Nonmonotonic reasoning,nonmonotonic logics and reasoning about change

In this paper we introduce nonmonotonic reasoning and the attempts at formalizing it using nonmonotonic logics. We examine and compare the best known of these. Despite the difference in motivation and technical construction there are strong similarities between these logics which are confirmed when they are finally shown to have a common basis. Finally we consider using nonmonotonic logics to represent reasoning about change.     

Local closed world reasoning with description logics under the well-founded semantics

An important question for the upcoming Semantic Web is how to best combine open world ontology languages, such as the OWL-based ones, with closed world rule-based languages. One of the most mature proposals for this combination is known as hybrid MKNF knowledge bases (Motik and Rosati, 2010 [52]), and it is based on an adaptation of the Stable Model Semantics to knowledge bases consisting of ontology axioms and rules. In this paper we propose a well-founded semantics for nondisjunctive hybrid MKNF knowledge bases that promises to provide better efficiency of reasoning, and that is compatible with both the OWL-based semantics and the traditional Well-Founded Semantics for logic programs. Moreover, our proposal allows for the detection of inconsistencies, possibly occurring in tightly integrated ontology axioms and rules, with only little additional effort. We also identify tractable fragments of the resulting language.     

Argument construction and reinstatement in logics for defeasible reasoning

This paper points out some problems with two recent logical systems – one due to Prakken and Sartor, the other due to Kowalski and Toni – designedfor the representation of defeasible arguments in general, but with a specialemphasis on legal reasoning.     

The effect of reasoning logics on real-time decision making

The advent of satellite tracking and communications technology has motivated organizations to investigate centralized real-time support for remote and mobile units and operations. Transportation companies have begun to use satellite tracking systems, production and energy plants are employing intelligent monitoring systems, and on-site emergency managers are being supported by headquarters in their assessment and decision making process. Although different reasoning logics have been proposed for real-time decision making, little attention has been given to the comparative assessment of these approaches. This paper presents empirical evidence on the impact of alternative reasoning logics on individual decision making in real-time. Following the definition of the decision tasks for hazardous operations, commonly used reasoning logics are discussed. Then, results of an empirical comparison of different reasoning approaches are presented. The data were gathered during an experiment with experienced operators. The conclusions of this research are that the selection of the appropriate reasoning logic in support of real-time decision making is crucial     

Quantified epistemic logics for reasoning about knowledge in multi-agent systems

We introduce quantified interpreted systems, a semantics to reason about knowledge in multi-agent systems in a first-order setting. Quantified interpreted systems may be used to interpret a variety of first-order modal epistemic languages with global and local terms, quantifiers, and individual and distributed knowledge operators for the agents in the system. We define first-order modal axiomatisations for different settings, and show that they are sound and complete with respect to the corresponding semantical classes.The expressibility potential of the formalism is explored by analysing two MAS scenarios: an infinite version of the muddy children problem, a typical epistemic puzzle, and a version of the battlefield game. Furthermore, we apply the theoretical results here presented to the analysis of message passing systems [R. Fagin, J. Halpern, Y. Moses, M. Vardi, Reasoning about Knowledge, MIT Press, 1995; L. Lamport, Time, clocks, and the ordering of events in a distributed system, Communication of the ACM 21 (7) (1978) 558–565], and compare the results obtained to their propositional counterparts. By doing so we find that key known meta-theorems of the propositional case can be expressed as validities on the corresponding class of quantified interpreted systems.     

Decidable fragments of many-sorted logic

Many natural specifications use types. We investigate the decidability of fragments of many-sorted first-order logic. We identified some decidable fragments and illustrated their usefulness by formalizing specifications considered in the literature. Often the intended interpretations of specifications are finite. We prove that the formulas in these fragments are valid iff they are valid over the finite structures. We extend these results to logics that allow a restricted form of transitive closure.     

