Showing papers by "Giuseppe De Giacomo published in 1996"

TBox and ABox reasoning in expressive description logics

Abstract: A Description Logic (DL) system is characterized by four fundamental aspects: the set of constructs used in concept and role expressions, the kind of assertions allowed in the TBox (assertions on concepts) and the ABox (assertions on individuals), and the inference mechanisms for reasoning on both the TBox and the ABox. Most of the research done in the last decade made several simplifying assumptions on the above aspects. However, the recent interest in DLs exhibited in many application areas (databases, software engineering, intelligent access to the network, planning, etc.) calls for investigating DL systems with full capabilities. The work presented in this paper represents a step in this direction. We present a sound, complete, and terminating (in worst-case EXPTIME) inference procedure that solves the problem of reasoning in a DL system with the following characteristics: it comes equipped with a very expressive language, it allows the most general form of TBox assertions, and it takes into account instance assertions on both concepts and roles in the ABox.

Exptime Tableaux for ALC.

Abstract: Abstract The last years have seen two major advances in Knowledge Representation and Reasoning. First, many interesting problems (ranging from Semi-structured Data to Linguistics) were shown to be expressible in logics whose main deductive problems are EXPtime -complete. Second, experiments in automated reasoning have substantially broadened the meaning of “practical tractability”. Instances of realistic size for Pspace -complete problems are now within reach for implemented systems. Still, there is a gap between the reasoning services needed by the expressive logics mentioned above and those provided by the current systems. Indeed, the algorithms based on tree-automata, which are used to prove EXPtime -completeness, require exponential time and space even in simple cases. On the other hand, current algorithms based on tableau methods can take advantage of such cases, but require double exponential time in the worst case. We propose a tableau calculus for the description logic ALC for checking the satisfiability of a concept with respect to a TBox with general axioms, and transform it into the first simple tableau-based decision procedure working in single exponential time. To guarantee the ease of implementation, we also discuss the effects that optimizations (propositional backjumping, simplification, semantic branching, etc.) might have on our complexity result, and introduce a few optimizations ourselves.

Tableaux and Algorithms for Propositional Dynamic Logic with Converse

Abstract: This paper presents a prefixed tableaux calculus for Propositional Dynamic Logic with Converse based on a combination of different techniques such as prefixed tableaux for modal logics and model checkers for mu-calculus. We prove the correctness and completeness of the calculus and illustrate its features. We also discuss the transformation of the tableaux method (naively NEXPTIME) into an EXPTIME algorithm.

Eliminating "converse" from converse PDL

Abstract: In this paper we show that it is possible to eliminate the “converse” operator from the propositional dynamic logic CPDL (Converse PDL), without compromising the soundness and completeness of inference for it. Specifically we present an encoding of CPDL formulae into PDL that eliminates the converse programs from a CPDL formula, but adds enough information so as not to destroy its original meaning with respect to satisfiability, validity, and logical implication. Notably, the resulting PDL formula is polynomially related to the original one. This fact allows one to build inference procedures for CPDL, by encoding CPDL formulae into PDL, and then running an inference procedure for PDL.

Moving a robot: the KR&R approach at work

Abstract: The paper describes an approach to reason ing about actions and plan generation within the framework of description logics From an epistemological viewpoint our approach is based on the formalization of actions given by dynamic logics but we exploit their corre spondence with description logics to turn the formalization into an actual implementation In particular we are able to carefully weaken the logical inference process thus making the reasoning of the robot computationally fea sible From a practical viewpoint we use a general purpose knowledge representation en vironment based on description logics and its associated reasoning tools in order to plan the actions of the mobile robot Tino starting from the knowledge about the envi ronment and the action speci cation The robot s reactive capabilities allow it to exe cute such plans in the real world

Intensional query answering by partial evaluation

Abstract: Intensional query answering aims at providing a response to a query addressed to a knowledge base by making use of the intensional knowledge as opposed to extensional Such a response is an abstract description of the conventional answer that can be of interest in many situations, for example it may increase the cooperativeness of the system, or it may replace the conventional answer in case access to the extensional part of the knowledge base is costly as for Mobile Systems In this paper we present a general framework to generate intensional answers in knowledge bases adhering to the logic programming paradigm Such a framework is based on a program transformation technique, namely Partial Evaluation, and allows for generating complete and procedurally complete (wrt SLDNF-resolution) sets of intensional answers, treating both recursion and negation conveniently

