Integrating Discrete and Continuous Change in a Logical Framework

The goal of our work is to develop theoretical foundations for the representation of knowledge in domains in which properties may vary continuously. One achievement of our research is that it extends the applicability of current research on theories of action. Furthermore, we are able to apply known approaches to the frame and ramification problems, developed for discretely changing worlds, to domains in which the world changes continuously.
Our approach is based on the discrete situation calculus and on a monotonic solution to the frame problem. In order to address the combined frame and ramification problems, we extend Lin and Reiter's work. We use Pinto and Reiter's extension to the situation calculus to represent occurrences . We extend this work further to allow for reasoning by default. For example, if we know that a ball is falling and we do not have any reason to believe that an action would interfere with the ball's motion, then we assume that the ball will hit the ground. Finally, we extend the language of the situation calculus to allow for properties that change within situations. We also show that our proposed situation calculus inherits the solutions to the frame and ramification problems.     

Foundation of logic programming based on inductive definition

A logical system of inference rules intended to give the foundation of logic programs is presented. The distinguished point of the approach taken here is the application of the theory of inductive definitions, which allows us to uniformly treat various kinds of induction schema and also allows us to regardnegation as failure as a kind of induction schema. This approach corresponds to the so-called least fixpoint semantics. Moreover, in our formalism, logic programs are extended so that a condition of a clause may be any first-order formula. This makes it possible to write a quantified specification as a logic program. It also makes the class of induction schemata much larger to include the usual course-of-values inductions.     

A Polynomial Approach to the Constructive Induction of Structural Knowledge

The representation formalism as well as the representation language is of great importance for the success of machine learning. The representation formalism should be expressive, efficient, useful, and applicable. First-order logic needs to be restricted in order to be efficient for inductive and deductive reasoning. In the field of knowledge representation, term subsumption formalisms have been developed which are efficient and expressive. In this article, a learning algorithm, KLUSTER, is described that represents concept definitions in this formalism. KLUSTER enhances the representation language if this is necessary for the discrimination of concepts. Hence, KLUSTER is a constructive induction program. KLUSTER builds the most specific generalization and a most general discrimination in polynomial time. It embeds these concept learning problems into the overall task of learning a hierarchy of concepts.     

Representing Knowledge within the Situation Calculus Using Interval-Valued Epistemic Fluents

The ability of interval arithmetic to provide a finite (and succinct) way to represent uncertainty about a large, possibly uncountable, set of alternatives turns out to be useful in building "intelligent" autonomous agents. In particular, consider the two important issues of reasoning and sensing in intelligent control for autonomous agents. Developing a principled way to combine the two raises complicated issues in knowledge representation. In this paper we describe a solution to the problem. The idea is to incorporate interval arithmetic into the situation calculus. The situation calculus is a well known formalism for describing changing worlds using sorted first-order logic. It can also be used to describe how an agent's knowledge of its world changes. Potentially, this provides a sound basis for incorporating sensing into logic programming. Previous work has relied on a possible worlds approach to knowledge. This leads to an elegant mathematical specification language. Unfortunately, there have been no proposals on how to implement the approach. This is because the number of possible worlds is potentially uncountable. We propose an alternative formalization of knowledge within the situation calculus. Our approach is based on intervals. The advantage is that it is straightforward to implement. Moreover, we can prove that it is sound and (sometimes) complete with respect to the previous possible worlds approach.     

Soundness and Completeness Proofs by Coinductive Methods

We show how codatatypes can be employed to produce compact, high-level proofs of key results in logic: the soundness and completeness of proof systems for variations of first-order logic. For the classical completeness result, we first establish an abstract property of possibly infinite derivation trees. The abstract proof can be instantiated for a wide range of Gentzen and tableau systems for various flavors of first-order logic. Soundness becomes interesting as soon as one allows infinite proofs of first-order formulas. This forms the subject of several cyclic proof systems for first-order logic augmented with inductive predicate definitions studied in the literature. All the discussed results are formalized using Isabelle/HOL’s recently introduced support for codatatypes and corecursion. The development illustrates some unique features of Isabelle/HOL’s new coinductive specification language such as nesting through non-free types and mixed recursion–corecursion.     

