Nonmonotonic Reasoning System Research Articles

On Cascade Products of Answer Set Programs

AbstractDescribing complex objects by elementary ones is a common strategy in mathematics and science in general. In their seminal 1965 paper, Kenneth Krohn and John Rhodes showed that every finite deterministic automaton can be represented (or “emulated”) by a cascade product of very simple automata. This led to an elegant algebraic theory of automata based on finite semigroups (Krohn-Rhodes Theory). Surprisingly, by relating logic programs and automata, we can show in this paper that the Krohn-Rhodes Theory is applicable in Answer Set Programming (ASP). More precisely, we recast the concept of a cascade product to ASP, and prove that every program can be represented by a product of very simple programs, the reset and standard programs. Roughly, this implies that the reset and standard programs are the basic building blocks of ASP with respect to the cascade product. In a broader sense, this paper is a first step towards an algebraic theory of products and networks of nonmonotonic reasoning systems based on Krohn-Rhodes Theory, aiming at important open issues in ASP and AI in general.

Semantical investigations into nonmonotonic and probabilistic logics

Different forms of semantics have been proposed for conditionals of the form "Usually, if A then B", ranging from quantitative probability distributions to qualitative approaches using plausibility orderings, possibility distributions, or conditional objects. Atomic-bound systems, also called big-stepped probabilities, allow qualitative reasoning with probabilities, aiming at bridging the gap between qualitative and quantitative argumentation and providing a model for the nonmonotonic reasoning system P. By using Goguen and Burstall's notion of institutions for the formalization of logical systems, we elaborate precisely which formal connections exist among big-stepped probabilities, standard probabilities, and qualitative logics. Based on our investigations, we also develop two variants of conditional objects, one of them having a simpler semantics while still providing a model for system P.

Dynamische Typisierung und non-monotonic Reasoning: Voraussetzungen für semantische Interoperabilität

Summary Semantic interoperabilit yi sac rucial conditio nf or eHealth. Not only formal aspects of the documents have to be considered ,b ut th es emantics, e.g., the meaning of the mentioned facts, must be made interoperable. We describe the main problems arising when as tatic standar di sc hosen as am edium for interoperability .A na lternative approach is introduced, no tas tandard, bu tam ethod to interoperate between given heterogeneous standards. The approach is based on am ultidimensional an dm ultifocal concept architecture .C oncepts are presented in as trict composite form ,i no rder to dea lw ith th em ultidimensional natur eo fs emantics. We explain why dynami ct ype definitions are essential for th eg ive nt ask and why the reasonin gm ust be non-monotonic. Whe no peratin go na n input ,t he non-monotonic reasoning system is controlled by as ystem of few dynami ct rigger concepts.

From the textual description of an accident to its causes

Every human being, reading a short report concerning a road accident, gets an idea of its causes. The work reported here attempts to enable a computer to do the same, i.e. to determine the causes of an event from a textual description of it. It relies heavily on the notion of norm for two reasons: • The notion of cause has often been debated but remains poorly understood: we postulate that what people tend to take as the cause of an abnormal event, like an accident, is the fact that a specific norm has been violated. • Natural Language Processing has given a prominent place to deduction, and for what concerns Semantics, to truth-based inference. However, norm-based inference is a much more powerful technique to get the conclusions that human readers derive from a text. The paper describes a complete chain of treatments, from the text to the determination of the cause. The focus is set on what is called “linguistic” and “semantico-pragmatic” reasoning. The former extracts so-called “semantic literals” from the result of the parse, and the latter reduces the description of the accident to a small number of “kernel literals” which are sufficient to determine its cause. Both of them use a non-monotonic reasoning system, viz. LPARSE and SMODELS. Several issues concerning the representation of modalities and time are discussed and illustrated by examples taken from a corpus of reports obtained from an insurance company.

