Clausal Logic and Logic Programming in Algebraic Domains

We introduce a domain-theoretic foundation for disjunctive logic programming. This foundation is built on clausal logic, a representation of the Smyth powerdomain of any coherent algebraic dcpo. We establish the completeness of a resolution rule for inference in such a clausal logic; we introduce a natural declarative semantics and a fixed-point semantics for disjunctive logic programs, and prove their equivalence; finally, we apply our results to give both a syntax and semantics for default logic in any coherent algebraic dcpo.     

逻辑程序语言中的集合

本文首先讨论了引入集合的意义，然后建立了一种基于集合基贩归约演算，并且对集合项的存储和含集合符号的逻辑数据语言的计算进行了一些探讨。本文所介绍的方法通过规则编译时对存储衣序集的改写，使得对集合匹配通过一般函数的匹配算法就可以完成，提高了计算的效率。     

Agent-Oriented Probabilistic Logic Programming

Currently, agent-based computing is an active research area, and great efforts have been made towards the agent-oriented programming both from a theoretical and practical view. However, most of them assume that there is no uncertainty in agents＇ mental state and their environment. In other words, under this assumption agent developers are just allowed to specify how his agent acts when the agent is 100% sure about what is true/false. In this paper, this unrealistic assumption is removed and a new agent-oriented probabilistic logic programming language is proposed, which can deal with uncertain information about the world. The programming language is based on a combination of features of probabilistic logic programming and imperative programming.     

Dense Time Logic Programming

In this paper, we describe a dense temporal logic programming (DTLP) framework based on infinite binary trees calledomega trees. We then look at an important subset of omega trees calledordinal treesthat represent only meaningful dense time models. Ordinal trees have the properties ofstabilityandrecurrence, which allow them to be represented finitely. The finite representations calledordinal structurescan be used as temporal data structures and its nodes can be labelled with formulae, giving us the basis for modeling temporally located information. In this paper, we label ordinal structure nodes with Prolog clauses to gettemporal horn clausesthat represent temporal facts, rules and queries. Temporal resolution tries to prove temporal queries from a set of temporal facts and rules using a process calledaligningwhich provides the counterpart of the conventional unification algorithm. Aligning restructures ordinal trees to facilitate the transfer of temporal information between them. We present theoretical results to show that aligning is computable, and that the procedures for aligning and resolution are correct.     

Mathematical Programming Embeddings of Logic

Can theorem proving in mathematical logic be addressed by classical mathematical techniques like the calculus of variations? The answer is surprisingly in the affirmative, and this approach has yielded rich dividends from the dual perspective of better understanding of the mathematical structure of deduction and in improving the efficiency of algorithms for deductive reasoning. Most of these results have been for the case of propositional and probabilistic logics. In the case of predicate logic, there have been successes in adapting mathematical programming schemes to realize new algorithms for theorem proving using partial instantiation techniques. A structural understanding of mathematical programming embeddings of predicate logic would require tools from topology because of the need to deal with infinite-dimensional embeddings. This paper describes the first steps in this direction. General compactness theorems are proved for the embeddings, and some specialized results are obtained in the case of Horn logic.     

The Logic of Computer Programming

Techniques derived from mathematical logic promise to provide an alternative to the conventional methodology for constructing, debugging, and optimizing computer programs. Ultimately, these techniques are intended to lead to the automation of many of the facets of the programming process.     

Incremental search in Constraint Logic Programming

Incremental search consists of adding new constraints or deleting old ones once a solution to a search problem has been found. Although incremental search is of primary importance in application areas such as scheduling, planning, trouble shooting, and interactive problem-solving, it is not presently supported by logic programming languages and little research has been devoted to this topic. This paper presents a scheme to deal efficiently with incremental search problems. The scheme allows the incremental addition and deletion of constraints and is based on re-execution, using parts of computation paths stored during previous computations. The scheme has been implemented as part of the constraint logic programming language CHIP and applied to practical problems. It has shown arbitrarily large (i.e. unbounded) speedups compared with previous approaches on practical problems.     

