to take a stand about what that tone and emphasis should be-set expectations for future addresses and to communicate to my fellow presidents. Only two foci are really possible for a presidential address: the state of the society or the state of the science. I believe the latter to be correct focus. AAAI itself, its nature and its relationship to the larger society that surrounds it, are surely important. However, our main business is to help AI become a science -- albeit a science with a strong engineering flavor. Thus, though a president's address cannot be narrow or highly technical, it can certainly address a substantive issue. That is what I propose to do.
An algorithm that infers theories from facts
A framework for inductive inference in logic is presented: a Model Inference Problem is defined, and it is shown that problems of machine learning and program synthesis from examples can be formulated naturally as model inference problems. A general, incremental inductive inference algorithm for solving model inference problems is developed. This algorithm is based on Popper's methodology of conjectures and refutations [II]. The algorithm can be shown to identify in the limit [3] any model in a family of complexity classes of models, is most powerful of its kind, and is flexible enough to have been successfully implemented for several concrete domains. The Model Inference System is a Prolog implementation of this algorithm, specialized to infer theories in Horn form.
Non-monotonic logic I
'Non-monotonic' logical systems are logics in which the introduction of new axioms can invalidate old theorems. Such logics are very important in modeling the benefits of active processes which, acting in the presence of incomplete information, must make and subsequently revise assumptions in light of new observations. We present the motivation and history of such logics. We develop model and proof theories, a proof procedure, and applications for one non-monotonic logic. In particular, we prove the completeness of the non-monotoic predicate calculus and the decidability of the non-monotonic sentential calculus. We also discuss characteristic properties of this logic and its relationship to stronger logics, logics of incomplete information, and truth maintenance systems. Artificial Intelligence 13:41-72.
Circumscription - A form of non-monotonic reasoning
"Circumscription is a rule of conjecture that can be used by a person or program for `jumping to certain conclusions'. Namely, the objects that can be shown to have a certain property P by reasoning from certain facts A are all the objects that satisfy P. More generally, circumscription can be used to conjecture that the tuples
Relational Programming
A programming language needs simple and well defined semantics. The two favoured theoretical bases for languages have been lambda calculus as advocated by Landin and others, and predicate calculus as advocated by Kowalski (see Landin (1966) and Kowalski (1973)). In this paper I adopt an approach based on predicate calculus, but in a manner that differs from the existing PROLOG language (Warren 1975 and Battani & Meloni 1973) in that I adopt a "forward inference" approach -- inferring conclusions from premises, rather than the "backward inference" approach of PROLOG, which starts with a desired conclusion and tries to find ways of inferring it. This difference is reflected in the internal structure of the associated implementations, that of PROLOG being a "backtrack search" kind of implementation, while the most obvious implementation of the system proposed here involves a kind of mass operation on tables of data, reminiscent of APL (Iverson 1962) but in fact identical in many respects with the work of Codd (Codd 1970) on relational data bases. Indeed, from one perspective this paper can be seen as an extension of Codd's work into the realm of general purpose computing. As in the case of PROLOG it is necessary for the user of the relational programming system to make statements which are not associated with the logical structure of the problem, but reflect the need to control the computation. In PROLOG these are effected by the use of extra-logical control primitives, but in our system control is exercised by the introduction of predicates for that purpose, which have exactly the same semantics as the predicates relevant to the logical structure of the problem.