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An Algebraic Glimpse at Bunched Implications and Separation Logic
We overview the logic of Bunched Implications (BI) and Separation Logic (SL) from a perspective inspired by Hiroakira Ono’s algebraic approach to...
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Implication via Spacetime
In this paper we intend to study implications in their most general form, generalizing different classes of implications including the...
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The Logic of Picturing: Wittgenstein, Sellars and Peirce’s EG-beta
The semantics of picturing, broadly understood as an isomorphism between relevant relations among parts of a picture and relations constituting a...
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Hard Problem and Free Will: An Information-Theoretical Approach
We explore definite theoretical assertions about consciousness, starting from a non-reductive psycho-informational solution of David Chalmers's hard...
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Pomset Logic
Thirty years ago, I introduced a noncommutative variant of classical linear logic, called pomset logic, coming from a particular categorical...
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Interacting Conceptual Spaces I: Grammatical Composition of Concepts
The categorical compositional approach to meaning has been successfully applied in natural language processing, outperforming other models in...
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The Hahn Embedding Theorem for a Class of Residuated Semigroups
Hahn’s embedding theorem asserts that linearly ordered abelian groups embed in some lexicographic product of real groups. Hahn’s theorem is...
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Higher Structures in Homotopy Type Theory
The intended model of the homotopy type theories used in Univalent Foundations is the ∞-category of homotopy types, also known as ∞-groupoids. The...
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Multisets and Distributions, in Drawing and Learning
Multisets are ‘sets’ in which elements may occur multiple times. Discrete probability distributions capture states in which elements may occur with...
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Terms and Automata Through Logic
This chapter gives an introduction to one kind of automata and logic connection in the setting of terms, represented as trees. Automata process terms...
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Studies in the logic of K-onfirmation
This research article revisits Hempel’s logic of confirmation in light of recent developments in categorical proof theory. While Hempel advocated...
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Dynamical States and the Conventionality of (Non-) Classicality
Itamar Pitowsky, along with Jeff Bub and others, long championed the view that quantum mechanics (QM) is best understood as a non-classical...
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A Categorical Equivalence for Stonean Residuated Lattices
We follow the ideas given by Chen and Grätzer to represent Stone algebras and adapt them for the case of Stonean residuated lattices. Given a Stonean...
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A Logic for Human Actions
The present paper introduces an action logic able to model human actions. We begin by providing an analysis of the proof-theory of action logics from...
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Terms and Automata Through Logic
This chapter gives an introduction to one kind of automata and logic connection in the setting of terms, represented as trees. Automata process terms...
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Towards a unified framework for decomposability of processes
The concept of process is ubiquitous in science, engineering and everyday life. Category theory, and monoidal categories in particular, provide an...
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A Type-Driven Vector Semantics for Ellipsis with Anaphora Using Lambek Calculus with Limited Contraction
We develop a vector space semantics for verb phrase ellipsis with anaphora using type-driven compositional distributional semantics based on the...
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On Quantum Computation, Anyons, and Categories
We explain the use of categoryCategory theory in describing certain sorts of anyonsAnyon . Yoneda’s lemmaYoneda’s lemma...
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Categorical Harmony and Paradoxes in Proof-Theoretic Semantics
There are two camps in the theory of meaning: the referentialist one including Davidson, and the inferentialist one including Dummett and Brandom....