Algorithmic Debugging and Hypothetical Reasoning

This paper presents a generalization of Shapiro style algorithmic debugging for generalized Horn clause intuitionistic logic. This logic offers hypothetical reasoning and negation is defined not by failure but by inconsistency. We extend Shapiro's notion of intended interpretation, symptoms and errors and give formal results paralleling those known for definite clauses. We also show how a corresponding diagnosis module for RISC- a logic programming system for generalized Horn clause intuitionistic logic-can be defined by meta interpretation. In contrast to Shapiro's PROLOG modules ours work independently of the specific computation rule that in RISC may be specified by the user.     

Techniques of integrating Datalog with PROLOG

Since extending DATALOG to a general-purpose programming language seems very difficult,many projects have embedded a DATALOG-based query laguage into a procedural host language,such as CORAL,Glue-Nail,etc.Although DATALOG can be consideed as function-free PROLOG,they are very different in many aspects.For instance,DATALOG is declarative while PROLOG isn‘t,DATALOG takes “a-set-at-a-time” mode of evaluation but PROLOG takes “a-tuple-at-a-time”one,DATALOG is only a query language whereas PROLOG is a general-purpose programming language.It is thought that integrating DATALOG with PROLOG may take their advantages.KBASEP is such a language.It uses KBASE as the query language and PROLOG as its procedural host language,where KBASE is a ne extemsion of DATALOG with negation and function.This paper introduces the integration techniques used in KBASE-P system.     

Production systems with negation as failure

We study action rule-based systems with two forms of negation, namely classical negation and "negation as failure to find a course of action". We show, by means of several examples, that adding negation as failure to such systems increases their expressiveness in the sense that real-life problems can be represented in a natural and simple way. Then we address the problem of providing a formal declarative semantics to these extended systems by adopting an argumentation-based approach which has been shown to be a simple unifying framework for understanding the declarative semantics of various nonmonotonic formalisms. In this way, we naturally define the grounded (well-founded), stable and preferred semantics for production systems with negation as failure. Next, we characterize the class of stratified production systems, which enjoy the properties that the above-mentioned semantics coincide and that negation as failure to find a course of action can be computed by a simple bottom-up operator. Stratified production systems can be implemented on top of conventional production systems in two ways. The first way corresponds to the understanding of stratification as a form of priority assignment between rules. We show that this implementation, though sound, is not complete in the general case. Hence, we propose a second implementation by means of an algorithm which transforms a finite stratified production system into a classical one. This is a sound and complete implementation, though it is computationally hard     

Nested expressions in logic programs

We extend the answer set semantics to a class of logic programs with nested expressions permitted in the bodies and heads of rules. These expressions are formed from literals using negation as failure, conjunction (,) and disjunction (;) that can be nested arbitrarily. Conditional expressions are introduced as abbreviations. The study of equivalent transformations of programs with nested expressions shows that any such program is equivalent to a set of disjunctive rules, possibly with negation as failure in the heads. The generalized answer set semantics is related to the Lloyd–Topor generalization of Clark’s completion and to the logic of minimal belief and negation as failure. This revised version was published online in June 2006 with corrections to the Cover Date.     

Logic programs with exceptions

We extend logic programming to deal with default reasoning by allowing the explicit representation of exceptions in addition to general rules. To formalise this extension, we modify the answer set semantics of Gelfond and Lifschitz, which allows both classical negation and negation as failure. We also propose a transformation which eliminates exceptions by using negation by failure. The transformed program can be implemented by standard logic programming methods, such as SLDNF. The explicit representation of rules and exceptions has the virtue of greater naturalness of expression. The transformed program, however, is easier to implement.     

