A formal definition and a sound implementation of analogical reasoning in logic programming

A formal model of analogy is introduced in the logic programming setting, and an analogical reasoning program (called DIANA, i.e. Declarative Inference by ANAlogy) is developed in accordance with precise procedural and declarative semantics. Given the source and target domains of analogy as two logic programsP _s andP _t , together with a specificationS of the analogical correspondence between predicate symbols, atoms involving these symbols are analogically derived fromP=P _s P _t givenS, which are not derivable fromP _s orP _t orP _s P _t alone. In this paper, the requirements of the analogical process are first stated. The declarative semantics of analogy is then given, by defining the least analogical model ofP as an extension of the classical semantics of Horn clauses. A procedural semantics is also described, in terms of an extension of SLD resolution. Both semantics rely on implicit analogical axioms defining the kind of analogical reasoning envisaged. The implementation of DIANA has been done in Reflective Prolog, a metalogic programming language previously developed by the first two authors. It is shown that analogical axioms can be viewed as an instance of reflection axioms used in Reflective Prolog. By exploiting this feature, the implementation of DIANA is argued to be sound w.r.t. the defined semantics. Examples of analogical reasoning in DIANA are also described. By comparison with the AI literature on analogy, it is claimed that this is the first approach which gives a declarative semantics to analogical reasoning, thanks to the possibility of carrying over in this field the basic logic programming concepts.     

Query processing in annotated logic programming: Theory and implementation

Annotated logic is a formalism that has been applied to a variety of situations in knowledge representation, expert database systems, quantitative reasoning, and hybrid databases [6], [13], [19], [20], [21], [22], [23], [24], [30], [33], [35], [36]. Annotated Logic Programming (ALP) is a subset of annotated logics that can be used directly for programming annotated logic applications [22], [23]. A top-down query processing procedure containing elements of constraint solving, called ca-resolution, is developed for ALPs. It simplifies a number of previously proposed procedures, and also improves on their efficiency. The key to its development is in observing that satisfaction, as introduced originally for ALPs, may be naturally generalized. A computer implementation of ca-resolution for ALPs is described which offers important theoretical and practical insights. Strategies for improving its efficiency are discussed.This material is based upon work supported by the NSF under Grant CCR9225037. A preliminary version of this paper appears in the proceedings of the International Conference on Logic Programming, 1994.     

CAL: A theoretical background of constraint logic programming and its applications

Constraint logic programming (CLP) is an extension of logic programming by introducing the facility of writing and solving constraints in a certain domain. CAL (Contrainte avec Logique) is a CLP language in which (possibly non-linear) polynomial equations can be written as constraints, while almost all the other CLP languages proposed so far have concentrated only on linear equations and inequations. This paper describes a general semantics of CLP including CAL, and shows the validity of CAL in this framework.     

Multi-level substructuring and its implementation in programming

With the development of the finite element method, FEM, increasing complex structures are being studied and the number of simultaneous equations to be processed is considerable. For many such complex structures, CPU-time, memory storage and data preparation can be reduced by means of multi-level substructuring. Multi-level substructuring and its implementation in computer software are the subject of this paper. With the program developed by authors, any-level of substructuring problem can be conveniently solved.     

A framework for linguistic logic programming

Lawry's label semantics for modeling and computing with linguistic information in natural language provides a clear interpretation of linguistic expressions and thus a transparent model for real‐world applications. Meanwhile, annotated logic programs (ALPs) and its fuzzy extension AFLPs have been developed as an extension of classical logic programs offering a powerful computational framework for handling uncertain and imprecise data within logic programs. This paper proposes annotated linguistic logic programs (ALLPs) that embed Lawry's label semantics into the ALP/AFLP syntax, providing a linguistic logic programming formalism for development of automated reasoning systems involving soft data as vague and imprecise concepts occurring frequently in natural language. The syntax of ALLPs is introduced, and their declarative semantics is studied. The ALLP SLD‐style proof procedure is then defined and proved to be sound and complete with respect to the declarative semantics of ALLPs. © 2010 Wiley Periodicals, Inc.     

A framed temporal logic programming language

We discuss the projection temporal logic (PTL), based on a primitive projection operator, prj. A framing technique is also presented, using which a synchronization operator, await, is defined within the underlying logic. A framed temporal logic programming language (FTLL) is presented. To illustrate how to use both the language and framing technique, some examples are given.     

An Inplementation of Pure Horn Clause Logic Programming in a Reduction System

Many reduction systems have been presented for implementing functional programming languages.We propose here an extension of a reduction architecture to realize a kind of logic programming-pure Horn clause logic programming.This is an attempt to approach amalgamation of the two important programming paradigms.     

