Related papers: Proof Nets, Coends and the Yoneda Isomorphism
This paper is addressed to logicians not familiar with category theory. It gives a new proof of coherence for symmetric monoidal closed categories, proven by Kelly and Mac Lane in early 1970s. We find this result of great importance for…
A new viewpoint of the G\"odel's incompleteness theorem be given in this article which reveals the deep relationship between the logic and computation. Upon the results of these studies, an algorithm be given which shows how to search a…
Coherence with respect to Kelly-Mac Lane graphs is proved for categories that correspond to the multiplicative fragment without constant propositions of classical linear first-order predicate logic without or with mix. To obtain this…
This paper presents a simple notion of proof net for multiplicative linear logic with units. Cut elimination is direct and strongly normalising, in contrast to previous approaches which resorted to moving jumps (attachments) of par units…
A symmetric monoidal category is a category equipped with an associative and commutative (binary) product and an object which is the unit for the product. In fact, those properties only hold up to natural isomorphisms which satisfy some…
Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We exhibit such a finite semantics for a polymorphic purely linear…
Combinatorial categories satisfy a stronger form of Yoneda Lemma, namely, the isomorphism type of an object can be recovered by counting the number of homomorphisms from all other objects into it. In this work, we show that this property…
Recent works using artificial neural networks based on distributed word representation greatly boost performance on various natural language processing tasks, especially the answer selection problem. Nevertheless, most of the previous works…
We study the correspondence between Bayesian Networks and graphical representation of proofs in linear logic. The goal of this paper is threefold: to develop a proof-theoretical account of Bayesian inference (in the spirit of the…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
We study the Yoneda lemma for arbitrary simplicial spaces. We do that by introducing left fibrations of simplicial spaces and and studying its associated model structure, the covariant model structure. In particular, we prove a recognition…
We prove an equivalence between cocomplete Yoneda structures and certain proarrow equipments on a 2-category $\mathcal K$. In order to do this, we recognize the presheaf construction of a cocomplete Yoneda structure as a relative, lax…
Inspired by the recent evolution of deep neural networks (DNNs) in machine learning, we explore their application to PL-related topics. This paper is the first step towards this goal; we propose a proof-synthesis method for the…
The large language models (LLMs) might produce a persuasive argument within mathematical and logical fields, although such argument often includes some minor missteps, including the entire omission of side conditions, invalid inference…
A similarity network is a tool for constructing belief networks for the diagnosis of a single fault. In this paper, we examine modifications to the similarity-network representation that facilitate the construction of belief networks for…
Multinets are certain configurations of lines and points with multiplicities in the complex projective plane $\mathbb{P}^2$. They appear in the study of resonance and characteristic varieties of complex hyperplane arrangement complements…
In this article, a new construction of derived equivalences is given. It relates different endomorphism rings and more generally cohomological endomorphism rings - including higher extensions - of objects in triangulated categories. These…
This paper is about equality of proofs in which a binary predicate formalizing properties of equality occurs, besides conjunction and the constant true proposition. The properties of equality in question are those of a preordering relation,…
Coherence phenomena appear in two different situations. In the context of category theory the term `coherence constraints' refers to a set of diagrams whose commutativity implies the commutativity of a larger class of diagrams. In the…
We characterize double adjunctions in terms of presheaves and universal squares, and then apply these characterizations to free monads and Eilenberg--Moore objects in double categories. We improve upon our earlier result in "Monads in…