Negation as Failure as Resolution

Providing a clean procedural semantics of the Negation As Failure rule in Logic Programming has been an open problem for some time now. This rule has been treated as a technique in nonmonotonic reasoning, not as a rule in classical logic. This paper contains a demonstration of the negation as failure rule as a resolution procedure in first-order logic. We present a sound and complete resolution scheme for negation as failure rule for the larger class of constraint logic programs. The approach is to consider a canonical partition of the completion of a definite (constraint) program into the IF and the FI programs. We show that a negated goal, provable from the completed definite program is provable from just the FI part. The clauses in this program have a structure dual to that of definite Horn clauses. We describe a sound and complete linear resolution rule for this fragment, and show that a resolution proof of the negated goal from the FI part corresponds to a finite failure tree resulting from classical linear resolution applied to the goal on the If part of the original definite program. Our work shows that negation as failure rule can be computationally efficient in the sense that the SLD-resolution on the If part of a definite program along with the negation as failure rule is more efficient than a direct resolution procedure on the completion of that program.     

SLDNF resolution with non-safe rule and fixpoint semantics for general logic programs

The SLDNF resolution (SLD resolution with negation as failure) is often restricted to yield a safe rule, that is, negation as failure rule is adopted only in the case that the selected negative literal in each goal should be in ground. In this paper we investigate extensions of goals in SLDNF resolutions with the case of selecting non-ground negative literals. Since Shepherdson's proposal is thought of as most general [16, 18] we formally show how the success and failure sets by Sherpherdson's SLDNFS resolution are related with a fixpoint semantics, which is generalized to be concerned with atom sets involving the variables.     

'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.     

不协调知识的缺省推理

提出了一个新的缺省推理理论,称为双缺省理论,使得缺省逻辑在四值语义下能够同时处理不协调的知识而不导致扩张的平凡性.为此,定义了命题公式的正变换和负变换,以便分离一个文字与其否定的语义联系.大多数关于缺省逻辑的定理都可以在双缺省逻辑下重建,证明了双缺省逻辑是缺省逻辑在不协调情形下的一般化.提供了一种方法使得超协调逻辑能够获得类似经典逻辑的推理能力.     

Login: a logic programming language with built-in inheritance

An elaboration of the PROLOG language is described in which the notion of first-order term is replaced by a more general one. This extended form of terms allows the integration of inheritance—an IS-A taxonomy—directly into the unification process rather than indirectly through the resolution-based inference mechanism of PROLOG. This results in more efficient computations and enhanced language expressiveness. The language thus obtained, called LOGIN, subsumes PROLOG, in the sense that conventional PROLOG programs are equally well executed by LOGIN.     

A logic-based calculus of events

We outline an approach for reasoning about events and time within a logic programming framework. The notion of event is taken to be more primitive than that of time and both are represented explicitly by means of Horn clauses augmented with negation by failure. The main intended applications are the updating of databases and narrative understanding. In contrast with conventional databases which assume that updates are made in the same order as the corresponding events occur in the real world, the explicit treatment of events allows us to deal with updates which provide new information about the past. Default reasoning on the basis of incomplete information is obtained as a consequence of using negation by failure. Default conclusions are automatically withdrawn if the addition of new information renders them inconsistent. Because events are differentiated from times, we can represent events with unknown times, as well as events which are partially ordered and concurrent.     

What is failure? An approach to constructive negation

A standard approach to negation in logic programming is negation as failure. Its major drawback is that it cannot produce answer substitutions to negated queries. Approaches to overcoming this limitation are termed constructive negation. This work proposes an approach based on construction offailed trees for some instances of a negated query. For this purpose a generalization of the standard notion of a failed tree is needed. We show that a straightforward generalization leads to unsoundness and present a correct one.The method is applicable to arbitrary normal programs. If finitely failed trees are concerned then its semantics is given by Clark completion in 3-valued logic (and our approach is a proper extension of SLDNF-resolution). If infinite failed trees are allowed then we obtain a method for the well-founded semantics. In both cases soundness and completeness are proved.     