A bridge between constructive logic and computer programming

Some logic notions have their analogies among programming concepts and vice versa. But people often try to understand these analogies in too straightforward a manner. A collection of analogies arising between constructive logics and programming is summarized and illustrated here. Some examples of complexities usually not taken into account are shown.     

A logic programming framework for planning and simulation

Planning and simulation models share the characteristic that they involve reasoning about hypothetical sequences of activities. These may be naturally described in a graph structure, e.g., a state transition diagram or a Petri net. A logic programming framework is proposed for describing the problem domain (‘model base’) of planning and simulation problems in logical form, separate from the inferencing mechanisms applied to them. Applications are to dynamic programming, decision trees, PERT networks, and discrete event simulation.     

Beamforming of UWB pulse array and its implementation

This paper firstly introduces a realistic ultra-wideband (UWB) pulse model and discusses the principle of sensor array beamforming for UWB pulse signals. Then the differences between a UWB pulse array and narrowband sinusoidal array are studied. Based on it, the problem of realizing a digital and applicable variable delay circuit (VDC) to compensate the channel propagation delay accurately for UWB pulse array beamforming is addressed. In our work, fractional sample delay compensation filters (FDCF) are combined with delay lines to build up accurate VDCs. As a result, the Lagrange interpolation method based on maximally flat criterion is found to be most suitable for the fixed beam steering; and Farrow structure is recommended to satisfy the need of rapid beam adjustment. In the simulation experiments, two kinds of directivity pattern for an UWB pulse array are studied and compared with that of sinusoidal array. The effectiveness of the presented scheme is verified by the simulation results, which show that the VDC implementation by digital lines and FDCF can remarkably improve the performance of the directivity patterns of UWB pulse array especially for the system with low sampling rate.     

Integrating answer set programming and constraint logic programming

We introduce a knowledge representation language ${\cal AC(C)}$ extending the syntax and semantics of ASP and CR-Prolog, give some examples of its use, and present an algorithm, $\mathcal{AC}\!solver$ , for computing answer sets of ${\cal AC(C)}$ programs. The algorithm does not require full grounding of a program and combines “classical” ASP solving methods with constraint logic programming techniques and CR-Prolog based abduction. The ${\cal AC(C)}$ based approach often allows to solve problems which are impossible to solve by more traditional ASP solving techniques. We believe that further investigation of the language and development of more efficient and reliable solvers for its programs can help to substantially expand the domain of applicability of the answer set programming paradigm.     

A typed functional extension of logic programming

A logic language is suitable for specification if it is equipped with features for data abstraction and modularization. In this paper, an effective mechanism to incorporate function and type into logic programming is presented as the means to embed data abstraction mechanism into logic programming. This incorporation is essentially based on Horn clause logic with equality and a polymorphic type system that is an extension of Mycroft and O’Keefe’s system. This paper also presents an implementation based on Warren Abstract Machine (WAM) and shows the performance, along with a comparison with WAM.     

A logic programming system for nonmonotonic reasoning

The evolution of logic programming semantics has included the introduction of a new explicit form of negation, beside the older implicit (or default) negation typical of logic programming. The richer language has been shown adequate for a spate of knowledge representation and reasoning forms.The widespread use of such extended programs requires the definition of a correct top-down querying mechanism, much as for Prolog wrt. normal programs. One purpose of this paper is to present and exploit a SLDNF-like derivation procedure, SLX, for programs with explicit negation under well-founded semantics (WFSX) and prove its soundness and completeness. (Its soundness wrt. the answer-sets semantics is also shown.) Our choice ofWFSX as the base semantics is justi-fied by the structural properties it enjoys, which are paramount for top-down query evaluation.Of course, introducing explicit negation requires dealing with contradiction. Consequently, we allow for contradiction to appear, and show moreover how it can be removed by freely changing the truth-values of some subset of a set of predefined revisable literals. To achieve this, we introduce a paraconsistent version ofWFSX, WFSX _p , that allows contradictions and for which our SLX top-down procedure is proven correct as well.This procedure can be used to detect the existence of pairs of complementary literals inWESX _p simply by detecting the violation of integrity rulesf L, -L introduced for eachL in the language of the program. Furthermore, integrity constraints of a more general form are allowed, whose violation can likewise be detected by SLX.Removal of contradiction or integrity violation is accomplished by a variant of the SLX procedure that collects, in a formula, the alternative combinations of revisable literals' truth-values that ensure the said removal. The formulas, after simplification, can then be satisfied by a number of truth-values changes in the revisable, among true, false, and undefined. A notion of minimal change is defined as well that establishes a closeness relation between a program and its revisions. Forthwith, the changes can be enforced by introducing or deleting program rules for the revisable literals.To illustrate the usefulness and originality of our framework, we applied it to obtain a novel logic programming approach, and results, in declarative debugging and model-based diagnosis problems.     