Logic Program Synthesis as Problem Reduction Using Combining Forms

This paper presents an approach to inductive synthesis of logic programs from examples using problem decomposition and problem reduction principles. This is in contrast to the prevailing logic program induction paradigm, which relies on generalization of programs from examples. The problem reduction is accomplished as a constrained top-down search process, which eventually is to reach trivial problems.Our induction scheme applies a distinguished logic programming language in which programs are combined from elementary predicates by means of combinators conceived of as problem reduction operators including list recursion forms. The operator form admits inductive synthesis as a top-down piecewise composition of semantically meaningful program elements according to the compositional semantics principle and with appeals neither to special generalization mechanisms nor to alternative forms of resolution and unification, or predicate invention.The search space is reduced by subjecting the induction process to various constraints concerning syntactical form, modes, data types, and computational resources. This is illustrated in the paper with well-modedness constraints with the aim of synthesising well-moded, procedurally acceptable programs.Preliminary experiments with the proposed induction method lead us to tentatively conclude that the presented approach forms a viable alternative to the prevailing inductive logic programming methods applying generalization from examples.     

A hybrid,decidable, logic-based knowledge representation system1

The major problem with using standard first-order logic as a basis for knowledge representation systems is its undecidability. A variant of first-order tautological entailment, a simple version of relevance logic, has been developed that has decidable inference and thus overcomes this problem. However, this logic is too weak for knowledge representation and must be strengthened. One way to strengthen the logic is to create a hybrid logic by adding a terminological reasoner. This must be done with care to retain the decidability of the logic as well as its reasonable semantics. The result, a stronger decidable logic, is used in the design of a hybrid, decidable, logic-based knowledge representation system.     

On the equivalence and range of applicability of graph-based representations of logic programs

Logic programs under Answer Sets semantics can be studied, and actual computation can be carried out, by means of representing them by directed graphs. Several reductions of logic programs to directed graphs are now available. We compare our proposed representation, called Extended Dependency Graph, to the Block Graph representation recently defined by Linke [Proc. IJCAI-2001, 2001, pp. 641-648]. On the relevant fragment of well-founded irreducible programs, extended dependency and block graph turns out to be isomorphic. So, we argue that graph representation of general logic programs should be abandoned in favor of graph representation of well-founded irreducible programs, which are more concise, more uniform in structure while being equally expressive.     

Parallel and Sequential Algorithms for Data Mining Using Inductive Logic

Inductive logic is a research area in the intersection of machine learning and logic programming, and has been increasingly applied to data mining. Inductive logic studies learning from examples, within the framework provided by clausal logic. It provides a uniform and expressive means of representation: examples, background knowledge, and induced theories are all expressed in first-order logic. Such an expressive representation is computationally expensive, so it is natural to consider improving the performance of inductive logic data mining using parallelism. We present a parallelization technique for inductive logic, and implement a parallel version of a core inductive logic programming system: Progol. The technique provides perfect partitioning of computation and data access and communication requirements are small, so almost linear speedup is readily achieved. However, we also show why the information flow of the technique permits superlinear speedup over the standard sequential algorithm. Performance results on several datasets and platforms are reported. The results have wider implications for the design on parallel and sequential data-mining algorithms. Received 30 August 2000 / Revised 30 January 2001 / Accepted in revised form 16 May 2001     

CDDL:动态描述逻辑的不确定性扩展

本体(Ontology)是语义Web中共享知识的形式化建模工具,其逻辑基础是描述逻辑.动态描述逻辑(DDL)具有同时表示静态和动态知识的优势.本文针对语义Web需要处理不确定性动态知识的需求,利用云模型对DDL进行不确定性扩展,提出了一种能够有效实现不确定性静态和动态知识进行表示和推理的不确定性动态描述逻辑CDDL.与...     

基于归纳逻辑程序设计的学习方法及其实现的研究

归纳逻辑程序设计是机器学习领域中的一个新方法，它研究的是从实例和背景知识进行逻辑程序（新知识）的构造．本文介绍了归纳逻辑程序设计的基本理论和方法，并介绍了这种学习方法在专家系统中的应用情况．     

Autoepistemic logics as a unifying framework for the semantics of logic programs

In this paper, it is shown that a three-valued autoepistemic logic provides an elegant unifying framework for some of the major semantics of normal and disjunctive logic programs and logic programs with classical negation, namely, the stable semantics, the well-founded semantics, supported models, Fitting's semantics, Kunen's semantics, the stationary semantics, and answer sets. For the first time, so many semantics are embedded into one logic. The framework extends previous results—by Gelfond, Lifschitz, Marek, Subrahmanian, and Truszczynski —on the relationships between logic programming and Moore's autoepistemic logic. The framework suggests several new semantics for negation-as-failure. In particular, we will introduce the epistemic semantics for disjunctive logic programs. In order to motivate the epistemic semantics, an interesting class of applications called ignorance tests will be formalized; it will be proved that ignorance tests can be defined by means of the epistemic semantics, but not by means of the old semantics for disjunctive programs. The autoepistemic framework provides a formal foundation for an environment that integrates different forms of negation. The role of classical negation and various forms of negation-by-failure in logic programming will be briefly discussed.     

