Related papers: Kleisli semantics and hypergraph composition for G…
We provide a compositional coalgebraic semantics for strategic games. In our framework, like in the semantics of functional programming languages, coalgebras represent the observable behaviour of systems derived from the behaviour of the…
In \cite{LS14} the analogy between the Kleisli construction and the construction of "warping a skew monoidale category" in the sense of \cite{LS12} was outlined. In this note we present the same work in a slightly more formal way.
In this thesis we present a semantic representation formalism based on directed graphs and explore its linguistic adequacy and explanatory benefits in the semantics of plurality and quantification. Our graph language covers the essentials…
Early work on narrative modeling used explicit plans and goals to generate stories, but the language generation itself was restricted and inflexible. Modern methods use language models for more robust generation, but often lack an explicit…
We introduce the normal produoidal category of monoidal contexts over an arbitrary monoidal category. In the same sense that a monoidal morphism represents a process, a monoidal context represents an incomplete process: a piece of a…
One of the fundamental requirements for models of semantic processing in dialogue is incrementality: a model must reflect how people interpret and generate language at least on a word-by-word basis, and handle phenomena such as fragments,…
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…
Trace semantics has been defined for various kinds of state-based systems, notably with different forms of branching such as non-determinism vs. probability. In this paper we claim to identify one underlying mathematical structure behind…
Neural Processes (NPs; Garnelo et al., 2018a,b) are a rich class of models for meta-learning that map data sets directly to predictive stochastic processes. We provide a rigorous analysis of the standard maximum-likelihood objective used to…
Formally verifying the properties of formal systems using a proof assistant requires justifying numerous minor lemmas about capture-avoiding substitution. Despite work on category-theoretic accounts of syntax and variable binding, raw,…
Humans possess the capability to reason at an abstract level and to structure information into abstract categories, but the underlying neural processes have remained unknown. Experimental evidence has recently emerged for the organization…
We examine a variant of hypergraphs that we call interfaced linear hypergraphs, with the aim of creating a sound and complete graphical language for symmetric traced monoidal categories (STMCs) suitable for graph rewriting. In particular,…
Modelling compositionality has been a longstanding area of research in the field of vector space semantics. The categorical approach to compositionality maps grammar onto vector spaces in a principled way, but comes under fire for requiring…
Lax monoidal powerset-enriched monads yield a monoidal structure on the category of monoids in the Kleisli category of a monad. Exponentiable objects in this category are identified as those Kleisli monoids with algebraic structure. This…
Human vision involves parsing and representing objects and scenes using structured representations based on part-whole hierarchies. Computer vision and machine learning researchers have recently sought to emulate this capability using…
Scientists construct and analyze computational models to understand the world. That understanding comes from efforts to augment, combine, and compare models of related phenomena. We propose SemanticModels.jl, a system that leverages…
Originally introduced in the context of the algebraic approach to term graph rewriting, the notion of gs-monoidal category has surfaced a few times under different monikers in the last decades. They can be thought of as symmetric monoidal…
Answering compositional questions requiring multi-step reasoning is challenging. We introduce an end-to-end differentiable model for interpreting questions about a knowledge graph (KG), which is inspired by formal approaches to semantics.…
Sheaves are objects of a local nature: a global section is determined by how it looks locally. Hence, a sheaf cannot describe mathematical structures which contain global or nonlocal geometric information. To fill this gap, we introduce the…
In the theory of coalgebras, trace semantics can be defined in various distinct ways, including through algebraic logics, the Kleisli category of a monad or its Eilenberg-Moore category. This paper elaborates two new unifying ideas: 1)…