Qualitative spatial representation approaches which rely on Goodman-style predicative mereological theories and on a pseudo-topology, often causes some problems either for their use as a meta-information for knowledge conceptualization in advanced geometric reasoning, since they lack Euclidean geometry and fully-fledged topological spaces in the classical sense. Therefore, this paper seeks to extend an existing formalization, grounded in an underlying type theory using the Coq language, together with the Whitehead-like point-free Tarski's geometry. More precisely, we leverage an available library called lambda-MM to formalize Tarski's geometry of solids by investigating an algebraic formulation of topological relations on top of the library. Given that Tarski's work is grounded in Lesniewski’s mereology, and despite the fact that lambda-MM barely implements Tarski's geometry, the first part of the paper supplements their work by proving that mereological classes correspond to regular open sets. It forms a topology of individual names extensible with Tarski's geometric primitives. Unlike classical approaches used in qualitative logical theories, we adopt a solution that enables the specification of a topological space from mereology and a geometric subspace, thereby enhancing the theory’s expressiveness. Then, in a second part, we prove that Tarski’s geometry forms a subspace of the previous topology in which regions are restricted classes. We prove three postulates of Tarski’s work reducing his axiomatic system and extend the theory with the T2 (Hausdorff) property and additional definitions.

Generally, part-whole 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 ontological reasoning such as Description Logics + Logic Programming lack of expressive formal foundations resulting in ambiguous interpretations of relations. Moreover, they show some difficulties to prove that a given meta property is logically correct. In order to address 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). All properties of part-whole relations are formalized through abstract constructs called parameterized specifications (p-specifications). We detail their content and explain how they are suitable to build an ontology of formal properties that can be further used for reasoning about higher-order properties.

In the area of knowledge representation, a challenging topic is the formalization of context knowledge on the basis of logical foundations and ontological semantics. However, most attempts to provide a formal model of contexts suffer from a number of difficulties, such as limited expressiveness of representation, restricted variable quantification, lack of (meta) reasoning about properties, etc. In addition, type theory originally developed for formal modeling of mathematics has also been successfully applied to the correct specification of programs and in the semantics of natural language. In this paper, we suggest a type theoretical approach to the problem of context and action modeling. Type theory is used both for representing the system's knowledge of the discourse domain and for reasoning about it. For that purpose, we extend an existing dependent type theory having nice properties, with context-based rules and appropriate inductive types. We claim that the resulting theory exploiting the power of dependent types is able to provide a very expressive system together with a unified theory allowing higher-order reasoning.

This paper presents a modeling of intelligent sensors based on a representation of the sensor by services it uses or it proposes, and by its user operating modes (USOMs). This modeling is used for the definition of the reactive layer of distributed agent based intelligent sensors. Our area of interest is the agent-level layer in which the concept of IIC (intelligent instrument cluster) is defined. An application that uses fuzzy-based intelligent sensors is presented in order to illustrate the concepts.