Reasoning about nondeterministic and concurrent actions: a process algebra approach

Abstract: In this paper, we study reasoning about actions following a model checking approach in contrast to the usual validity checking one. Specifically, we model a dynamic system as a transition graph which represents all the possible system evolutions in terms of state changes caused by actions. Such a transition graph is defined by means of a suitable process algebra associated with an explicit global store. To reason about system properties we introduce an extension of modal µ-calculus. This setting, although directly applicable only when complete information on the system is available, has several interesting features for reasoning about actions. On one hand, it inherits from the vast literature on process algebras tools for dealing with complex systems, treating suitably important aspects like parallelism, communications, interruptions, coordinations among agents. On the other hand, reasoning by model checking is typically much easier than more general logical services such as validity checking.

TBox and ABox Reasoning in Expressive Description Logics.

Abstract: A Description Logic (DL) system is characterized by four fundamental aspects: the set of constructs used in concept and role expressions, the kind of assertions allowed in the TBox (assertions on concepts) and the ABox (assertions on individuals), and the inference mechanisms for reasoning on both the TBox and the ABox. Most of the research done in the last decade made several simplifying assumptions on the above aspects. However, the recent interest in DLs exhibited in many application areas (databases, software engineering, intelligent access to the network, planning, etc.) calls for investigating DL systems with full capabilities. The work presented in this paper represents a step in this direction. We present a sound, complete, and terminating (in worst-case EXPTIME) inference procedure that solves the problem of reasoning in a DL system with the following characteristics: it comes equipped with a very expressive language, it allows the most general form of TBox assertions, and it takes into account instance assertions on both concepts and roles in the ABox.

Moving a robot starting from a theory of actions

Abstract: The paper describes an approach to reasoning about actions and planning that starting from a logical formalization arrives at the realization of an actual agent, the mobile robot "Tino". The reasoning tools allow the robot to derive plans from the knowledge about the environment and the action specification, while its reactive capabilities allow it to execute its plans in the real world. The formalization is based on the propositional dynamic logics framework, but exploits the correspondence that exists between propositional dynamic logics and description logics, to carefully weaken the logical inference process in order to keep the reasoning tools of the robot both effective and efficient. Such reasoning tools are then implemented by making use of a general knowledge representation system based on description logics, namely the system CLASSIC.

Representing SGML Documents in Description Logics.

Abstract: Recent proposals to improve the quality of interaction with the World Wide Web suggest considering the Web as a huge semistructured database, so that retrieving information can be supported by the task of database querying. Under this view, it is important to represent the form of both the network, and the documents placed in the nodes of the network. However, the current proposals do not pay sufficient attention to represent document structures and reasoning about them. In this paper, we address these problems by providing a framework where Document Type Definitions (DTDs) expressed the Standard Generalized Markup Language are formalized in an expressive Description Logic equipped with sound and complete inference algorithms. We provide a method for verifying structural equivalence of DTDs, which works in worst case deterministic exponential time, in contrast to the known algorithms for this problem which are double exponential. We also deal with parametric versions of structural equivalence, and investigate other forms of reasoning on DTDs. The reasoning services studied in this paper can be seen as the fundamental building blocks for devising more complex inference systems supporting the task of querying the World Wide Web.

Knowledge-based access to the Web

Abstract: The idea that knowledge can be used for finding information through the network has been developed in several directions. Most proposals use knowledge representation techniques in order to model the information stored in the network (Web) nodes, and then access the information through ad hoc procedures. On the other hand, the information that we access through the browsers is organized into structures that are coded in terms of the content of each page and of its relationship to other pages. Such structures typically guide humans in the search for a specific information. Our idea is to use this kind of structural information to build knowledge based tools for the access to the network. More specifically, we are working at a system which acquires information on a subject matter by extracting from the pages an explicit representation of the underlying structure, and use it to answer user’s requests by directly pointing to the page containing the desired answer. Therefore, our envisioned system, is meant to act as an intelligent browser, which allows the user to reach the requested information by automatically performing navigation steps. In this abstract we first present an architecture for a knowledge-based approach to the construction of the system with the above described goals. The system is based on a formalization of Web pages in terms of description logics. We then illustrate such a formalization, and discuss the reasoning features that are required in our framework.