Related papers: Cobordisms and commutative categorial grammars

We continue work of our earlier paper (Lewitzka and Brunner: Minimally generated abstract logics, Logica Universalis 3(2), 2009), where abstract logics and particularly intuitionistic abstract logics are studied. Abstract logics can be…

We develop a new, intrinsic, computationally friendly approach to Lie coalgebras through graph coalgebras, which are new and likely to be of independent interest. Our graph coalgebraic approach has advantages both in finding relations…

In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon…

We present a family of neural-network--inspired models for computing continuous word representations, specifically designed to exploit both monolingual and multilingual text. This framework allows us to perform unsupervised training of…

Most graph query languages are rooted in logic. By contrast, in this paper we consider graph query languages rooted in linear algebra. More specifically, we consider MATLANG, a matrix query language recently introduced, in which some basic…

The class of Parikh word representable graphs were recently introduced. In this work, we further develop its general theory beyond the binary alphabet. Our main result shows that this class is equivalent to the class of bipartite…

We shall discuss how the notions of multicategories and their linear representations are related with tensor categories. When one focuses on the ones arizing from planar diagrams, it particularly implies that there is a natural one-to-one…

In this work, we explore a double categorical framework for categories of enriched graphs, categories and the newly introduced notion of cocategories. A fundamental goal is to establish an enrichment of V-categories in V-cocategories, which…

Recently researchers working in the LFG framework have proposed algorithms for taking advantage of the implicit context-free components of a unification grammar [Maxwell 96]. This paper clarifies the mathematical foundations of these…

We present a polymorphic linear lambda-calculus as a proof language for second-order intuitionistic linear logic. The calculus includes addition and scalar multiplication, enabling the proof of a linearity result at the syntactic level.

We show that an interesting class of feed-forward neural networks can be understood as quantitative argumentation frameworks. This connection creates a bridge between research in Formal Argumentation and Machine Learning. We generalize the…

We investigate the notion of associated graded coalgebra (algebra) of a bialgebra with respect to a subbialgebra (quotient bialgebra) and characterize those which are bialgebras of type one in the framework of abelian braided monoidal…

We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…

V.V. Sharko in his papers and books has investigated functions on manifolds and cobordism. Braids intimately connect with functions on manifolds. These connections are represented by mapping class groups of corresponding discs, by…

Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences,…

I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…

We introduce two constructions of a coassociative comultiplication in the algebra of phrases in a given alphabet. As a preliminary step we give two constructions of a pre-Lie comultiplication in the module generated by words.

In this paper we study cobordism categories consisting of manifolds which are endowed with geometric structure. Examples of such geometric structures include symplectic structures, flat connections on principal bundles, and complex…

This paper discusses the semantics of weighted argumentation graphs that are biplor, i.e. contain both attacks and support graphs. The work builds on previous work by Amgoud, Ben-Naim et. al., which presents and compares several semantics…

We explore a proof language for intuitionistic multiplicative additive linear logic, incorporating the sup connective that introduces additive pairs with a probabilistic elimination, and sum and scalar products within the proof-terms. We…