Using abduction and induction for operational requirements elaboration

Requirements Engineering involves the elicitation of high-level stakeholder goals and their refinement into operational system requirements. A key difficulty is that stakeholders typically convey their goals indirectly through intuitive narrative-style scenarios of desirable and undesirable system behaviour, whereas goal refinement methods usually require goals to be expressed declaratively using, for instance, a temporal logic. In actual software engineering practice, the extraction of formal requirements from scenario-based descriptions is a tedious and error-prone process that would benefit from automated tool support. This paper presents an Inductive Logic Programming method for inferring operational requirements from a set of example scenarios and an initial but incomplete requirements specification. The approach is based on translating the specification and the scenarios into an event-based logic programming formalism and using a non-monotonic reasoning system, called eXtended Hybrid Abductive Inductive Learning, to automatically infer a set of event pre-conditions and trigger-conditions that cover all desirable scenarios and reject all undesirable ones. This learning task is a novel application of logic programming to requirements engineering that also demonstrates the utility of non-monotonic learning capturing pre-conditions and trigger-conditions.

Issues in parallel execution of non-monotonic reasoning systems

We explore the major issues involved in the automatic exploitation of parallelism from the execution models of logic-based non-monotonic reasoning systems. We describe orthogonal techniques to parallelize the computation of models of non-monotonic logic theories, and demonstrate the effectiveness of the proposed techniques in prototypical implementation.

On using human nonmonotonic reasoning to inform artificial systems

People seem adept at drawing tentative conclusions when premises do not lead to a necessary conclusion. In contrast, the artificial nonmonotonic reasoning systems that have been developed are complex and do not function with ease. This apparent difference between human and artificial computational reasoning is sometimes considered puzzling and frustrating - if people can do it so easily, why can't we get computers to do it easily? The present paper explores the ways in which people attempt to solve nonmonotonic problems which contain conflict and shows that people do not in fact reason about these nonmonotonic problems so easily; they jump to conclusions easily, but they do not reason so well. However, some people do manage to sometimes reason quite well, in that their reasoning is based on ideas that are (classically) logically justifiable. This paper explores differences between these reasoners and others who cope less well. It also explores how the identification of the way in which these people reason can be used to inform artificial nonmonotonic reasoning systems.

A stratified first order logic approach for access control

Modeling information security policies is an important problem in many domains. This is particularly true in the health care sector, where information systems often manage sensitive and critical data. This article proposes to use nonmonotonic reasoning systems to control access to sensitive data in accordance with a security policy. In the first part of the article, we propose an access control model that overcomes several limitations of existing systems. In particular, it allows us to deal with contexts and to represent the two main kinds of privileges: permissions and prohibitions. This model will then be formally encoded using stratified (or prioritized) first-order knowledge bases. In the second part of the article, we discuss the problem of conflicts due to the joint handling of permissions and prohibitions. We show that approaches proposed for solving conflicts in propositional knowledge bases are not appropriate for handling inconsistent first-order knowledge bases. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 817–836, 2004.

A BIG-STEPPED PROBABILITY APPROACH FOR DISCOVERING DEFAULT RULES

This paper deals with the extraction of default rules from a database of examples. The proposed approach is based on a special kind of probability distributions, called "big-stepped probabilities", which are known to provide a semantics for non-monotonic reasoning. The rules which are learnt are genuine default rules, which could be used (under some conditions) in a non-monotonic reasoning system and can be encoded in possibilistic logic.

A compositional reasoning system for executing nonmonotonic theories of reasoning

In this paper the framework DESIRE for the design of compositional reasoning systems and multi-agent systems was applied to build a generic nonmonotonic reasoning system. The outcome is a general reasoning system that can be used to model different nonmonotonic reasoning formalisms and that can be executed by a generic execution mechanism. The main advantages of using DESIRE (for example, compared to a direct implementation in a programming language such as PROLOG) are that the design is generic and has a transparent compositional structure, and the explicit declarative specification of both the static and dynamic aspects of the nonmonotonic reasoning processes, including their control. © 2003 Wiley Periodicals, Inc.

