Part-whole relations in object-centered systems: an overview
Data & Knowledge Engineering - Special issue on modeling parts and wholes
A Unifying Theory of Dependent Types: The Schematic Approach
TVER '92 Proceedings of the Second International Symposium on Logical Foundations of Computer Science
On the General Ontological Foundations of Conceptual Modeling
ER '02 Proceedings of the 21st International Conference on Conceptual Modeling
Proof-assistants using dependent type systems
Handbook of automated reasoning
The Description Logic Handbook
The Description Logic Handbook
Structured objects in owl: representation and reasoning
Proceedings of the 17th international conference on World Wide Web
Representing and reasoning over a taxonomy of part-whole relations
Applied Ontology - Ontological Foundations of Conceptual Modelling
A Theorem Prover with Dependent Types for Reasoning about Actions
Proceedings of the 2008 conference on STAIRS 2008: Proceedings of the Fourth Starting AI Researchers' Symposium
Manifest Fields and Module Mechanisms in Intensional Type Theory
Types for Proofs and Programs
Computational ontologies of parthood, componenthood, and containment
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Reasoning on UML class diagrams
Artificial Intelligence
Part-whole representation and reasoning in formal biomedical ontologies
Artificial Intelligence in Medicine
Part-Whole relations in object-role models
OTM'06 Proceedings of the 2006 international conference on On the Move to Meaningful Internet Systems: AWeSOMe, CAMS, COMINF, IS, KSinBIT, MIOS-CIAO, MONET - Volume Part II
Meronymy-based aggregation of activities in business process models
ER'10 Proceedings of the 29th international conference on Conceptual modeling
| Hi-index | 0.00 |
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.