Asynchronous communication model based on linear logic

We propose a new framework called ACL for concurrent computation based on linear logic. ACL is a kind oflinear logic programming framework, where its operational semantics is described in terms ofproof construction in linear logic. We also give a model-theoretic semantics based onphase semantics, a model of linear logic. Our framework well captures concurrent computation based on asynchronous communication. It will, therefore, provide us with a new insight into other models of asynchronous concurrent computation from alogical point of view. We also expect ACL to become a formal framework for analysis, synthesis and transformation of concurrent programs by the use of techniques for traditional logic programming. ACL's attractive features for concurrent programming paradigms are also discussed.     

A Rewriting Logic Approach to Operational Semantics (Extended Abstract)

This paper shows how rewriting logic semantics (RLS) can be used as a computational logic framework for operational semantic definitions of programming languages. Several operational semantics styles are addressed: big-step and small-step structural operational semantics (SOS), modular SOS, reduction semantics with evaluation contexts, and continuation-based semantics. Each of these language definitional styles can be faithfully captured as an RLS theory, in the sense that there is a one-to-one correspondence between computational steps in the original language definition and computational steps in the corresponding RLS theory. A major goal of this paper is to show that RLS does not force or pre-impose any given language definitional style, and that its flexibility and ease of use makes RLS an appealing framework for exploring new definitional styles.     

Beyond multi-adjoint logic programming

In ‘multi-adjoint logic programming’, MALP in brief, each fuzzy logic program is associated with its own ‘multi-adjoint lattice’ for modelling truth degrees beyond the simpler case of true and false, where a large set of fuzzy connectives can be defined. On this wide repertoire, it is crucial to connect each implication symbol with a proper conjunction thus conforming constructs of the form (←_i, &_i) called ‘adjoint pairs’, whose use directly affects both declarative and operational semantics of the MALP framework. In this work, we firstly show how the strong dependence of adjoint pairs can be largely weakened for an interesting ‘sub-class’ of MALP programs. Then, we reason in a similar way till conceiving a ‘super-class’ of fuzzy logic programs beyond MALP, which definitively drops out the need for using adjoint pairs, since the new semantics behaviour relies on much more relaxed lattices than multi-adjoint ones.     

Simplifying dynamic programming via mode‐directed tabling

In the dynamic programming paradigm the value of an optimal solution is recursively defined in terms of optimal solutions to subproblems. Such dynamic programming definitions can be tricky and error‐prone to specify. This paper presents an elegant method based on tabled logic programming (TLP) that simplifies the specification of such dynamic programming solutions. Our method introduces a new mode declaration for tabled predicates. The arguments of each tabled predicate are divided into indexed and non‐indexed arguments so that tabled predicates can be regarded as functions: indexed arguments represent input values and non‐indexed arguments represent output values. The non‐indexed arguments in a tabled predicate can be further declared to be aggregated, for example, the minimum, so that while generating answers, the global table will dynamically maintain the smallest value for that argument. This mode‐declaration scheme, coupled with recursion, provides an easy‐to‐use method for dynamic programming: there is no need to define the value of an optimal solution recursively, as the definition of a general solution suffices. The optimal value as well as its corresponding concrete solution can be derived implicitly and automatically using tabled logic programming systems. Our experimental results show that mode declarations improve performance in solving dynamic programming problems on TLP systems. Copyright © 2007 John Wiley & Sons, Ltd.     

'Classical' Negation in Nonmonotonic Reasoning and Logic Programming

Gelfond and Lifschitz were the first to point out the need for a symmetric negation in logic programming and they also proposed a specific semantics for such negation for logic programs with the stable semantics, which they called 'classical'. Subsequently, several researchers proposed different, often incompatible, forms of symmetric negation for various semantics of logic programs and deductive databases. To the best of our knowledge, however, no systematic study of symmetric negation in non-monotonic reasoning was ever attempted in the past. In this paper we conduct such a systematic study of symmetric negation. We introduce and discuss two natural, yet different, definitions of symmetric negation: one is called strong negation and the other is called explicit negation. For logic programs with the stable semantics, both symmetric negations coincide with Gelfond–Lifschitz' 'classical negation'. We study properties of strong and explicit negation and their mutual relationship as well as their relationship to default negation 'not', and classical negation '¬'. We show how one can use symmetric negation to provide natural solutions to various knowledge representation problems, such as theory and interpretation update, and belief revision. Rather than to limit our discussion to some narrow class of nonmonotonic theories, such as the class of logic programs with some specific semantics, we conduct our study so that it is applicable to a broad class of non-monotonic formalisms. In order to achieve the desired level of generality, we define the notion of symmetric negation in the knowledge representation framework of AutoEpistemic logic of Beliefs, introduced by Przymusinski.     

