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.

Constraint logic programming : A survey

Constraint Handling Rules (CHR) are our proposal to allow more flexibility and application-oriented customization of constraint systems. CHR are a declarative language extension especially designed for writing user-defined constraints. CHR are essentially a committed-choice language consisting of multi-headed guarded rules that rewrite constraints into simpler ones until they are solved. In this broad survey we aim at covering all aspects of CHR as they currently present themselves. Going from theory to practice, we will define syntax and semantics for CHR, introduce an important decidable property, confluence, of CHR programs and define a tight integration of CHR with constraint logic programming languages. This survey then describes implementations of the language before we review several constraint solvers – both traditional and nonstandard ones – written in the CHR language. Finally we introduce two innovative applications that benefited from using CHR.

Theory and practice of constraint handling rules

Functional Grammar describes grammar in functional terms in which a language is interpreted as a system of meanings. The language system consists of three macro-functions known as meta-functional components: the interpersonal function, the ideational function, and the textual function, all of which make a contribution to the structure of a text. The concepts discussed in Functional Grammar aims at giving contribution to the understanding of a text and evaluation of a text, which can be applied for text analysis. Using the concepts in Functional Grammar, English teachers may help the students learn how various grammatical features and grammatical systems are used in written texts so that they can read and write better.

A Functional Grammar

Paramodulation-Based Theorem Proving.

The Oz Programming Model (OPM) is a concurrent programming model subsuming higher-order functional and object-oriented programming as facets of a general model. This is particularly interesting for concurrent object-oriented programming, for which no comprehensive formal model existed until now. The model can be extended so that it can express encapsulated problem solvers generalizing the problem solving capabilities of constraint logic programming. OPM has been developed together with a concomitant programming language Oz, which is designed for applications that require complex symbolic computations, organization into multiple agents, and soft real-time control. An efficient, robust, and interactive implementation of Oz is freely available.

The Oz Programming Model

CFT is a new constraint system providing records as logical data structure for constraint (logic) programming. It can be seen as a generalization of the rational tree system employed in Prolog II, where finer-grained constraints are used and where subtrees are identified by keywords rather than by position. CFT is defined by a first-order structure consisting of so-called feature trees. Feature trees generalize the ordinary trees corresponding to first-order terms by having their edges labeled with field names called features. The mathematical semantics given by the feature tree structure is complemented with a logical semantics given by five axiom schemes, which we conjecture to comprise a complete axiomatization of the feature tree structure. We present a decision method for CFT, which decides entailment and disentailment between possibly existentially quantified constraints. Since CFT satisfies the independence property, our decision method can also be employed for checking the satisfiability of conjunctions of positive and negative constraints. This includes quantified negative constraints such as ∀ y ∀ z(x≠f(y,z)) . The paper also presents an idealized abstract machine processing negative and positive constraints incrementally. We argue that an optimized version of the machine can decide satisfiability and entailment in quasilinear time.

Records for logic programming

A new method for undecidability proofs of first order theories

We claim that the reduction of Post's Correspondence Problem to the decision problem of a theory provides a useful tool for proving undecidability of first order theories given by an interpretation. The goal of this paper is to propose a framework for such reduction proofs. The method proposed is illustrated by proving the undecidability of the theory of a term algebra modulo AC and the theory of a partial lexicographic path ordering.

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Dominance constraints for finite tree structures are widely used in several areas of computational linguistics including syntax, semantics, and discourse. In this paper, we investigate algorithmic and complexity questions for dominance constraints and their first-order theory. The main result of this paper is that the satisfiability problem of dominance constraints is NP-complete. We present two NP algorithms for solving dominance constraints, which have been implemented in the concurrent constraint programming language Oz. Despite the intractability result, the more sophisticated of our algorithms performs well in an application to scope underspecification. We also show that the positive existential fragment of the first-order theory of dominance constraints is NP-complete and that the full first-order theory has non-elementary complexity.

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Dominance Constraints: Algorithms and Complexity

We survey recent results about ordering constraints on trees and discuss their applications. Our main interest lies in the family of recursive path orderings which enjoy the properties of being total, well-founded and compatible with the tree constructors. The paper includes some new results, in particular the undecidability of the theory of lexicographic path orderings in case of a non-unary signature.

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Ralf Treinen

Papers

Records for logic programming

A new method for undecidability proofs of first order theories

A new method for undecidability proofs of first order theories

Dominance Constraints: Algorithms and Complexity

Ordering Constraints on Trees