Patrick Barlatier

Formal foundations for situation awareness based on dependent type theory

Cognitive situation awareness has recently caught the attention of the information fusion community. Some approaches have developed formalizations that are both ontology-based and underpinned with Situation Theory. While the semantics of Situation Theory is very attractive from the cognitive point of view, the languages that are used to express knowledge and to reason with suffer from a number of limitations concerning both expressiveness and reasoning capabilities. In this paper we propose a more general formal foundation denoted S-DTT (Situation-based Dependent Type Theory) that is expressed with the language of the Extended Calculus of Constructions (ECC), a widely used theory in mathematical formalization and in software validation. Situation awareness relies on small blocks of knowledge called situation fragment types whose composition leads to a very expressive and unifying theory. The semantic part is provided by an ontology that is rooted in the S-DTT theory and, on which higher-order reasoning can be performed. The basis of the theory is summarized and its expressing power is illustrated with numerous examples. A scenario in the healthcare context for patient safety issues is detailed and a comparison with well-known approaches is discussed.

A type-theoretical approach for ontologies: The case of roles

In the domain of ontology design as well as in Knowledge Representation, modeling universals is a challenging problem. Most approaches that have addressed this problem rely on Description Logics DLs but many difficulties remain, due to under-constrained representation which reduces the inferences that can be drawn and further causes problems in expressiveness. In mathematical logic and program checking, type theories have proved to be appealing but, so far they have not been applied in the formalization of ontologies. To bridge this gap, we present in this paper a theory for representing ontologies in a dependently-typed framework which relies on strong formal foundations including both a constructive logic and a functional type system. The language of this theory defines in a precise way what ontological primitives such as classes, relations, properties, etc., and thereof roles, are. The first part of the paper details how these primitives are defined and used within the theory. In a second part, we focus on the formalization of the role primitive. A review of significant role properties leads to the specification of a role profile and most of the remaining work details through numerous examples, how the proposed theory is able to fully satisfy this profile. It is demonstrated that dependent types can model several non-trivial aspects of roles including a formal solution for generalization hierarchies, identity criteria for roles and other contributions. A discussion is given on how the theory is able to cope with many of the constraints inherent in a good role representation.

Modeling Ontological Structures with Type Classes in Coq

In the domain of ontology design as well as in Conceptual Modeling, representing universals is a challenging problem. Most approaches which have addressed this problem rely either on Description Logics (DLs) or on First Order Logic (FOL), but many difficulties remain especially about expressiveness. In mathematical logic and program checking, type theories have proved to be appealing but so far, they have not been applied in the formalization of ontologies. To bridge this gap, we present here the main capabilities of a theory for representing ontological structures in a dependently-typed framework which relies both on a constructive logic and on a functional type system. The usability of the theory is demonstrated with the Coq language which defines in a precise way what ontological primitives such as classes, relations, properties and meta-properties, are in terms of type classes.

Formal goal generation for intelligent control systems

In the engineering context of control or measurement systems, there is a growing need to incorporate more and more intelligence towards sensing/actuating components. These components achieve some global service related with an intended goal through a set of elementary services intended to achieve atomic goals. There are many possible choices and non-trivial relations between services. As a consequence, both novices and specialists need assistance to prune the search space of possible services and their relations. To provide a sound knowledge representation for functional reasoning, we propose a method eliciting a goal hierarchy in Intelligent Control Systems. To refine the concept of goal with sub-concepts, we investigate a formalization which relies on a multilevel structure. The method is centered both on a mereological approach to express both physical environment and goal concepts, and on Formal Concept Analysis (FCA) to model concept aggregation/decomposition. The interplay between mereology and FCA is discussed.