On vague logics and approximate reasoning based on vague linear transformation

As a generalisation of the Fuzzy Sets theory, vague set has been proven to be a new tool in dealing with vague information. In this article, we attempt to generalise the techniques of fuzzy inference in a vague environment. In the rule-based inference system, an ‘if?…?then?…’ rule can be considered a transformer that implements information conversion between input–output ends. Thus, according to the logical operations of vague linguistic variables, we introduce an approach to approximation inference based on linear transformation, and then discuss the representations for several inference structures regarding single rule, multi-rules and compound rules. By defining the inclusion function of vague sets, we provide vague rough approximation based on measure of inclusion, and then present a method on rule creation from a decision system. A case study on the prediction for welding deformation is used to illustrate the effectiveness of the proposed approaches.     

Inherited extension of many-sorted theories

A formalism is proposed treating many-sorted theories as an extension of first-order theories. The formalism is defined in the mathematical specification language of the SINAL verification programming system.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 165–169, September–October, 1992.     

Alternative logics for approximate reasoning in expert systems: a comparative study

In this paper we report the results of an empirical study to compare eleven alternative logics for approximate reasoning in expert systems. The several “compositional inference” axiom systems (described below) were used in an expert knowledge-based system. The quality of the system outputs—fuzzy linguistic phrases—were compared in terms of correctness and precision (non-vagueness).In the first section of the paper we discuss fuzzy expert systems. The second section provides a brief review of logic systems and their relation to approximate reasoning. Section three contains the experimental design, and section four supplies the results of the experiment. Finally, a summary is given.     

Sequent calculi for skeptical reasoning in predicate default logic and other nonmonotonic logics

Sequent calculi for skeptical consequence in predicate default logic, predicate stable model logic programming, and infinite autoepistemic theories are presented and proved sound and complete. While skeptical consequence is decidable in the finite propositional case of all three formalisms, the move to predicate or infinite theories increases the complexity of skeptical reasoning to being ₁¹-complete. This implies the need for sequent rules with countably many premises, and such rules are employed. AMS subject classification 03B42, 68N17, 68T27This paper grew directly out of the authors dissertation, written under the direction of Anil Nerode.     

带函数的描述逻辑

描述逻辑是包含了概念、角色以及概念和角色构造子的一阶逻辑的子逻辑,具有表达能力强且推理可判定的特征。但现有描述逻辑无法表示概念和角色上的函数,因此在图书馆的概念模型中,有一些问题便不能表示,如图书的本数、借书的条目数等。在现有描述逻辑基础上引入函数来解决这个问题。首先分析现有描述逻辑在图书馆的概念模型中不能表示的一些问题并提出解决方法,然后给出带函数的描述逻辑的语法和形式语义,最后用带函数的描述逻辑形式化表示图书馆概念模型中的一些实际问题。     

Presenting functors on many-sorted varieties and applications

This paper studies several applications of the notion of a presentation of a functor by operations and equations. We show that the technically straightforward generalisation of this notion from the one-sorted to the many-sorted case has several interesting consequences. First, it can be applied to give equational logic for the binding algebras modelling abstract syntax. Second, it provides a categorical approach to algebraic semantics of first-order logic. Third, this notion links the uniform treatment of logics for coalgebras of an arbitrary type T with concrete syntax and proof systems. Analysing the many-sorted case is essential for modular completeness proofs of coalgebraic logics.     

Boolean logics with relations

The language of our Boolean logic with relations is a Boolean language to which relation symbols have been added. Such a language turns out to be a useful tool for describing relational structures and algebraic structures. This paper introduces the concepts of Kripke semantics and Boolean semantics for our language. It addresses the traditional issues of decidability/complexity and axiomatization/completeness but it also defines the new concepts of weak canonicity and strong canonicity.     

Combining knowledge with many-valued logics

We compare EER and OO data models from the point of view of design quality. Quality is measured in terms of (a) correctness of the conceptual schemas being designed, (b) time to complete the design task, and (c) designers' preferences of the models. Result of an experimental comparison of the two models reveal that the EER model surpasses the OO model for designing unary and ternary relationships, it takes less time to design EER schemas, and the EER model is preferred by designers. We conclude that even if the objective is to implement an OO database schema, the recommended procedure is to: (1) create an EER conceptual scheme, (2) map it to an OO schema, and augment the target schema with behavioral constructs that are unique to the OO approach.