A lingua franca for concurrent logic programming

Two of the more important concurrent logic programming languages with nonflat guards are GHC and Parlog. They balance the requirements of having clean semantics and providing good control facilities rather differently, and their respective merits are compared and contrasted. Since concurrent logic programming would benefit from both, but neither language is able to express all the programs expressible in the other language, a lingua franca of these languages is defined and justified. A method is given for translating GHC and Parlog to and from it. The method preserves the arities and execution conditions of each clause. It enables a lingua franca implementation to support both languages transparently, and to provide a simple concurrent logic programming language suitable for programming in its own right     

A proof outline logic for object-oriented programming

This paper describes a proof outline logic that covers most typical object-oriented language constructs in the presence of inheritance and subtyping. The logic is based on a weakest precondition calculus for assignments and object allocation which takes field shadowing into account. Dynamically bound method calls are tackled with a variant of Hoare's rule of adaptation that deals with the dynamic allocation of objects in object-oriented programs. The logic is based on an assertion language that is closely tailored to the abstraction level of the programming language.     

Translations and similarity-based logic programming

In order to provide approximate reasoning capabilities, in Gerla G, Sessa MI (1999) Chen G, Ying M, Cai K-Y (Eds) Fuzzy Logic and Soft computing, 19–31, Kluwer Academic Publishers, Boston an extension of Logic Programming has been proposed. Logic programs on function-free languages are considered, and approximate and imprecise information are represented by introducing a similarity relation ? in the set of predicate names and object names of the language. The inference system exploits the classical resolution rule of the Logic Programming paradigm. Moreover, the notion of fuzzy least Herbrand model is also provided. In this paper, by introducing the general notion of structural translation of languages, we generalize these results to the case of logic programs with function symbols. Some properties of the similarity relations are also proven.     

Regulation management and logic programming

Regulations are pervasive in information systems. They manifest themselves as design rules, integrity constraints, deadlines, conventions, information disclosure requirements, policies, procedures, contracts, taxes, quotas and other statutes. Managing regulations is difficult. Regulations are complex, change frequently and rest on models of the real world that involve unusual vocabulary if not unusual concepts. Consequently, checking compliance with regulations is tedious and error-prone. Logic programming appears to provide a good framework for developing regulation management systems. Besides permitting arbitrary regulations to be modelled, it offers rapidity and ease of development, readability, incremental modifiability, extensibility and portability. These features are not provided by existing DP programming tools, database managers or conventional expert-system shells. This paper investigates the application of logic programming in a significant regulation management application: Workers' Compensation Insurance premium auditing. The insurance premium computation rules for the State of California were encoded as a large Prolog program. This application illustrates specific strengths and weaknesses of logic programming and Prolog in dealing with large-scale real-world regulations.     

Integrating logic and functional programming

The intent of this article is twofold: To survey prominent proposals for the integration of logic and functional programming and to present a new paradigm for the same purpose. We categorize current research into four types of approaches, depending on the level at which the proposed integration is achieved. Unlike most current work, our approach is not based on extending unification to general-purpose equation solving. Rather, we propose a computation delaying mechanism calledresiduation. This allows a clear distinction between functionalevaluation and logicaldeduction. The former is based on the-calculus, and the latter on Horn clause resolution. Residuation is built into the unification operation which may then account for-reduction. In clear contrast with equation-solving approaches, our model supports higher-order function evaluation and efficient compilation of both functional and logic programming expressions, without being plagued by non-deterministic term-rewriting. In addition, residuation lends itself naturally to process synchronization and constrained search. We describe an operational semantics and an implementation of a prototype language called LeFun—Logic, equations, and Functions.This article is a revised and extended version of [1].     

Defeasible reasoning and logic programming

The general conditions of epistemic defeat are naturally represented through the interplay of two distinct kinds of entailment, deductive and defeasible. Many of the current approaches to modeling defeasible reasoning seek to define defeasible entailment via model-theoretic notions like truth and satisfiability, which, I argue, fails to capture this fundamental distinction between truthpreserving and justification-preserving entailments. I present an alternative account of defeasible entailment and show how logic programming offers a paradigm in which the distinction can be captured, allowing for the modeling of a larger range of types of defeat. This is possible through a natural extension of the declarative and procedural semantics of Horn clauses.