Approximate coherence-based reasoning

It has long been recognized that the concept of inconsistency is a central part of commonsense reasoning. In this issue, a number of authors have explored the idea of reasoning with maximal consistent subsets of an inconsistent stratified knowledge base. This paradigm, often called “coherent-based reasoning", has resulted in some interesting proposals for para-consistent reasoning, non-monotonic reasoning, and argumentation systems. Unfortunately, coherent-based reasoning is computationally very expensive. This paper harnesses the approach of approximate entailment by Schaerf and Cadoli [SCH 95] to develop the concept of “approximate coherent-based reasoning". To this end, we begin to present a multi-modal propositional logic that incorporates two dual families of modalities: □S and ?S defined for each subset S of the set of atomic propositions. The resource parameter S indicates what atoms are taken into account when evaluating formulas. Next, we define resource-bounded consolidation operations that limit and control the generation of maximal consistent subsets of a stratified knowledge base. Then, we present counterparts to existential, universal, and argumentative inference that are prominent in coherence-based approaches. By virtue of modalities □S and ?S, these inferences are approximated from below and from above, in an incremental fashion. Based on these features, we show that an anytime view of coherent-based reasoning is tenable.

Resolution for Skeptical Stable Model Semantics

An extension of resolution for skeptical stable model semantics is introduced. Unlike previous approaches, our calculus is not derived from credulous inference and enjoys a number of properties that are not satisfied by current nonmonotonic reasoning systems. Skeptical resolution is top down, in general, and goal directed on call-consistent programs. It does not need the given program to be instantiated before reasoning. It may compute nonground answer substitutions efficiently. It is compatible with different implementations of negation as failure. Some inferences, which depend on nonground negative goals, can be drawn without resorting to negation-as-failure; as a consequence, many goals that flounder in the standard setting have a successful skeptical derivation. The paper contains a preliminary study of some interesting derivation strategies and a sketch of a prototype implementation of the calculus.

INDED: a distributed knowledge-based learning system

The INDED (induction-deduction, pronounced "indeed") system performs rule discovery using the techniques of inductive logic programming, and accumulates and handles knowledge using a deductive nonmonotonic reasoning engine. Using the language of logic programming, we use a hypergraph to represent the knowledge base from which rules are mined. Because the hypergraph gets inordinately large in INDED's serial version, we have devised a parallel implementation that creates smaller subhypergraphs. We investigate the integrity and meaning of decomposing data so that many processors can attempt to learn the same global pattern simultaneously (although locally, each discovered pattern is usually unique). Many data decompositions are fallacious and lead to nonsensical discovered rules. Some data, however, exhibits enough mutual exclusivity to render it partitionable among processors. This examination of partitionability of data has been the underlying driving force of this work. A great deal of work has been done in parallelizing unguided discovery of association rules. The novel aspects of our work include the parallelization of both a nonmonotonic reasoning system and an inductive logic programming learner. We describe the schemes we have explored and are exploring in this pursuit. We also present our data-partitioning algorithms that we based on data locality.

Strategies in Human Nonmonotonic Reasoning

Although humans seem adept at drawing nonmonotonic conclusions, the nonmonotonic reasoning systems that researchers develop are complex and do not function with such ease. This paper explores people's reasoning processes in nonmonotonic problems. To avoid the problem of people's conclusions being based on knowledge rather than on some reasoning process, we developed a scenario about life on another planet. Problems were chosen to allow the systematic study of people's understanding of strict and nonstrict rules and their interactions. We found that people had great difficulty reasoning and we identified a number of negative factors influencing their reasoning. We also identified three positive factors which, if used consistently, would yield rational and coherent reasoning—but no subject achieved total consistency. (Another possible positive factor, specificity, was considered but we found no evidence for its use.) It is concluded that nonmonotonic reasoning is hard. When people need to reason in a domain where they have no preconceived ideas, the foundation for their reasoning is neither coherent nor rational. They do not use a nonmonotonic reasoning system that would work regardless of content. Thus, nonmonotonic reasoning systems that researchers develop are expected to do more reasoning than humans actually do!

Computing with default logic

Default logic was proposed by Reiter as a knowledge representation tool. In this paper, we present our work on the Default Reasoning System, DeReS, the first comprehensive and optimized implementation of default logic. While knowledge representation remains the main application area for default logic, as a source of large-scale problems needed for experimentation and as a source of intuitions needed for a systematic methodology of encoding problems as default theories we use here the domain of combinatorial problems.To experimentally study the performance of DeReS we developed a benchmarking system, the TheoryBase. The TheoryBase is designed to support experimental investigations of nonmonotonic reasoning systems based on the language of default logic or logic programming. It allows the user to create parameterized collections of default theories having similar properties and growing sizes and, consequently, to study the asymptotic performance of nonmonotonic systems under investigation. Each theory generated by the TheoryBase has a unique identifier, which allows for concise descriptions of test cases used in experiments and, thus, facilitates comparative studies. We describe the TheoryBase in this paper and report on our experimental studies of DeReS performance based on test cases generated by the TheoryBase.

