Related papers: From Proof Nets to the Free *-Autonomous Category

We associate to every proof structure in multiplicative linear logic an ideal which represents the logical content of the proof as polynomial equations. We show how cut-elimination in multiplicative proof nets corresponds to instances of…

In principle, the rules of links formation of a network model can be considered as a kind of link prediction algorithm. By revisiting the preferential attachment mechanism for generating a scale-free network, here we propose a class of…

Recently, data abstraction has been studied in the context of separation logic, with noticeable practical successes: the developed logics have enabled clean proofs of tricky challenging programs, such as subject-observer patterns, and they…

The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…

We use string-net models to accomplish a direct, purely two-dimensional, approach to correlators of two-dimensional rational conformal field theories. We obtain concise geometric expressions for the objects describing bulk and boundary…

We show that it is coNP-complete to decide whether a given proof structure of pomset logic is a correct proof net, using the graph-theoretic used in a previous paper of ours (arXiv:1901.10247).

Cut-elimination theorems constitute one of the most important classes of theorems of proof theory. Since Gentzen's proof of the cut-elimination theorem for the system $\mathbf{LK}$, several other proofs have been proposed. Even though the…

A proof procedure, in the spirit of the sequent calculus, is proposed to check the validity of entailments between Separation Logic formulas combining inductively defined predicates denoted structures of bounded tree width and theory…

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 an abstract, mathematical formulation of classical propositional logic. It proceeds layer by layer: (1) abstract, syntax-free propositions; (2) abstract, syntax-free contraction-weakening proofs; (3) distribution; (4)…

Each Multiplicative Exponential Linear Logic (MELL) proof-net can be expanded into a differential net, which is its Taylor expansion. We prove that two different MELL proof-nets have two different Taylor expansions. As a corollary, we prove…

We consider the canonical pseudodistributive law between various free limit completion pseudomonads and the free coproduct completion pseudomonad. When the class of limits includes pullbacks, we show that this consideration leads to notions…

The notion of free link is a generalized notion of virtual link. In the present paper we define the group of free braids, prove the Alexander theorem that all free links can be obtained as closures of free braids and prove a Markov theorem,…

This paper gives a detailed account of the relationship between (a variant of) the call-by-value lambda calculus and linear logic proof nets. The presentation is carefully tuned in order to realize a strong bisimulation between the two…

The multiplicative fragment of Linear Logic is the formal system in this family with the best understood proof theory, and the categorical models which best capture this theory are the fully complete ones. We demonstrate how the Hyland-Tan…

Network classification aims to group networks (or graphs) into distinct categories based on their structure. We study the connection between classification of a network and of its constituent nodes, and whether nodes from networks in…

Different automated theorem provers reason in various deductive systems and, thus, produce proof objects which are in general not compatible. To understand and analyze these objects, one needs to study the corresponding proof theory, and…

We describe a notion of categorical model for unitless fragments of (multiplicative) linear logic. The basic definition uses promonoidal categories, and we also give an equivalent elementary axiomatisation.

Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…

We introduce "book links" as a generalization of braids in open book decompositions; this new class of objects includes both braids and plats as special cases. We then prove a version of Markov's theorem in this general setting by extending…