Fundamenta Informaticae - Volume 57, issue 2-4

Authors: Doherty, Patrick | Skowron, Andrzej | Łukaszewicz, Witold | Szałas, Andrzej

Article Type: Other

Citation: Fundamenta Informaticae, vol. 57, no. 2-4, pp. i-iii, 2003

Authors: Dubois, Didier | Konieczny, Sébastien | Prade, Henri

Article Type: Research Article

Abstract: Possibilistic logic and quasi-classical logic are two logics that were developed in artificial intelligence for coping with inconsistency in different ways, yet preserving the main features of classical logic. This paper presents a new logic, called quasi-possibilistic logic, that encompasses possibilistic logic and quasi-classical logic, and preserves the merits of both logics. Indeed, it can handle plain conflicts taking place at the same level of certainty (as in quasi-classical logic), and take advantage of …the stratification of the knowledge base into certainty layers for introducing gradedness in conflict analysis (as in possibilistic logic). When querying knowledge bases, it may be of interest to evaluate the extent to which the relevant available information is precise and consistent. The paper review measures of (im)precision and inconsistency/conflict existing in possibilistic logic and quasi-classical logic, and proposes generalized measures in the unified framework. Show more

Keywords: possibilistic logic, possibilistic logic, measures of information, inconsistency, uncertainty

Citation: Fundamenta Informaticae, vol. 57, no. 2-4, pp. 101-125, 2003

Authors: Godo, Lluís | Hájek, Petr | Esteva, Francesc

Article Type: Research Article

Abstract: In this paper we introduce a new logical approach to reason explicitly about Dempster-Shafer belief functions. We adopt the following view: one just starts with Boolean formulas φ and a belief function on them; the belief of φ is taken to be the truth degree of the (fuzzy) proposition B φ standing for φ is believed. For our complete axiomatization (Hylbert-style) we use one of the possible definitions of belief, namely as probability of (modal) necessity. …This enables us to define a logical system combining the modal logic S5 with an already proposed fuzzy logic approach to reason about probabilities. In particular, our fuzzy logic is the logic ŁΠ½ which puts Lukasiewicz and Product fuzzy logics together. Show more

Keywords: fuzzy logic, Dempster–Shafer belief functions, probability logic, probability logic, completeness

Citation: Fundamenta Informaticae, vol. 57, no. 2-4, pp. 127-146, 2003

Authors: Doherty, Patrick | Grabowski, Michał | Łukaszewicz, Witold | Szałas, Andrzej

Article Type: Research Article

Abstract: Currently, there is a great deal of interest in developing tools for the generation and use of ontologies on the WWW. These knowledge structures are considered essential to the success of the semantic web, the next phase in the evolution of the WWW. Much recent work with ontologies assumes that the concepts used as building blocks are crisp as opposed to approximate. It is a premise of this paper that approximate concepts and ontologies will become …increasingly more important as the semantic web becomes a reality. We propose a framework for specifying, generating and using approximate ontologies. More specifically, (1) a formal framework for defining approximate concepts, ontologies and operations on approximate concepts and ontologies is presented. The framework is based on intuitions from rough set theory; (2) algorithms for automatically generating approximate ontologies from traditional crisp ontologies or from large data sets together with additional knowledge are presented. The knowledge will generally be related to similarity measurements between individual objects in the data sets, or constraints of a logical nature which rule out particular constellations of concepts and dependencies in generated ontologies. The techniques for generating approximate ontologies are parameterizable. The paper provides specific instantiations and examples. Show more

Keywords: approximate concept, approximate reasoning, approximate space, category, concept, approximate concept, approximate ontology, ontology, tolerance space, tolerance-based ontology

Citation: Fundamenta Informaticae, vol. 57, no. 2-4, pp. 147-165, 2003

Authors: Grosskreutz, Henrik | Lakemeyer, Gerhard

Article Type: Research Article

Abstract: Uncertainty seems to be inherent in most robotic applications. This is because a robot's sensors and actuators are in general imprecise and prone to error. The logic-based action language GOLOG was introduced for the purpose of high-level robot control, but its usefulness was limited because it did not address uncertainty. bIn this paper we show how this deficiency can be overcome.

