Semantic Unification A sheaf theoretic approach to natural language

Language is contextual and sheaf theory provides a high level mathematical framework to model contextuality. We show how sheaf theory can model the contextual nature of natural language and how gluing can be used to provide a global semantics for a discourse by putting together the local logical semantics of each sentence within the discourse. We introduce a presheaf structure corresponding to a basic form of Discourse Representation Structures. Within this setting, we formulate a notion of semantic unification --- gluing meanings of parts of a discourse into a coherent whole --- as a form of sheaf-theoretic gluing. We illustrate this idea with a number of examples where it can used to represent resolutions of anaphoric references. We also discuss multivalued gluing, described using a distributions functor, which can be used to represent situations where multiple gluings are possible, and where we may need to rank them using quantitative measures. Dedicated to Jim Lambek on the occasion of his 90th birthday.Comment: 12 page

Function classification for the retro-engineering of malwares

International audienceIn the past ten years, our team has developed a method called morphological analysis that deals with malware detection. Morphological analysis focuses on algorithms. Here, we want to identify programs through their functions, and more precisely with the intention of those functions. The intention is described as a vector in a high dimensional vector space in the spirit of compositional semantics. We show how to use the intention of functions for their clustering. In a last step, we describe some experiments showing the relevance of the clustering and some of some possible applications for malware identification