1. 


2. 
 Doherty, Patrick, 1957, et al.
(författare)

A reduction result for circumscribed semihorn formulas
 1996

Ingår i: Fundamenta Informaticae.  IOS Press.  01692968. ; 28:3,4, s. 261272

Tidskriftsartikel (refereegranskat)abstract
 Circumscription has been perceived as an elegant mathematical technique for modeling nonmonotonic and commonsense reasoning, but difficult to apply in practice due to the use of secondorder formulas. One proposal for dealing with the computational problems is to identify classes of firstorder formulas whose circumscription can be shown to be equivalent to a firstorder formula. In previous work, we presented an algorithm which reduces certain classes of secondorder circumscription axioms to logically equivalent firstorder formulas. The basis for the algorithm is an elimination lemma due to Ackermann. In this paper, we capitalize on the use of a generalization of Ackermann's Lemma in order to deal with a subclass of universal formulas called semiHorn formulas. Our results subsume previous results by Kolaitis and Papadimitriou regarding a characterization of circumscribed definite logic programs which are firstorder expressible. The method for distinguishing which formulas are reducible is based on a boundedness criterion. The approach we use is to first reduce a circumscribed semiHorn formula to a fixpoint formula which is reducible if the formula is bounded, otherwise not. In addition to a number of other extensions, we also present a fixpoint calculus which is shown to be sound and complete for bounded fixpoint formulas.


3. 
 Doherty, Patrick, 1957, et al.
(författare)

A study in modal embeddings of NML3.
 1996

Ingår i: Partiality, Modality, and Nonmonotonicity, Studies in Logic, Language and Information..  Stanford, California : CSLI Publications.  1575860317  1575860309 ; s. 145168

Bokkapitel (övrigt vetenskapligt)


4. 
 Doherty, Patrick, 1957, et al.
(författare)

Approximate Databases and Query Techniques for Agents with Heterogenous Perceptual Capabilities
 2004

Ingår i: Proceedings of the 7th International Conference on Information Fusion.  Mountain View, CA : ISIF.  917056115X ; s. 175182

Konferensbidrag (refereegranskat)abstract
 In this paper, we propose a framework that provides software and robotic agents with the ability to ask approximate questions to each other in the context of heterogeneous and contextually limited perceptual capabilities. The framework focuses on situations where agents have varying ability to perceive their environments. These limitations on perceptual capability are formalized using the idea of tolerance spaces. It is assumed that each agent has one or more approximate databases where approximate relations are represented using intuitions from rough set theory. It is shown how sensory and other limitations can be taken into account when constructing approximate databases for each respective agent. Complex relations inherit the approximativeness inherent in the sensors and primitive relations used in their definitions. Agents then query these databases and receive answers through the filters of their perceptual limitations as represented by tolerance spaces and approximate queries. The techniques used are all tractable.


5. 
 Doherty, Patrick, 1957, et al.
(författare)

Approximation Transducers and Trees : A Technique for Combining Rough and Crisp Knowledge
 2004

Ingår i: RoughNeural Computing: Techniques for Computing with Words.  Berlin, Heidelberg, New York : Springer.  9783540430599  3540430598 ; s. 189218

Bokkapitel (övrigt vetenskapligt)abstract
 Soft computing comprises various paradigms dedicated to approximately solving realworld problems, e.g., in decision making, classification or learning; among these paradigms are fuzzy sets, rough sets, neural networks, and genetic algorithms.It is well understood now in the soft computing community that hybrid approaches combining various paradigms provide very promising attempts to solving complex problems. Exploiting the potential and strength of both neural networks and rough sets, this book is devoted to roughneurocomputing which is also related to the novel aspect of computing based on information granulation, in particular to computing with words. It provides foundational and methodological issues as well as applications in various fields.