A Correct Logic Programming Computation of Default Logic Extensions

We present a method of representing some classes of default theories as normal logic programs. The main point is that the standart semantics (i.e., SLDNF-resolution) computes answer substitutions that correspond exactly to the extensions of the represented default theory. This means that we give a correct implementation of default logic. We explain the steps of constructing a logic program LogProg(P, D) from a given default theory (P, D), give some examples, and derive soundness and completeness results.     

归纳逻辑程序设计综述

归纳逻辑程序设计是由机器学习与逻辑程序设计交叉所形成的一个研究领域,是机器学习的前沿研究课题。该文首先从归纳逻辑程序设计的问题背景、类型划分和搜索程序子句三个方面介绍了归纳逻辑程序设计系统的概貌;然后结合实验室的相关研究工作,回顾了归纳逻辑程序设计研究的发展;之后介绍了归纳逻辑程序设计领域中需要深入研究的若干问题,并提出了新的解决思路;最后是总结,以引起读者对归纳逻辑程序设计领域研究的进一步关注。     

约束归纳逻辑程序设计系统

提出了一种新的约束归纳逻辑程序设计方法,并初步实现了一个自顶向下的约束归纳逻辑程序原型系统。该系统能够导出不受变量个数限制的多种形式的线性约束,得出覆盖正例而排斥负例的含约束的Hom子句程序。     

Extracting Context-Sensitive Models in Inductive Logic Programming

Given domain-specific background knowledge and data in the form of examples, an Inductive Logic Programming (ILP) system extracts models in the data-analytic sense. We view the model-selection step facing an ILP system as a decision problem, the solution of which requires knowledge of the context in which the model is to be deployed. In this paper, "context" will be defined by the current specification of the prior class distribution and the client's preferences concerning errors of classification. Within this restricted setting, we consider the use of an ILP system in situations where: (a) contexts can change regularly. This can arise for example, from changes to class distributions or misclassification costs; and (b) the data are from observational studies. That is, they may not have been collected with any particular context in mind. Some repercussions of these are: (a) any one model may not be the optimal choice forall contexts; and (b) not all the background information provided may be relevant for all contexts. Using results from the analysis of Receiver Operating Characteristic curves, we investigate a technique that can equip an ILP system to reject those models that cannot possibly be optimal in any context. We present empirical results from using the technique to analyse two datasets concerned with the toxicity of chemicals (in particular, their mutagenic and carcinogenic properties). Clients can, and typically do, approach such datasets with quite different requirements. For example, a synthetic chemist would require models with a low rate of commission errors which could be used to direct efficiently the synthesis of new compounds. A toxicologist on the other hand, would prefer models with a low rate of omission errors. This would enable a more complete identification of toxic chemicals at a calculated cost of misidentification of non-toxic cases as toxic. The approach adopted here attempts to obtain a solution that contains models that are optimal for each such user according to the cost function that he or she wishes to apply. In doing so, it also provides one solution to the problem of how the relevance of background predicates is to be assessed in ILP.     

Predicate invention-based specialization in Inductive Logic Programming

Three relevant areas of interest in symbolic Machine Learning are incremental supervised learning, multistrategy learning and predicate invention. In many real-world tasks, new observations may point out the inadequacy of the learned model. In such a case, incremental approaches allow to adjust it, instead of learning a new model from scratch. Specifically, when a negative example is wrongly classified by a model, specialization refinement operators are needed. A powerful way to specialize a theory in Inductive Logic Programming is adding negated preconditions to concept definitions. This paper describes an empowered specialization operator that allows to introduce the negation of conjunctions of preconditions using predicate invention. An implementation of the operator is proposed, and experiments purposely devised to stress it prove that the proposed approach is correct and viable even under quite complex conditions.