Consistency-based and abductive diagnoses as generalised stable models

If realistic systems are to be successfully modelled and efficiently diagnosed using model-based techniques, a more expressive language than classical logic is required. In this paper, we present a definition of diagnosis which allows the use of a nonmonotonic construct, negation as failure, in the modelling language. This definition is based on thegeneralised stable model semantics of abduction. Furthermore, we argue that, if negation as failure is permitted in the modelling language, the distinction between abductive and consistency-based diagnosis is no longer clear. Our definition allows both forms of diagnosis to be expressed in a single framework. It also allows a single interference procedure to perform abductive or consistency-based diagnosis, as appropriate.This paper is an extended and revised version of ref. [29].     

概念知识表示和推理

Nilsson教授首先提出了代数格应用于概念知识表示的思想．其优点在于知识表示的代数特性和图示特性，在此基础上．表文把代数格与PROLOG相结合．定义了一种基于概念的逻辑编程语言．其语言具有比PROLOG更抽象、更方便的编程风格．此外．给出了该逻辑编程语言的匹配算法．     

A logic programming framework for modeling temporal objects

We present a general approach for modeling temporal aspects of objects in a logic programming framework. Change is formulated in the context of a database which stores explicitly a record of all changes that have occurred to objects and thus (implicitly) all states of objects in the database. A snapshot of the database at any given time is an object-oriented database, in the sense that it supports an object-based data model. An object is viewed as a collection of simple atomic formulas, with support for an explicit notion of object identity, classes and inheritance. The event calculus is a treatment of time and change in first-order classical logic augmented with negation as failure. The paper develops a variant of the event calculus for representing changes to objects, including change in internal state of objects, creation and deletion of objects, and mutation of objects over time. The concluding sections present two natural and straightforward extensions, to deal with versioning of objects and schema evolution, and a sketch of implementation strategies for practical application to temporal object-oriented databases     

Classical negation in logic programs and disjunctive databases

An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic programs by including classical negation, in addition to negation-as-failure. The semantics of such extended programs is based on the method of stable models. The concept of a disjunctive database can be extended in a similar way. We show that some facts of commonsense knowledge can be represented by logic programs and disjunctive databases more easily when classical negation is available. Computationally, classical negation can be eliminated from extended programs by a simple preprocessor. Extended programs are identical to a special case of default theories in the sense of Reiter.     

Hypothetical reasoning in logic programs

In order to express incomplete knowledge, extended logic programs have been proposed as logic programs with classical negation along with negation as failure. This paper discusses ways to deal with a broad class of common sense knowledge by using extended logic programs. For this purpose, we present a uniform approach for dealing with both incomplete and contradictory programs, as a simple framework of hypothetical reasoning in which some rules are dealt with as candidate hypotheses that can be used to augment the background theory. This theory formation framework can be used for default reasoning, contradiction removals, the closed world assumption, and abduction. We also show a translation of the theory formation framework to an extended logic program whose answer sets correspond to the consistent belief sets of augmented theories.     

Relative negations in non-commutative fuzzy structures

In this paper we investigate the properties of the relative negations in non-commutative residuated lattices and their applications. We define the notion of a relative involutive FL-algebra and we generalize to relative negations some results proved for involutive pseudo-BCK algebras. The relative locally finite IFL-algebra is defined and it is proved that an interval algebra of a relative locally finite divisible IFL-algebra is relative involutive. Starting from the observation that in the definition of states, the standard MV-algebra structure of [0, 1] intervenes, there were introduced the states on bounded pseudo-BCK algebras, pseudo-hoops and residuated lattices with values in the same kind of structures and they were studied under the name of generalized states. For the case of commutative residuated lattices the generalized states were studied in the sense of relative negation. We define and study the relative generalized states on non-commutative residuated lattices. One of the main results consists of proving that every order-preserving generalized Bosbach state is a relative generalized Rie?an state. Some conditions are given for a relative generalized Rie?an state to be a generalized Bosbach state. Finally, we develop a concept of states on IFL-algebras.