Michael J. Maher

Constraint logic programming: a survey

Abstract Constraint Logic Programming (CLP) is a merger of two declarative paradigms: constraint solving and logic programming. Although a relatively new field, CLP has progressed in several quite different directions. In particular, the early fundamental concepts have been adapted to better serve in different areas of applications. In this survey of CLP, a primary goal is to give a systematic description of the major trends in terms of common fundamental concepts. The three main parts cover the theory, implementation issues, and programming for applications.

Representation results for defeasible logic

The importance of transformations and normal forms in logic programming, and generally in computer science, is well documented. This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but efficient formalism for nonmonotonic reasoning based on rules and priorities. The transformations described in this paper have two main benefits: on one hand they can be used as a theoretical tool that leads to a deeper understanding of the formalism, and on the other hand they have been used in the development of an efficient implementation of defeasible logic.

Argumentation Semantics for Defeasible Logic

Defeasible reasoning is a simple but efficient rule-based approach to nonmonotonic reasoning. It has powerful implementations and shows promise to be applied in the areas of legal reasoning and the modelling of business rules. This paper establishes significant links between defeasible reasoning and argumentation. In particular, Dung-like argumentation semantics is provided for two key defeasible logics, of which one is ambiguity propagating and the other ambiguity blocking. There are several reasons for the significance of this work: (a) establishing links between formal systems leads to a better understanding and cross-fertilization, in particular our work sheds light on the argumentation-theoretic features of defeasible logic; (b) we provide the first ambiguity blocking Dung-like argumentation system; (c) defeasible reasoning may provide an efficient implementation platform for systems of argumentation; and (d) argumentation-based semantics support a deeper understanding of defeasible reasoning, especially in the context of the intended applications.

The semantics of constraint logic programs

Abstract The Constraint Logic Programming (CLP) Scheme was introduced by Jaffar and Lassez. The scheme gave a formal framework, based on constraints, for the basic operational, logical and algebraic semantics of an extended class of logic programs. This paper presents for the first time the semantic foundations of CLP in a self-contained and complete package. The main contributions are threefold. First, we extend the original conference paper by presenting definitions and basic semantic constructs from first principles, giving new and complete proofs for the main lemmas. Importantly, we clarify which theorems depend on conditions such as solution compactness, satisfaction completeness and independence of constraints. Second, we generalize the original results to allow for incompleteness of the constraint solver. This is important since almost all CLP systems use an incomplete solver. Third, we give conditions on the (possibly incomplete) solver which ensure that the operational semantics is confluent, that is, has independence of literal scheduling.

Propositional defeasible logic has linear complexity

Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts markedly with most other propositional nonmonotonic logics, in which inference is intractable.

EFFICIENT DEFEASIBLE REASONING SYSTEMS

For many years, the non-montonic reasoning community has focussed on highly expressive logics. Such logics have turned out to be computationally expensive, and have given little support to the practical use of non-monotonic reasoning. In this work we discuss defeasible logic, a less-expressive but more efficient non-monotonic logic. We report on two new implemented systems for defeasible logic: a query answering system employing a backward-chaining approach, and a forward-chaining implementation that computes all conclusions. Our experimental evaluation demonstrates that the systems can deal with large theories (up to hundreds of thousands of rules). We show that defeasible logic has linear complexity, which contrasts markedly with most other non-monotonic logics and helps to explain the impressive experimental results. We believe that defeasible logic, with its efficiency and simplicity, is a good candidate to be used as a modeling language for practical applications, including modelling of regulations and business rules.

A theory of complete logic programs with equality

Abstract Incorporating equality into the unification process has added great power to automated theorem provers. We see a similar trend in logic programming where a number of languages are proposed with specialized or extended unification algorithms. There is a need to give a logical basis to these languages. We present here a general framework for logic programming with definite clauses, equality theories, and generalized unification. The classic results for definite clause logic programs are extended in a simple and natural manner. The extension of the soundness and completeness of the negation-as-failure rule for complete logic programs is conceptually more delicate and represents the main result of this paper.

Embedding defeasible logic into logic programming

Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of defeasible reasoning methods. So far no relationship has been established between defeasible logic and mainstream nonmonotonic reasoning approaches. In this paper we establish close links to known semantics of logic programs. In particular, we give a translation of a defeasible theory

Defeasible logic versus Logic programming without negation as failure

D

On the analysis of regulations using defeasible rules

into a meta-program