Christophe Fouqueré

Extending Conceptual Definitions with Default Knowledge

In description logics, default knowledge is exclusively treated as incidental rules. However, as few concepts are definable using only strict knowledge, imposing strict definitions leads to terminological knowledge bases that mostly contain partially defined concepts. This is a real problem because such concepts can only be inserted as leaves of the terminology. Moreover, instance recognition is biased as these concepts must be explicitly mentioned as properties of these instances. It follows that partially defined concepts are described with necessary but not sufficient conditions. As a solution to these problems, we propose to integrate defaults in concept definitions and we argue that this is essential for our diagnosis application. We introduce a description language ALεδ with default(δ) and exception(ε) connectives. The cornerstone of our approach is the introduction of a definitional point of view where a default can be part of a concept definition, whereas in the classical inheritance one it is only viewed as a weak implication. We go on to describe a map between the definition of a concept and its inherited properties, and we show that the combination of these definitional and inheritance levels considerably improves the capabilities of classification processes. In particular this allows us to distinguish sure from probable instances and typical from exceptional instances. Finally we provide a specific operation, object refinement, which consists in enlarging object descriptions with exceptions in order to find additional concepts the object is an instance of. This operation is useful for our diagnosis application.

Ludics and web: another reading of standard operations

The development of the Web lead to new programming languages. They merely come from well-known sequential languages augmented by specific libraries dedicated to web usage. They do not seriously take into account interaction, that is the most important principle in action. Relevant to the dialogue paradigm, we show that a web language may be fully designed in this spirit. We explain in which extent interaction is a central concept in web analysis. For that purpose, we use ludics as a logical framework. Ludics was developed by J.-Y. Girard as a semantics able to rebuild the logics from the notion of interaction. We present then a concrete web language whose type system is derived from ludics.

Formalizing partial matching and similarity in case-based reasoning with a description logic

Our aim is to use a description logic including default delta and exception epsilon connectives as a formal framework for a case-based reasoning (CBR) system. This approach allows the retrieval of similar cases to be formalized. Subsumption and (sure, probable, typical, and exceptional) inheritance relations of the description logic are the foundations for the different retrieval tasks: abstracting the new case; classifying it in the index base (full and partial matching); evaluating similarity of the conceptual abstraction of the new case with the concepts of the index base, using conceptual preference criteria; and retrieving similar cases (instances) and applying instance preference criteria to order them. Our preference criteria are symbolic rather than numerical or those of fuzzy logic. Using description logic offers several advantages: the classification process can be used to retrieve similar cases, the formal properties and the efficiency of the system can easily be evaluated, and preference crite...

Rewritings for Polarized Multiplicative and Exponential Proof Structures

We study conditions for a concurrent construction of proof-nets in the framework of linear logic following Andreolis works. We define specific correctness criteria for that purpose. We first study the multiplicative case and show how the correctness criterion given by Danos and decidable in linear time, may be extended to closed modules (i.e. validity of polarized proof structures). We then study the exponential case and give a correctness criterion by means of a contraction relation that helps to discover frontiers of exponential boxes.

Ontologies and coherence spaces

Semantic Web is the initiative supported by the W3C that aims to make the WorldWideWeb a place of interaction among machines – or at least among their “representatives” known as autonomous agents [3] – thanks to the exchange of “labelled” data. It is clearly something more complex and more interesting than today’s Web, which allows only for the exchange of files and “raw” data that machines simply display on a monitor.

Tree components programming: an application to XML

We present a new programming approach based on a contextual component specification. The language we propose integrates XML and functional aspects in a coherent and homogeneous framework. This enables us to fully have static typing and to specify formal properties with respect to interactions. Our language FICX, Functional Interactive and Compositional XML, defines a new kind of data structure called Xobjects and relies on a statically typed functional language (currently OCaml). An Xobject is an abstract structure made in two parts: the Xdata part is an XML structure extended by means of triggers dedicated to interactions, the reaction part gives the code associated to triggers that is evaluated on demand. The modularity is ensured by a parameterization of Xobjects: compound Xobjects form a tree structure, rendering a complex XML tree together with appropriate reactions for triggers. A program is a set of structures, each structure being a tree of Xobjects.