Towards an Ontological Modeling with Dependent Types: Application to Part-Whole Relations

Generally, mereological relations are modeled using fragments of first-order logic(FOL) and difficulties arise when meta-reasoning is done over their properties, leading to reason outside the logic. Alternatively, classical languages for conceptual modeling such as UML lack of formal foundations resulting in ambiguous interpretations of mereological relations. Moreover, they cannot prove that a given specification is correct from a logical perspective. In order to address all these problems, we suggest a formal framework using a dependent (higher-order) type theory such as those used in program checking and theorem provers (e.g., Coq). It is based on constructive logic and allows reasoning in different abstraction levels within the logic. Furthermore, it maximizes the expressiveness while preserving decidability of type checking and results in a coherent theory with a powerful sub-typing mechanism.

Deriving Behavior from Goal Structure for the Intelligent Control of Physical Systems

Given a physical system described by a structural decomposition together with additional constraints, a major task in Artificial Intelligence concerns the automatic identification of the system behavior. We will show in the present paper how concepts and techniques from different AI disciplines help solve this task in the case of the intelligent control of engineering systems. Following generative approaches grounded in Qualitative Physics, we derive behavioral specifications from structural and equational information input by the user in the context of the intelligent control of physical systems. The behavioral specifications stem from a teleological representation based on goal structures which are composed of three primitive concepts, i.e. physical entities, physical roles and actions. An ontological representation of goals extracted from user inputs facilitates both local and distributed reasoning. The causal reasoning process generates inferences of possible behaviors from the ontological representation of intended goals. This process relies on an Event Calculus approach. An application example focussing on the control of an irrigation channel illustrates the behavioral identification process.

Specifying Well-Formed Part-Whole Relations in Coq

In the domain of ontology design as well as in Conceptual Modeling, representing part-whole relations is a long-standing challenging problem. However, in most papers the focus has been on properties of the part-whole relation, rather than on its semantics. In the last decades, most approaches which have addressed the formal specification of the part-whole relation (i) rely on First Order Logic (FOL) which is unable to address multiple levels of granularity and (ii) do not support any typing mechanism useful for the extensional side of concepts and then, many difficulties remain especially about expressiveness. In mathematical logic and program checking, type theories have proved to be appealing but so far, they have not been applied in the formalization of ontological relations. To bridge this gap, we present an axiomatization of the part-whole relation which hold between typed terms. Relation structures in the dependently-typed framework rely on a constructive logic. We define in a precise way what relation structures and their meta-properties, are in term of type classes using the Coq language.

Formalizing Context for Domain Ontologies in Coq

While context is crucial for reasoning about ontologies as well as for conceptual modeling, its formal definition is often imprecise and its implementation in standard classical logic-based theories suffers from a lack of expressiveness and leads to ambiguities. In this chapter, it is shown that a two-layered language using the Calculus of Inductive Constructions (i.e., the Coq language) as a lower layer, and an ontological upper layer for giving types their meaning is able to support a clear and expressive semantics for context specification.

Dependent Record Types for Dynamic Context Representation

The context paradigm emerges from different areas of Artificial Intelligence (AI). However, while significative formalizations have been proposed, contexts are either mapped on independent micro-theories or considered as different concurrent viewpoints with mappings between contexts to export/import knowledge. These logical formalisms focus on the semantic level and do not take into account dynamic low-level information such as those available from sensors via physical variables. This information is a key element of contexts in pervasive computing environments. In this paper, we introduce a formal framework where the knowledge representation of context bridges the gap between semantic high-level and low-level knowledge. The logical reasoning based on intuitionistic type theory and the Curry-Howard isomorphism is able to incorporate expert knowledge as well as technical resources such as computing variable properties.

Reasoning about Relations with Dependent Types: Application to Context-Aware Applications

Generally, ontological relations are modeled using fragments of first order logic (FOL) and difficulties arise when meta-reasoning is done over ontological properties, leading to reason outside the logic. Moreover, when such systems are used to reason about knowledge and meta-knowledge, classical languages are not able to cope with different levels of abstraction in a clear and simple way. In order to address these problems, we suggest a formal framework using a dependent (higher order) type theory. It maximizes the expressiveness while preserving decidability of type checking and results in a coherent theory. Two examples of meta-reasoning with transitivity and distributivity and a case study illustrate this approach.