A finite basis for the set of EL-implications holding in a finite model

Formal Concept Analysis (FCA) can be used to analyze data given in the form of a formal context. In particular, FCA provides efficient algorithms for computing a minimal basis of the implications holding in the context. In this paper, we extend classical FCA by considering data that are represented by relational structures rather than formal contexts, and by replacing atomic attributes by complex formulae defined in some logic. After generalizing some of the FCA theory to this more general form of contexts, we instantiate the general framework with attributes defined in the Description Logic (DL) EL, and with relational structures over a signature of unary and binary predicates, i.e., models for EL. In this setting, an implication corresponds to a so-called general concept inclusion axiom (GCI) in EL. The main technical result of this report is that, in EL, for any finite model there is a finite set of implications (GCIs) holding in this model from which all implications (GCIs) holding in the model follow

Exploring finite models in the Description Logic ELgfp

In a previous ICFCA paper we have shown that, in the Description Logics EL and ELgfp, the set of general concept inclusions holding in a finite model always has a finite basis. In this paper, we address the problem of how to compute this basis efficiently, by adapting methods from formal concept analysis

Algorithms for solving dynamic models with occasionally binding constraints

A description and comparison of several algorithms for approximating the solution to a model in which inequality constraints occasionally bind. Their performance is evaluated using various parameterizations of the one-sector growth model with irreversible investment.

A MODEL OF GRAIN STORAGE AND HEDGING BY FARMERS

The model analyzed represents circumstances as faced by a grain farmer when his harvest is known and he is making storage and hedging decisions. The scope of the analysis is limited in several respects. A one-period model is employed; only a limited number of options are recognized; and interrelations between the grain enterprise and other economic activities of the decision maker are neglected.Marketing,

PDDL2.1: An extension of PDDL for expressing temporal planning domains

In recent years research in the planning community has moved increasingly towards application of planners to realistic problems involving both time and many types of resources. For example, interest in planning demonstrated by the space research community has inspired work in observation scheduling, planetary rover ex ploration and spacecraft control domains. Other temporal and resource-intensive domains including logistics planning, plant control and manufacturing have also helped to focus the community on the modelling and reasoning issues that must be confronted to make planning technology meet the challenges of application. The International Planning Competitions have acted as an important motivating force behind the progress that has been made in planning since 1998. The third competition (held in 2002) set the planning community the challenge of handling time and numeric resources. This necessitated the development of a modelling language capable of expressing temporal and numeric properties of planning domains. In this paper we describe the language, PDDL2.1, that was used in the competition. We describe the syntax of the language, its formal semantics and the validation of concurrent plans. We observe that PDDL2.1 has considerable modelling power --- exceeding the capabilities of current planning technology --- and presents a number of important challenges to the research community