6. 
 Doherty, Patrick, 1957, et al.
(författare)

Approximative Query Techniques for Agents with Heterogeneous Ontologies and Perceptive Capabilities
 2004

Ingår i: Proceedings of the 9th International Conference on the Principles of Knowledge Representation and Reasoning.  Menlo Park, California : AAAI Press.  9781577351993 ; s. 459468

Konferensbidrag (refereegranskat)abstract
 In this paper, we propose a framework that provides software and robotic agents with the ability to ask approximate questions to each other in the context of heterogeneous ontologies and heterogeneous perceptive capabilities.The framework combines the use of logicbased techniques with ideas from approximate reasoning. Initial queries by an agent are transformed into approximate queries using weakest sufficient and strongest necessary conditions on the query and are interpreted as lower and upper approximations on the query. Once the base communication ability is provided, the framework is extended to situations where there is not only a mismatch between agent ontologies, but the agents have varying ability to perceive their environments. This will affect each agent’s ability to ask and interpret results of queries. Limitations on perceptive capability are formalized using the idea of tolerance spaces.


7. 
 Doherty, Patrick, 1957, et al.
(författare)

CAKE : A computer aided knowledge engineering technique.
 2002

Ingår i: Proceedings of the 15th European Conference on Artificial Intelligence,2002.  IOS Press. ; s. 220224

Konferensbidrag (refereegranskat)abstract
 Introduction: Logic engineering often involves the development of modeling tools and inference mechanisms (both standard and nonstandard) which are targeted for use in practical applications where expressiveness in representation must be traded off for efficiency in use. Some representative examples of such applications would be the structuring and querying of knowledge on the semantic web, or the representation and querying of epistemic states used with softbots, robots or smart devices. In these application areas, declarative representations of knowledge enhance the functionality of such systems and also provide a basis for insuring the pragmatic properties of modularity and incremental composition. In addition, the mechanisms developed should be tractable, but at the same time, expressive enough to represent such aspects as default reasoning, or approximate or incomplete representations of the environments in which the entities in question are embedded or used, be they virtual or actual. [...]


8. 
 Doherty, Patrick, 1957, et al.
(författare)

Circumscribing features and fluents
 1994

Ingår i: Temporal Logic : First International Conference, ICTL'94 Bonn, Germany, July 11–14, 1994 Proceedings.  Berlin/New York : Springer Berlin/Heidelberg.  354058241X (Berlin)  038758241X (New York) ; s. 82100

Bokkapitel (övrigt vetenskapligt)abstract
 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.


9. 


10. 
 Doherty, Patrick, 1957, et al.
(författare)

Computing circumscription revisited : A reduction algorithm
 1997

Ingår i: Journal of automated reasoning.  Kluwer Academic Publishers.  01687433. ; 18:3, s. 297336

Tidskriftsartikel (refereegranskat)abstract
 In recent years, a great deal of attention has been devoted to logics of commonsense reasoning. Among the candidates proposed, circumscription has been perceived as an elegant mathematical technique for modeling nonmonotonic reasoning, but difficult to apply in practice. The major reason for this is the secondorder nature of circumscription axioms and the difficulty in finding proper substitutions of predicate expressions for predicate variables. One solution to this problem is to compile, where possible, secondorder formulas into equivalent firstorder formulas. Although some progress has been made using this approach, the results are not as strong as one might desire and they are isolated in nature. In this article, we provide a general method that can be used in an algorithmic manner to reduce certain circumscription axioms to firstorder formulas. The algorithm takes as input an arbitrary secondorder formula and either returns as output an equivalent firstorder formula, or terminates with failure. The class of secondorder formulas, and analogously the class of circumscriptive theories that can be reduced, provably subsumes those covered by existing results. We demonstrate the generality of the algorithm using circumscriptive theories with mixed quantifiers (some involving Skolemization), variable constants, nonseparated formulas, and formulas with nary predicate variables. In addition, we analyze the strength of the algorithm, compare it with existing approaches, and provide formal subsumption results.