Keywords: knowledge representation, uncertainty, cognitive robotics

Citation: Fundamenta Informaticae, vol. 57, no. 2-4, pp. 167-192, 2003

Authors: Madalińska-Bugaj, Ewa | Łukaszewicz, Witold

Article Type: Research Article

Abstract: Due to its efficiency, defeasible logic is one of the most interesting non-monotonic formalisms. Unfortunately, the logic has one major limitation: it does not properly deal with cyclic defeasible rules. In this paper, we provide a new variant of defeasible logic, using CAKE method. The resulting formalism is tractable and properly deals with circular defeasible rules.

Keywords:

Citation: Fundamenta Informaticae, vol. 57, no. 2-4, pp. 193-213, 2003

Authors: Vitória, Aida | Damásio, Carlos Viegas | Małuszyński, Jan

Article Type: Research Article

Abstract: This paper presents an expressive language for representing knowledge about vague concepts. It is based on the rough set formalism and it caters for implicit definition of rough relations by combining different regions (e.g. upper approximation, lower approximation, boundary) of other rough relations. The semantics …of the proposed language is obtained by translating it to the language of extended logic programs whose meaning is captured by paraconsistent stable models. A query language is also discussed to retrieve information about the defined rough relations. Motivating examples illustrating the use of the language are described. Show more

Keywords: rough sets, logic programming, stable models, uncertain reasoning, incomplete reasoning

Citation: Fundamenta Informaticae, vol. 57, no. 2-4, pp. 215-246, 2003

Authors: Baader, Franz | Hladik, Jan | Lutz, Carsten | Wolter, Frank

Article Type: Research Article

Abstract: This paper investigates the relationship between automata-and tableau-based inference procedures for description logics. To be more precise, we develop an abstract notion of what a tableau-based algorithm is, and then show, on this abstract level, how tableau-based algorithms can be converted into automata-based algorithms. In particular, this allows us to characterize a large class of tableau-based algorithms that imply an ExpTime upper-bound for reasoning in the description logics for which such an …algorithm exists. Show more

Citation: Fundamenta Informaticae, vol. 57, no. 2-4, pp. 247-279, 2003

Authors: Harrenstein, Paul | van der Hoek, Wiebe | Meyer, John-Jules | Witteveen, Cees

Article Type: Research Article

Abstract: Multi-agent systems comprise entities whose individual decision making behavior may depend on one another's. Game-theory provides apposite concepts to reason in a mathematically precise fashion about such interactive and interdependent situations. This paper concerns a logical analysis of the game-theoretical notions of Nash equilibrium and its subgame perfect variety as they apply to a particular class of extensive games of perfect information. Extensive games are defined as a special type of labelled …graph and we argue that modal languages can be employed in their description. We propose a logic for a multi-modal language and prove its completeness with respect to a class of frames that correspond with a particular class of extensive games. In this multi-modal language (subgame perfect) Nash equilibria can be characterized. Finally, we show how this approach can formally be refined by using Propositional Dynamic Logic (PDL), though we leave completeness as an open question. Show more

Keywords: modal logic, dynamic logic, game theory, nash equilibrium

Citation: Fundamenta Informaticae, vol. 57, no. 2-4, pp. 281-321, 2003

Authors: Herzig, Andreas

Article Type: Research Article

Abstract: We investigate a modal logic of probability with a unary modal operator expressing that a proposition is more probable than its negation. Such an operator is not closed under conjunction, and its modal logic is therefore non-normal. Within this framework we study the relation of probability with other modal concepts: belief and action. We focus on the evolution of belief, and propose an integration of revision. For that framework we give a regression algorithm.

Keywords: modal probability, belief, action, epistemic logic, dynamic logic, successor state axioms, regression

Citation: Fundamenta Informaticae, vol. 57, no. 2-4, pp. 323-344, 2003