Autoepistemic logic of first order and its expressive power

We study the expressive power of first-order autoepistemic logic. We argue that full introspection of rational agents should be carried out by minimizing positive introspection and maximizing negative introspection. Based on full introspection, we propose the maximal well-founded semantics that characterizes autoepistemic reasoning processes of rational agents, and show that breadth of the semantics covers all theories in autoepistemic logic of first order, Moore's AE logic, and Reiter's default logic. Our study demonstrates that the autoepistemic logic of first order is a very powerful framework for nonmonotonic reasoning, logic programming, deductive databases, and knowledge representation.This research is partially supported by NSERC grant OGP42193.     

函数式逻辑语言的操作语义

函数式语言和逻辑语言在下列意义上是互补的,基于归约的函数式程序设计语言具有确定和懒惰求解等性质.但同时它又缺少诸如存在量化的变量以及部分数据结构等所希望的性质.相反,基于HORN子句逻辑和消解原理的逻辑程序设计语言允许存在量化的变量和部分数据结构但又缺少确定和懒惰求解的性质.从这个角度出发,把函数和逻辑程序设计语言结合成一种范型是很自然的,这种结合提供了一种比逻辑和函数语言表达能力更强的合一语言.提出了函数式逻辑语言的操作语义,同时表明这种操作语义在实践中是可见的.     

Semantic forgetting in answer set programming

The notion of forgetting, also known as variable elimination, has been investigated extensively in the context of classical logic, but less so in (nonmonotonic) logic programming and nonmonotonic reasoning. The few approaches that exist are based on syntactic modifications of a program at hand. In this paper, we establish a declarative theory of forgetting for disjunctive logic programs under answer set semantics that is fully based on semantic grounds. The suitability of this theory is justified by a number of desirable properties. In particular, one of our results shows that our notion of forgetting can be entirely captured by classical forgetting. We present several algorithms for computing a representation of the result of forgetting, and provide a characterization of the computational complexity of reasoning from a logic program under forgetting. As applications of our approach, we present a fairly general framework for resolving conflicts in inconsistent knowledge bases that are represented by disjunctive logic programs, and we show how the semantics of inheritance logic programs and update logic programs from the literature can be characterized through forgetting. The basic idea of the conflict resolution framework is to weaken the preferences of each agent by forgetting certain knowledge that causes inconsistency. In particular, we show how to use the notion of forgetting to provide an elegant solution for preference elicitation in disjunctive logic programming.     

Autoepistemic logic programming

An autoepistemic logic programming language is derived from a subset of a three-valued autoepistemic logic, called 3AEL. Autoepistemic programs generalize several ideas underlying logic programming: stable, supported, and well-founded models, Fitting's semantics, Kunen's semantics, and abductive frameworks can all be captured through simple autoepistemic translations; moreover, SLDNF-resolution and a generate-and-test method for stable semantics are generalized to provide sound and complete proof methods for autoepistemic programs. These methods extend existing proof methods for 3AEL. Thus autoepistemic logic programming, besides contributing to the understanding of 3AEL, can be seen as a unifying framework for the theory of logic programs. It should also be regarded as a first step toward a flexible environment where different forms of inference can be formally integrated.This paper is an extended version of [8]. I am grateful to my advisor, Giorgio Levi, to Paolo Mancarella, who read the first version of the paper, and to the anonymous referees, whose comments led to sensible improvements.     

概率逻辑程序

1 引言最近几十年来,不确定性的管理在知识描述和推理中扮演着越来越重要的角色。为了处理不确定知识,人们提出了各种不同的形式化和方法论,其中大部分是直接或间接地基于概率论的。     

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.     

