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Coherence via Focusing for Symmetric Skew Monoidal Categories
The symmetric skew monoidal categories of Bourke and Lack are a weakening of Mac Lane’s symmetric monoidal categories where: (i) the three structural...
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On Strictifying Extensional Reflexivity in Compact Closed Categories
This chapter has two related aims. The first is to study the categorical setting of Abramsky, Haghverdi, & Scott’s untyped linear combinatory...
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The Game Semantics of Game Theory
We use a reformulation of compositional game theory to reunite game theory with game semantics, by viewing an open game as the System and its choice...
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Maximally Multi-focused Proofs for Skew Non-Commutative MILL
Multi-focusing is a generalization of Andreoli’s focusing procedure which allows the parallel application of synchronous rules to multiple formulae...
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An Axiomatic Account of a Fully Abstract Game Semantics for General References
We present an analysis of the game semantics of general references introduced by Abramsky, Honda and McCusker which exposes the algebraic structure...
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Semantics for a Lambda Calculus for String Diagrams
Linear/non-linear (LNL) models, as described by Benton, soundly model a LNL term calculus and LNL logic closely related to intuitionistic linear...
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Compact Inverse Categories
We prove a structure theorem for compact inverse categories. The Ehresmann-Schein-Nambooripad theorem gives a structure theorem for inverse monoids:...
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Aspects of Categorical Recursion Theory
We present a survey of some developments in the general area of category-theoretic approaches to the theory of computation, with a focus on topics...
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The Problem of Truth in Quantum Mechanics
There is a large literature on the issue of the lack of properties (i.e. accidents) in quantum mechanics (the problem of “hidden variables”) and also...
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Logical Journeys: A Scientific Autobiography
A short scientific biography emphasising the main phases of Abramsky’s research: duality theory and domains in logical form, game semantics,...
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Multilayer networks as embodied consciousness interactions. A formal model approach
An algebraic interpretation of multigraph networks is introduced in relation to conscious experience, brain and body. These multigraphs have the...
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A Tale of Additives and Concurrency in Game Semantics
Twenty years ago, Abramsky and Melliès published their famous paper, Concurrent Games and Full Completeness. In that paper, they advocated the switch...
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Fuzzy Generalised Quantifiers for Natural Language in Categorical Compositional Distributional Semantics
Recent work on compositional distributional models shows that bialgebras over finite dimensional vector spaces can be applied to treat generalised...
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Implementing Algorithmic and Computational Design in Philosophical Pedagogy
This paper argues that using diagrammatically compositional forms of representation may enhance the teaching and learning of computational and...
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On the Naturalness of Mal’tsev Categories
Mal’tsev categories turned out to be a central concept in categorical algebra. On the one hand, the simplicity and the beauty of the notion is...
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Simple Systems and Complex Systems
In relational system theory, the difference between a simple system and a complex system is that a simple system is predicative while a complex...
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Local causation
The counterfactual and regularity theories are universal accounts of causation. I argue that these should be generalized to produce local accounts of...
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The Mathematics of Text Structure
In previous work we gave a mathematical foundation, referred to as DisCoCat, for how words interact in a sentence in order to produce the meaning of...