Mobile Multi-Agent Systems: A Programming Language and Its Semantics

This paper proposes a language called CLAIM and its operational semantics. The agents implemented in CLAIM are endowed with cognitive capabilities, are able to communicate with other agents and are mobile. The primitives of mobility are inspired from the ambient calculus.

Tree Adjoining Grammars in Noncommutative Linear Logic

This paper presents a logical formalization of Tree-Adjoining Grammar (TAG). TAG deals with lexicalized trees and two operations are available: substitution and adjunction. Adjunction is generally presented as an insertion of a tree inside another, surrounding the subtree at the adjunction node. This seems to be contradictory with standard logical ability. We prove that some logic, namely a fragment of non-commutative intuitionistic linear logic (N-ILL), can serve this purpose. Briefly speaking, linear logic is a logic considering facts as resources. NILL can then be considered either as an extension of Lambek calculus, or as a restriction of linear logic. We model the TAG formalism in four steps: trees (initial or derived) and the way they are constituted, the operations (substitution and adjunction), and the elementary trees, i.e. the grammar. The sequent calculus is a restriction of the standard sequent calculus for N-ILL. Trees (initial or derived) are then obtained as the closure of the calculus under two rules that mimic the grammatical ones. We then prove the equivalence between the language generated by a TAG grammar and the closure under substitution and adjunction of its logical representation. Besides this nice property, we relate parse trees to logical proofs, and to their geometric representation: proofnets. We briefly present them and give examples of parse trees as proofnets. This process can be interpreted as an assembling of blocks (proofnets corresponding to elementary trees of the grammar).

Taxonomic Linear Theories

A semantic network is a structure for representing knowledge as a pattern of interconnected nodes and edges. This paper focuses on the means linear logic offers to represent these networks. In order to compare our inferences, we have chosen one nonmonotonic logic: default logic [9] serves as a reference. The main result proves the equivalence between linear logic and default logic in taxonomic default theories. We hope this will help to better understand the relations between nonmonotonicity and defeasible knowledge representation.

Study of Behaviours via Visitable Paths

Ludics is a logical theory that J.-Y. Girard developed around 2000. At first glance, it may be considered as a Brouwer-Heyting-Kolmogorov interpretation of Logic as a formula is denoted by the set of its proofs. More primitively, Ludics is a theory of interaction that models (a variant of) second-order multiplicative-additive Linear Logic. A formula is denoted by a set of objects called a behaviour, a proof by an object that satisfies some criteria. Our aim is to analyze the structure of behaviours in order to better understand and refine the usual notion of formulas or types. More precisely, we study properties that guarantee a behaviour to be recursively decomposable by means of multiplicative-additive linear connectives and linear constants.Around 2000, J.-Y. Girard developed a logical theory, called Ludics. This theory was a step in his program of Geometry of Interaction, the aim of which being to account for the dynamics of logical proofs. In Ludics, objects called designs keep only what is relevant for the cut elimination process, hence the dynamics of a proof: a design is an abstraction of a formal proof. The notion of behaviour is the counterpart in Ludics of the notion of type or the logical notion of formula. Formally a behaviour is a closed set of designs. Our aim is to explore the constructions of behaviours and to analyse their properties. In this paper a design is viewed as a set of coherent paths. We recall or give variants of properties concerning visitable paths, where a visitable path is a path in a design or a set of designs that may be traversed by interaction with a design of the orthogonal of the set. We are then able to answer the following question: which properties should satisfy a set of paths for being exactly the set of visitable paths of a behaviour? Such a set and its dual should be prefix-closed, daimon-closed and satisfy two saturation properties. This allows us to have a means for defining the whole set of visitable paths of a given set of designs without closing it explicitly, that is without computing the orthogonal of this set of designs. We finally apply all these results for making explicit the structure of a behaviour generated by constants and multiplicative/additive connectives. We end by proposing an oriented tensor for which we give basic properties.