Witold Lukaszewicz

Knowledge Representation Techniques. : a rough set approach

The basis for the material in this book centers around a long term research project with autonomous unmanned aerial vehicle systems. One of the main research topics in the project is knowledge repr ...

Tolerance Spaces and Approximative Representational Structures

In traditional approaches to knowledge representation, notions such as tolerance measures on data, distance between objects or individuals, and similarity measures between primitive and complex data structures are rarely considered. There is often a need to use tolerance and similarity measures in processes of data and knowledge abstraction because many complex systems which have knowledge representation components such as robots or software agents receive and process data which is incomplete, noisy, approximative and uncertain. This paper presents a framework for recursively constructing arbitrarily complex knowledge structures which may be compared for similarity, distance and approximativeness. It integrates nicely with more traditional knowledge representation techniques and attempts to bridge a gap between approximate and crisp knowledge representation. It can be viewed in part as a generalization of approximate reasoning techniques used in rough set theory. The strategy that will be used is to define tolerance and distance measures on the value sets associated with attributes or primitive data domains associated with particular applications. These tolerance and distance measures will be induced through the different levels of data and knowledge abstraction in complex representational structures. Once the tolerance and similarity measures are in place, an important structuring generalization can be made where the idea of a tolerance space is introduced. Use of these ideas is exemplified using two application domains related to sensor modeling and communication between agents.

Efficient Reasoning Using the Local Closed-World Assumption

We present a sound and complete, tractable inference method for reasoning with localized closed world assumptions (LCWAs) which can be used in applications where a reasoning or planning agent can not assume complete information about planning or reasoning states. This Open World Assumption is generally necessary in most realistic robotics applications. The inference procedure subsumes that described in Etzioni et al [9], and others. In addition, it provides a great deal more expressivity, permitting limited use of negation and disjunction in the representation of LCWAs, while still retaining tractability. The approach is based on the use of circumscription and quantifier elimination techniques and inference is viewed as querying a deductive database. Both the preprocessing of the database using circumscription and quantifier elimination, and the inference method itself, have polynomial time and space complexity.

Cicumscribing Features and Fluents

Sandewall has recently proposed a systematic approach to the representation of knowledge about dynamical systems that includes a general framework in which to assess the range of applicability of existing and new logics for action and change and to provide a means of studying whether and in what sense the logics of action and change are relevant for intelligent agents. As part of the framework, a number of logics of preferential entailment are introduced and assessed for particular classes of action scenario descriptions. This paper provides syntactic characterizations of several of these relations of preferential entailment in terms of standard FOPC and circumscription axioms. The intent is to simplify the process of comparison with existing formalisms which use more traditional techniques and to provide a basis for studying the feasibility of compiling particular classes of problems into logic programs.

Declarative PTIME queries for relational databases using quantifier elimination

In this paper, we consider the problem of expressing and computing queries on relational deductive databases in a purely declarative query language, called SHQL (Semi-Horn Query Language). Assuming the relational databases in question are ordered, we show that all SHQL queries are computable in PTIME (polynomial time) and the whole class of PTIME queries is expressible in SHQL. Although similar results have been proven for fixpoint languages and extensions to datalog, the claim is that SHQL has the advantage of being purely declarative, where the negation operator is interpreted as classical negation, mixed quantifiers may be used and a query is simply a restricted first-order theory not limited by the rule-based syntactic restrictions associated with logic programs in general. We describe the PTIME algorithm used to compute queries in SHQL which is based in part on quantifier elimination techniques and also consider extending the method to incomplete relational databases using intuitions related to circumscription techniques.

Approximation Transducers and Trees: A Technique for Combining Rough and Crisp Knowledge

Soft computing comprises various paradigms dedicated to approximately solving real-world problems, e.g., in decision making, classification or learning; among these paradigms are fuzzy sets, rough ...

Explaining Explanation Closure

Recently, Haas, Schubert, and Reiter, have developed an alternative approach to the frame problem which is based on the idea of using explanation closure axioms. The claim is that there is a monotonic solution for characterizing nonchange in serial worlds with fully specified actions, where one can have both a succinct representation of frame axioms and an effective proof theory for the characterization. In the paper, we propose a circumscriptive version of explanation closure, PMON, that has an effective proof theory and works for both context dependent and nondeterministic actions. The approach retains representational succinctness and a large degree of elaboration tolerance, since the process of generating closure axioms is fully automated and is of no concern to the knowledge engineer. In addition, we argue that the monotonic/nonmonotonic dichotomy proposed by others is not as sharp as previously claimed and is not fully justified.

Reasoning about Action and Change: Actions with Abnormal Effects

Most of the research devoted to reasoning about action and change has been based on the assumption that each action behaves in a fixed way. More specifically, to each action A there is assigned a unique specification S describing the effects of A in terms of a state in which A is performed.1 For instance, the well-known action shoot is usually defined as making a gun unloaded and a turkey dead, provided that a gun was loaded. Accordingly, each time the action is executed in a state in which the gun is loaded, it is taken for granted that the turkey is made dead.

Circumscribing Features and Fluents: A Fluent Logic for Reasoning about Action and Change

Sandewall has recently proposed a systematic approach to the representation of knowledge about dynamical systems that includes a general framework in which to assess the range of applicability of existing and new logics for action and change. As part of the framework, several logics of preferential entailment are introduced and assessed for particular classes of action scenario descriptions. The intent of this paper is to provide syntactic characterizations of several of these relations of preferential entailment in terms of circumscription with a standard base logic consisting of FOPC with temporal terms and discrete time. It turns out that occluded circumscription, which covers the broadest class of action scenarios, and includes many of the most problematic scenarios studied in the literature, is one of the most straightforward logics considered. The class includes scenarios with non-deterministic actions, actions with duration, partial specification of any state including the first, and incomplete specification of the timing and order of actions.

Program Verification Techniques as a Tool for Reasoning about Action and Change

We apply Dijkstras semantics for programming languages to formalize reasoning about action and change. The basic idea is to view an action A as a transformation which to each formula β assigns a formula α, with the intention that α represents the set of all initial states such that execution of A begun in any one of them is guaranteed to terminate in a state satisfying β.