Reasoning with incomplete and changing information: The CIN project

Most information systems are faced with incomplete information, even for simple database applications; therefore, they must make plausible conjectures in order to operate in a satisfactory way. A simple example is the closed world assymption, which is used extensively in the database area. Nonmonotonic reasoning (NMR) provides formal methods which support such a behavior; in default logic, for example, the plausible conjectures are based on “rules of thumb.” Information is subject to change due to the inherent uncertainty of information or because the environment is volatile and dynamic. Current nonmonotonic reasoning systems neglect the problems raised by change. Belief revision (BR) is the research area that has developed techniques capable of dealing with changing information. This paper presents the motivations, the design decisions, and the current state of the CIN Project ( Changing Information), whose aim is to provide an integrated toolkit of nonmonotonic reasoning and belief revision methods. The reason we design an open system is our contention that finding the right method for NMR and BR is an elusive dream, and that we should instead seek to determine the most appropriate method for the specific problem at hand.

Process and production planning for circuit board assembly

Process planning output can be post-processed into criteria for job scheduling decisions in printed circuit board assembly using surface-mount technology (SMT). Artificial intelligence-based techniques used in computerized planning and scheduling systems in other industries can be extended to printed circuit board operations. These techniques include blackboard architectures, object-oriented programming systems, and nonmonotonic reasoning systems. These techniques were used to demonstrate a unique architecture of blackboard systems that communicate via object-oriented messages to arrive at a shop-floor process plan and production schedule. The methodology was specialized to the assembly of printed circuit boards using surface-mounted components in a high-variety/low-volume product mix. The assembly facility was represented as a hierarchical object of product, process, and organizational knowledge. The system of working heuristics was integrated within a prototype environment with the practitioners that assisted in its development. The end result is a good working methodology for system development, implementation, and maintenance by knowledge worker involvement.

ON THE COMPLETION OF PRIORITY ORDERINGS IN NONMONOTONIC REASONING SYSTEMS

We discuss the structure of nonmonotonic reasoning. We suggest that an important aspect of nonmonotonic reasoning systems is the ordering relationship (preference structure) on the propositions in the knowledge. We suggest that this ordering relationship must be a weak order, a complete and transitive relationship. We provide a comprehensive discussion of some central issues in preference theory. In most real applications of nonmonotonic knowledge bases the ordering relationship available is often not complete. We suggest a mechanism for completing these relationships. The basic imperative used in providing this completion is to do it in such a manner as to add as few unjustified inferences as necessary. To formally accomplish this task we introduce a measure of buoyancy associated with a weak order and suggest that the preferred completion is the one with the maximal buoyancy.

A heuristic in rules-based systems

The aim of this paper is to present a probability measure associated to the set of complex formulas of P (set of single logic propositions), CP. This probability measure will be used in the construction of heuristic algorithms in artificial intelligence problems. Throughout this work it will be seen how knowledge base systems (KBS) act when they receive incomplete information. Calculation of KBS inconsistent entries will also be assessed. A nonmonotonic reasoning system is involved in the approximate reasoning system studied in the present project.

Linear resolution for consequence finding

In this paper, we re-evaluate the consequence finding problem within first-order logic. Firstly, consequence finding is generalized to the problem in which only interesting clauses having a certain property (called characteristic clauses) should be found. The use of characteristic clauses enables characterization of various reasoning problems of interest to AI, including abduction, nonmonotonic reasoning, prime implicates and truth maintenance systems. Secondly, an extension of the Model Elimination theorem proving procedure (SOL-resolution) is presented, providing an effective mechanism complete for finding the characteristic clauses. An important feature of SOL-resolution is that it constructs such a subset of consequences directly without testing each generated clause for the required property. We also discuss efficient but incomplete variations of SOL-resolution and their properties, which address finding the most specific and the least specific abductive explanations.