Philippe Balbiani

Axiomatization of Logics Based on Kripke Models with Relative Accessibility Relations

This paper presents a systematic study of the logics based on Kripke models with relative accessibility relations as well as a general method for proving their completeness. The Kripke models with relative accessibility relations come out in the context of the analysis of indiscernability in the information systems.

Global and Local Graph Modifiers

We define two modal logics that allow to reason about modifications of graphs. Both have a universal modal operator. The first one only involves global modifications (of some state label, or of some edge label) everywhere in the graph. The second one also allows for modifications that are local to states. The global version generalizes logics of public announcements and public assignments, as well as a logic of preference modification introduced by van Benthem et Liu. By means of reduction axioms we show that it is just as expressive as the underlying logic without global modifiers. We then show that adding local modifiers dramatically increases the power of the logic: the logic of global and local modifiers is undecidable. We finally study its relation with hybrid logic with binder.

A Tractable Subclass of the Block Algebra: Constraint Propagation and Preconvex Relations

We define, in this paper, for every n ≥ 1, n-dimensional block algebra as a set of relations, the block relations, together with the fundamental operations of composition, conversion and intersection. We examine the 13n atomic relations of this algebra which constitute the exhaustive list of the permitted relations that can hold between two blocks whose sides are parallel to the axes of some orthogonal basis in the n-dimensional Euclidean space over the field of real numbers. We organize these atomic relations in ascending order with the intention of defining the concept of convexity as well as the one of preconvexity. We will confine ourselves to the issue of the consistency of block networks which consist of sets of constraints between a finite number of blocks. Showing that the concepts of convexity and preconvexity are preserved by the fundamental operations, we prove the tractability of the problem of the consistency of strongly preconvex block networks, on account of our capacity for deciding it in polynomial time by means of the path-consistency algorithm.

The Modal Multilogic of Geometry

ABSTRACT A spatial logic is a modal logic of which the models are the mathematical models of space. Successively considering the mathematical models of space that are the incidence geometry and the projective geometry, we will successively establish the language, the semantical basis, the axiomatical presentation, the proof of the decidability and the proof of the completeness of INC, the modal multilogic of incidence geometry, and PRO, the modal multilogic of projective geometry.

LOGICAL THEORIES FOR FRAGMENTS OF ELEMENTARY GEOMETRY

We survey models and theories of geometric structures of parallelism, orthogonality, incidence, betweenness and order, thus gradually building towards full elementary geometry of Euclidean spaces, in Tarski’s sense. Besides the geometric aspects of such structures we look at their logical (first-order and modal) theories and discuss logical issues such as: expressiveness and definability, axiomatizations and representation results, completeness and decidability, and interpretations between structures and theories.

Algorithms and Complexity of Automata Synthesis by Asynhcronous Orchestration With Applications to Web Services Composition

Composition of services is necessary for realizing complex tasks on the Web. It has been characterized either as a plan synthesis problem or as a software synthesis problem: given a goal and a set of Web services, generate a composition of the Web services that satisfies the goal. We propose algorithms for performing automated Web service composition. We also examine the composition of services from the perspective of computational complexity.

A Modal Logic for Data Analysis

Modal logic is a natural framework for the representation and the mechanization of reasoning with incomplete information about objects in terms of attributes. Its use in the theory of the systems of information rests on the concept of a Kripke frame with relative accessibility relations. This paper presents the proof of the completeness of a logic based on these frames.

On the consistency problem for the INDU calculus

Abstract In this paper, we further investigate the consistency problem for the qualitative temporal calculus INDU introduced by Pujari et al. [A.K. Pujari, G.V. Kumari, A. Sattar, INDU: An interval and duration network, in: Australian Joint Conference on Artificial Intelligence, 1999, pp. 291–303]. We prove the intractability of the consistency problem for the subset of pre-convex relations, and the tractability of strongly pre-convex relations. Furthermore, we also define another interesting set of relations for which the consistency problem can be decided by the ⋄ - closure method , a method similar to the usual path-consistency method. Finally, we prove that the ⋄ - closure method is also complete for the set of atomic relations of INDU implying that the intervals have the same duration.

Composition of Services with Constraints

Composition of Web services consists of the interleaving of the sequence of actions executed by the elementary services in accordance with a client specification. We model Web services as automata executing actions and also sending and receiving messages. This paper provides a theoretical study for three service composition problems, and in particular for the problem of computing a Boolean formula which exactly characterises the conditions required for services to answer the clients request. New complexity results are established for these problems within the framework of service composition with constraints.

Modal Logics with Relative Accessibility Relations

This paper presents a systematic study of the logics based on Kripke models with relative accessibility relations as well as a general method for proving their completeness.