对象式逻辑程序设计语言LKO的说明性语义

本文基于逻辑程序设计语言的良基模型语义，探讨了对象逻辑程序设计语言ＬＫＯ的说明性语义，该语义由组合迭代的极小不动点定义，具有构造性和组合性，迷在ＬＫＯ中进一步引入非单调继承和逻辑奠定了基础。     

Formulae Meet Programs Over the Net: A Framework for Correct Network Aware Programming

A general framework for network aware programming is presented that consists of a language for programming mobile applications, a logic for specifying properties of the applications and an automatic tool for verifying such properties. The framework is based on X-KLAIM, eXtended KLAIM, an experimental programming language specifically designed to program distributed systems composed of several components interacting through multiple tuple spaces and mobile code. The proposed logic is a modal logic inspired by Hennessy-Milner logic and is interpreted over the same labelled structures used for the operational semantics of X-KLAIM. The automatic verification tool is based on a complete proof system that has been previously developed for the logic.     

A rewriting logic approach to operational semantics

This paper shows how rewriting logic semantics (RLS) can be used as a computational logic framework for operational semantic definitions of programming languages. Several operational semantics styles are addressed: big-step and small-step structural operational semantics (SOS), modular SOS, reduction semantics with evaluation contexts, continuation-based semantics, and the chemical abstract machine. Each of these language definitional styles can be faithfully captured as an RLS theory, in the sense that there is a one-to-one correspondence between computational steps in the original language definition and computational steps in the corresponding RLS theory. A major goal of this paper is to show that RLS does not force or pre-impose any given language definitional style, and that its flexibility and ease of use makes RLS an appealing framework for exploring new definitional styles.     

The rewriting logic semantics project

Rewriting logic is a flexible and expressive logical framework that unifies algebraic denotational semantics and structural operational semantics (SOS) in a novel way, avoiding their respective limitations and allowing succinct semantic definitions. The fact that a rewrite logic theory’s axioms include both equations and rewrite rules provides a useful “abstraction dial” to find the right balance between abstraction and computational observability in semantic definitions. Such semantic definitions are directly executable as interpreters in a rewriting logic language such as Maude, whose generic formal tools can be used to endow those interpreters with powerful program analysis capabilities.     

Towards a Declarative Semantics of Inheritance with Exceptions

This paper presents a declarative semantics of compositional inheritance in an object-oriented logic programming framework with explicit exceptions,based on the iterated least fixpoint semantics to normal logic programs.Taking logic objects with exceptions as a kind of non-monotonic theory,the nonmonotonicity of inheritance is achieved,which is of importance for modeling incoplete knowledge and requirement specifications in both artificial intelligence and software engineering.     

PRL: A probabilistic relational language

In this paper, we describe the syntax and semantics for a probabilistic relational language (PRL). PRL is a recasting of recent work in Probabilistic Relational Models (PRMs) into a logic programming framework. We show how to represent varying degrees of complexity in the semantics including attribute uncertainty, structural uncertainty and identity uncertainty. Our approach is similar in spirit to the work in Bayesian Logic Programs (BLPs), and Logical Bayesian Networks (LBNs). However, surprisingly, there are still some important differences in the resulting formalism; for example, we introduce a general notion of aggregates based on the PRM approaches. One of our contributions is that we show how to support richer forms of structural uncertainty in a probabilistic logical language than have been previously described. Our goal in this work is to present a unifying framework that supports all of the types of relational uncertainty yet is based on logic programming formalisms. We also believe that it facilitates understanding the relationship between the frame-based approaches and alternate logic programming approaches, and allows greater transfer of ideas between them. Editors: Hendrik Blockeel, David Jensen and Stefan Kramer An erratum to this article is available at .     

Towards the uniform implementation of declarative languages

Current implementation techniques for functional languages differ considerably from those for logic languages. This complicates the development of flexible and efficient abstract machines that can be used for the compilation of declarative languages combining concepts of functional and logic programming. We propose an abstract machine, called the JUMP-machine, which systematically integrates the operational concepts needed to implement the functional and logic programming paradigm. The use of a tagless representation for heap objects, which originates from the Spineless Tagless G-machine, supports the integration of different concepts. In this paper, we provide a functional logic kernel language and show how to translate it into the abstract machine language of the JUMP-machine. Furthermore, we define the operational semantics of the machine language formally and discuss the mapping of the abstract machine to concrete machine architectures. We tested the approach by writing a compiler for the functional logic language GTML. The obtained performance results indicate that the proposed method allows to implement functional logic languages efficiently.