John W. Lloyd

Partial evaluation in logic programming

Abstract This paper gives a theoretical foundation for partial evaluation in logic programming. Let P be a normal program, G a normal goal, A a finite set of atoms, and P ′ a partial evaluation of P wrt A . We study, for both the declarative and procedural semantics, conditions under which P ′ is sound and complete wrt P for the goal G . We identify two relevant conditions, those of closedness and independence. For the procedural semantics, we show that, if P ′ ∪ { G } is A -closed and A is independent, then P ′ is sound and complete wrt P for the goal G . For the declarative semantics, we show that, if P ′ ∪ { G } is A -closed, then P ′ is sound wrt P for the goal G . However, we show that, unless strong conditions are imposed, we do not have completeness for the declarative semantics. A practical consequence of our results is that partial evaluators should enforce the closedness and independence conditions.

Making prolog more expressive

Abstract This paper introduces extended programs and extended goals for logic programming. A clause in an extended program can have an arbitrary first-order formula as its body. Similarly, an extended goal can have an arbitrary first-order formula as its body. The main results of the paper are the soundness of the negation as failure rule and SLDNF-resolution for extended programs and goals. We show how the increased expressibility of extended programs and goals can be easily implemented in any PROLOG system which has a sound implementation of the negation as failure rule. We also show how these ideas can be used to implement first-order logic as a query language in a deductive database system. An application to integrity constraints in deductive database systems is also given.

Kernels and Distances for Structured Data

This paper brings together two strands of machine learning of increasing importance: kernel methods and highly structured data. We propose a general method for constructing a kernel following the syntactic structure of the data, as defined by its type signature in a higher-order logic. Our main theoretical result is the positive definiteness of any kernel thus defined. We report encouraging experimental results on a range of real-world data sets. By converting our kernel to a distance pseudo-metric for 1-nearest neighbour, we were able to improve the best accuracy from the literature on the Diterpene data set by more than 10%.

Integrity constraint checking in stratified databases

Abstract We prove the correctness of a simplification method for checking static integrity constraints in stratified deductive databases.

Kernels for structured data

Learning from structured data is becoming increasingly important. However, most prior work on kernel methods has focused on learning from attribute-value data. Only recently have researchers started investigating kernels for structured data. This paper describes how kernel definitions can be simplified by identifying the structure of the data and how kernels can be defined on this structure. We propose a kernel for structured data, prove that it is positive definite, and show how it can be adapted in practical applications.

Declarative error diagnosis

This paper presents an error diagnoser which finds errors in logic programs which use the extended syntax and advanced control facilities. The diagnoser isdeclarative, in the sense that the programmer need only know the intended interpretation of an incorrect program to use the diagnoser. In particular, the programmer needs no understanding whatever of the underlying computational behaviour of the PROLOG system which runs the program. It is argued that declarative error diagnosers will be indispensable components of advanced logic programming systems, which are currently under development.

Updating knowledge bases

We consider the problem of updating a knowledge base, where a knowledge base is realised as a normal (logic) program. We present procedures for deleting an atom from a normal program and inserting an atom into a normal program, concentrating particularly on the case when negative literals appear in the bodies of program clauses. We also prove various properties of the procedures including their correctness.

A completeness theorem for SLDNF resolution

Abstract We prove the completeness of SLDNF resolution and negation as failure for stratified, normal programs and normal goals, under the conditions of strickness and allowedness. In particular, this result settles positively a conjecture of Apt, Blair, and Walker.

Logic for Learning: Learning comprehensible theories from structured data

1. Introduction.- 2. Logic.- 3. Individuals.- 4. Predicates.- 5. Computation.- 6. Learning.- A. Appendix.- A.1 Well-Founded Sets.- References.- Notation.

Strongly Typed Inductive Concept Learning

In this paper we argue that the use of a language with a type system, together with higher-order facilities and functions, provides a suitable basis for knowledge representation in inductive concept learning and, in particular, illuminates the relationship between attribute-value learning and inductive logic programming (ILP). Individuals are represented by closed terms: tuples of constants in the case of attribute-value learning; arbitrarily complex terms in the case of ILP. To illustrate the point, we take some learning tasks from the machine learning and ILP literature and represent them in Escher, a typed, higher-order, functional logic programming language being developed at the University of Bristol. We argue that the use of a type system provides better ways to discard meaningless hypotheses on syntactic grounds and encompasses many ad hoc approaches to declarative bias.