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The logics of the family := are formally defined by means of finite matrices, as a simultaneous generalization of the weakly-intuitionistic logic and of the paraconsistent logic . It is proved that this family can be naturally ordered, and it is shown a sound and complete axiomatics for each logic of the form . The involved completeness proof showed here is obtained by means of a generalization of the well-known Kalmár’s method, usually applied for many-valued logics.
A continuous linear extension operator, different from Whitney’s, for -Whitney fields (p finite) on a closed o-minimal subset of is constructed. The construction is based on special geometrical properties of o-minimal sets earlier studied by K. Kurdyka with the author.
We present a system providing a set of tools for developing natural language processing (NLP) applications such as natural language interfaces, communication aid systems, etc. This system is based on two principles: modularity of knowledge representation to ensure the portability of the system, and guided sentence composition to ensure transparency, i.e. to ensure that the produced sentences are well-formed at the lexical, syntactic, semantic and conceptual levels. We first describe the formalisms...
We show that a version of López-Escobar’s theorem holds in the setting of model theory for metric structures. More precisely, let denote the Urysohn sphere and let Mod(,) be the space of metric -structures supported on . Then for any Iso()-invariant Borel function f: Mod(,) → [0,1], there exists a sentence ϕ of such that for all M ∈ Mod(,) we have . This answers a question of Ivanov and Majcher-Iwanow. We prove several consequences, for example every orbit equivalence relation of a Polish group...
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