Thomas Ehrhard
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View article: On the denotation of circular and non-wellfounded proofs in linear logic with fixed points
On the denotation of circular and non-wellfounded proofs in linear logic with fixed points Open
International audience
View article: Variable Elimination as Rewriting in a Linear Lambda Calculus
Variable Elimination as Rewriting in a Linear Lambda Calculus Open
Variable Elimination (VE) is a classical exact inference algorithm for probabilistic graphical models such as Bayesian Networks, computing the marginal distribution of a subset of the random variables in the model. Our goal is to understan…
View article: Integration in Cones
Integration in Cones Open
Measurable cones, with linear and measurable functions as morphisms, are a model of intuitionistic linear logic and of call-by-name probabilistic PCF which accommodates "continuous data types" such as the real line. So far howeve…
View article: Variable Elimination as Rewriting in a Linear Lambda Calculus
Variable Elimination as Rewriting in a Linear Lambda Calculus Open
Variable Elimination ( $$\textsf{VE}$$ ) is a classical exact inference algorithm for probabilistic graphical models such as Bayesian Networks, computing the marginal distribution of a subset of the random variables in the model. Our goa…
View article: Functorial Models of Differential Linear Logic
Functorial Models of Differential Linear Logic Open
Differentiation in logic has several sources of inspiration. The most recent is differentiable programming, models of which demand functoriality and good typing properties. More historical is reverse denotational semantics, taking inspirat…
View article: Classical Linear Logic in Perfect Banach Lattices
Classical Linear Logic in Perfect Banach Lattices Open
In recent years, researchers have proposed various models of linear logic with strong connections to measure theory, with probabilistic coherence spaces (PCoh) being one of the most prominent. One of the main limitations of the PCoh model …
View article: Bayesian Networks and Proof-Nets: a proof-theoretical account of Bayesian Inference
Bayesian Networks and Proof-Nets: a proof-theoretical account of Bayesian Inference Open
We uncover a strong correspondence between Bayesian Networks and (Multiplicative) Linear Logic Proof-Nets, relating the two as a representation of a joint probability distribution and at the level of computation, so yielding a proof-theore…
View article: From Differential Linear Logic to Coherent Differentiation
From Differential Linear Logic to Coherent Differentiation Open
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
View article: A coherent differential PCF
A coherent differential PCF Open
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential li…
View article: Coherent Taylor expansion as a bimonad
Coherent Taylor expansion as a bimonad Open
We extend the recently introduced setting of coherent differentiation for taking into account not only differentiation, but also Taylor expansion in categories which are not necessarily (left)additive. The main idea consists in extending s…
View article: Coherent differentiation
Coherent differentiation Open
The categorical models of differential linear logic (LL) are additive categories and those of the differential lambda-calculus are left-additive categories because of the Leibniz rule which requires the summation of two expressions. This m…
View article: Cartesian Coherent Differential Categories
Cartesian Coherent Differential Categories Open
We extend to general Cartesian categories the idea of Coherent\nDifferentiation recently introduced by Ehrhard in the setting of categorical\nmodels of Linear Logic. The first ingredient is a summability structure which\ninduces a partial …
View article: Cartesian Coherent Differential Categories
Cartesian Coherent Differential Categories Open
We extend to general Cartesian categories the idea of Coherent Differentiation recently introduced by Ehrhard in the setting of categorical models of Linear Logic. The first ingredient is a summability structure which induces a partial lef…
View article: Differentiation in probabilistic coherence spaces
Differentiation in probabilistic coherence spaces Open
Probabilistic coherence spaces are a model of classical linear logic but not a model of differential linear logic. Nevertheless differentiation is a perfectly meaningful operation in this model. I will explain its meaning, some of its prop…
View article: The Sum-Product Algorithm For Quantitative Multiplicative Linear Logic
The Sum-Product Algorithm For Quantitative Multiplicative Linear Logic Open
We consider an extension of multiplicative linear logic which encompasses bayesian networks and expresses samples sharing and marginalisation with the polarised rules of contraction and weakening. We introduce the necessary formalism to im…
View article: Differentials and distances in probabilistic coherence spaces
Differentials and distances in probabilistic coherence spaces Open
In probabilistic coherence spaces, a denotational model of probabilistic functional languages, morphisms are analytic and therefore smooth. We explore two related applications of the corresponding derivatives. First we show how derivatives…
View article: A coherent differential PCF
A coherent differential PCF Open
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential li…
View article: Polarized Linear Logic with Fixpoints
Polarized Linear Logic with Fixpoints Open
We introduce and study µLLP, which can be viewed both as an extension of Laurent's Polarized Linear Logic, LLP, with least and greatest fixpoints, and as a polarized version of Baelde's Linear Logic with fixpoints (µMALL and µLL). We take …
View article: Coherent differentiation
Coherent differentiation Open
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential li…
View article: Acknowledgments
Acknowledgments Open
Dying to Learn tries to explain why some militaries are better at learning than others.I have strug gled with this question for the better part of two de cades, and I owe a great deal to those who have helped me along the way.I am particul…
View article: Categorical models of Linear Logic with fixed points of formulas
Categorical models of Linear Logic with fixed points of formulas Open
We develop a denotational semantics of muLL, a version of propositional Linear Logic with least and greatest fixed points extending David Baelde's propositional muMALL with exponentials. Our general categorical setting is based on the noti…
View article: Upper approximating probabilities of convergence in probabilistic coherence spaces
Upper approximating probabilities of convergence in probabilistic coherence spaces Open
We develop a theory of probabilistic coherence spaces equipped with an additional extensional structure and apply it to approximating probability of convergence of ground type programs of probabilistic PCF whose free variables are of groun…
View article: Upper approximating probabilities of convergence in probabilistic\n coherence spaces
Upper approximating probabilities of convergence in probabilistic\n coherence spaces Open
We develop a theory of probabilistic coherence spaces equipped with an\nadditional extensional structure and apply it to approximating probability of\nconvergence of ground type programs of probabilistic PCF whose free variables\nare of gr…
View article: Cones as a model of intuitionistic linear logic
Cones as a model of intuitionistic linear logic Open
International audience
View article: On the linear structure of cones
On the linear structure of cones Open
For encompassing the limitations of probabilistic coherence spaces which do not seem to provide natural interpretations of continuous data types such as the real line, Ehrhard and al. introduced a model of probabilistic higher order comput…
View article: On the denotational semantics of Linear Logic with least and greatest fixed points of formulas
On the denotational semantics of Linear Logic with least and greatest fixed points of formulas Open
We develop a denotational semantics of Linear Logic with least and greatest fixed points in coherence spaces (where both fixed points are interpreted in the same way) and in coherence spaces with totality (where they have different interpr…
View article: The Design and Regulation of Exchanges: A Formal Approach
The Design and Regulation of Exchanges: A Formal Approach Open
We use formal methods to specify, design, and monitor continuous double auctions, which are widely used to match buyers and sellers at exchanges of foreign currencies, stocks, and commodities. We identify three natural properties of such a…