A new methodology of fuzzy constraint-based controller design viaconstraint-network processing

A complete design framework for a fuzzy constraint-based controller based on fuzzy-constraint processing and its semantics and relationship to fuzzy logic is presented. In this paper, the concept of “fuzzy constraints” in problem solving is introduced, and some basic definitions of fuzzy-constraint processing in a constraint network and its semantic modeling are addressed. Then a fuzzy local propagation inference mechanism for reasoning about imprecise information applying the filter operation in a network of constraints is proposed. Moreover, we advance the concurrent fuzzy-logic controller (FLC) to a new type of controller, the fuzzy constraint-based controller (FCC), using a more general predicate calculus and full first-order logic knowledge representation and making use of the idea of fuzzy-constraint processing to model practical dynamic control systems. Finally, simulation results show that a FCC achieves equivalent performance as PD type and PI type FLCs and it also demonstrates superior outcomes to a conventional PID controller in terms of rise time and peak-percent overshoot     

Existential rigidity and many modalities in order-sorted logic

Order-sorted logic is a useful tool for knowledge representation and reasoning because it enables representation of sorted terms and formulas along with partially ordered sorts (called sort-hierarchy). However, this logic cannot represent more complex sorted expressions when they are true in any possible world (as rigid) or some possible worlds (as modality) such as time, space, belief, or situation. In this study, we extend order-sorted logic by introducing existential rigidity and many modalities. In the extended logic, sorted modal formulas are interpreted over the Cartesian product of sets of possible worlds. We present a new labeled tableau calculus to check the (un)satisfiability and validity of sorted modal formulas.     

HYPOTHETICAL REASONING ABOUT ACTIONS: FROM SITUATION CALCULUS TO EVENT CALCULUS

Hypothetical reasoning about actions is the activity of preevaluating the effect of performing actions in a changing domain; this reasoning underlies applications of knowledge representation, such as planning and explanation generation. Action effects are often specified in the language of situation calculus, introduced by McCarthy and Hayes in 1969. More recently, the event calculus has been defined to describe actual actions, i.e., those that have occurred in the past, and their effects on the domain. Altough the two formalisms share the basic ontology of atomic actions and fluents, situation calculus cannot represent actual actions while event calculus cannot represent hypotethical actions. In this article, the language and the axioms of event calculus are extended to allow representing and reasoning about hypothetical actions, performed either at the present time or in the past, altough counterfactuals are not supported. Both event calculus and its extension are defined as logic programs so that theories are readily adaptable for Prolog query interpretation. For a reasonably large class of theories and queries, Prolog interpretation is shown to be sound and complete w.r.t. the main semantics for logic programs.     

Well-founded semantics and stratification for ordered logic programs

This paper present an extension of traditional logic programming, called ordered logic (OL) programming, to support classical negation as well as constructs from the object-oriented paradigm. In particular, such an extension allows to cope with the notions of object, multiple inheritance and non-monotonic reasoning. The contribution of the work is mainly twofold. First, a rich wellfounded semantics for ordered logic programs is defined. Second, an efficient method for the well-founded model computation of a meaningful class of ordered logic programs, called stratified programs, is provided.     

Manipulating Tree Tuple Languages by Transforming Logic Programs

We introduce inductive definitions over language expressions as a framework for specifying tree tuple languages. Inductive definitions and their sub-classes correspond naturally to classes of logic programs, and operations on tree tuple languages correspond to the transformation of logic programs. We present an algorithm based on unfolding and definition introduction that is able to deal with several classes of tuple languages in a uniform way. Termination proofs for clause classes translate directly to closure properties of tuple languages, leading to new decidability and computability results for the latter.     

Tree Tuple Languages from the Logic Programming Point of View

We introduce inductive definitions over language expressions as a framework for specifying tree tuple languages. Inductive definitions and their subclasses correspond naturally to classes of logic programs, and operations on tree tuple languages correspond to the transformation of logic programs. We present an algorithm based on unfolding and definition introduction that is able to deal with several classes of tuple languages in a uniform way. Termination proofs for clause classes translate directly to closure properties of tuple languages, leading to new decidability and computability results for the latter.