This paper describes a uniform formalization of much of the current work in AI on inference systems. We show that many of these systems, including first-order theorem provers, assumption-based truth maintenance systems (atms's) and unimplemented formal systems such as default logic or circumscription can be subsumed under a single general framework. We begin by defining this framework, which is based on a mathematical structure known as a bilattice. We present a formal definition of inference using this structure, and show that this definition generalizes work involving atms's and some simple nonmonotonic logics. Following the theoretical description, we describe a constructive approach to inference in this setting; the resulting generalization of both conventional inference and atms's is achieved without incurring any substantial computational overhead. We show that our approach can also be used to implement a default reasoner, and discuss a combination of default and atms methods th...

This paper introduces the concept and the general theory of multi-valued model checking, and describes a multi-valued symbolic model-checker \Chi Chek. Multi-valued

We introduce a new approach to dealing with the well-known logical omniscience problem in epistemic logic. Instead of taking possible worlds where each world is a model of classical propositional logic, we take possible worlds which are models of a nonstandard propositional logic we call NPL, which is somewhat related to relevance logic. This approach gives new insights into the logic of implicit and explicit'belief considered by Levesque and Lakemeyer. In particular, we show that in a precise sense agents in the structures considered by Levesque and Lakemeyer are perfect reasoners in NPL. 1

The paper considers the fundamental notions of many- valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon actual theoretical considerations about infinite valued logics. Key words: mathematical fuzzy logic, algebraic semantics, continuous t-norms, left-continuous t-norms, Pavelka-style fuzzy logic, fuzzy set theory, non-monotonic fuzzy reasoning 1 Basic ideas 1.1 From classical to many-valued logic Logical systems in general are based on some formalized language which includes a notion of well formed formula, and then are determined either semantically or syntactically. That a logical system is semantically determined means that one has a notion of interpretation or model 1 in the sense that w.r.t. each such interpretation every well formed formula has some (truth) value or represents a function into

Deduction-based software component retrieval uses preand postconditions as indexes and search keys and an automated theorem prover (ATP) to check whether a component matches. This idea is very simple but the vast number of arising proof tasks makes a practical implementation very hard. We thus pass the components through a chain of filters of increasing deductive power. In this chain, rejection filters based on signature matching and model checking techniques are used to rule out non-matches as early as possible and to prevent the subsequent ATP from "drowning." Hence, intermediate results of reasonable precision are available at (almost) any time of the retrieval process. The final ATP step then works as a confirmation filter to lift the precision of the answer set. We implemented a chain which runs fully automatically and uses MACE for model checking and the automated prover SETHEO as confirmation filter. We evaluated the system over a medium-sized collection of components. The resul...

. HySpirit is a retrieval engine for hypermedia retrieval integrating concepts from information retrieval (IR) and deductive databases. The logical view on IR models retrieval as uncertain inference, for which we use probabilistic reasoning. Since the expressiveness of classical IR models is not sufficient for hypermedia retrieval, HySpirit is based on a probabilistic version of Datalog. In hypermedia retrieval, different nodes may contain contradictory information; thus, we introduce probabilistic four-valued Datalog. In order to support fact queries as well as contentbased retrieval, HySpirit is based on an open world assumption, but allows for predicate-specific closed world assumptions. For performing efficient retrieval on large databases, our system provides access to external data. We demonstrate the application of HySpirit by giving examples for retrieval on images, structured documents and large databases. 1 Introduction Due to the advances in hardware, processing of multimed...

In this paper we present a framework of reasoning with inconsistent ontologies, in which pre-defined selection functions are used to deal with concept relevance. We examine how the notion of ”concept relevance ” can be used for reasoning with inconsistent ontologies. We have implemented a prototype called PION (Processing Inconsistent ONtologies), which is based on a syntactic relevance-based selection function. In this paper, we also report the experiments with PION. 1

Classical logic cannot be used to effectively reason about systems with uncertainty (lack of essential information) or inconsistency (contradictory information often occurring when information is gathered from multiple sources). In this paper we propose the use of quasi-boolean multi-valued logics for reasoning about such systems. We also give semantics to a multi-valued extension of CTL, describe an implementation of a symbolic multi-valued CTL model-checker called chek, and analyze its correctness and running time.

this paper, however, that the techniques of nonmonotonic logic may provide a better theoretical framework---at least for the formalization of commonsense normative reasoning---than the usual modal treatment. After reviewing some standard approaches to deontic logic, I focus on two areas in which nonmonotonic techniques promise improved understanding: reasoning in the presence of conflicting obligations, and reasoning with conditional obligations. 2 Modal techniques in deontic logic

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